{"message": "", "1_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (1/3 probability), he might raise (70%) or call (30%). If he raises, it's likely that the public card is also a King, which would result in a draw. If he calls, it's likely that the public card is a Queen or Jack, which would result in a win for me. Therefore, the winning rate for this plan is 30% * 1/3 = 10%, the draw rate is 70% * 1/3 = 23.33%, and the lose rate is 0%.\n- If GoodGuy holds a Queen or Jack (2/3 probability), he might call (60%) or fold (40%). If he calls, it's likely that the public card is a Queen or Jack, which would result in a win for me. If he folds, I would also win. Therefore, the winning rate for this plan is 100% * 2/3 = 66.67%, the draw rate is 0%, and the lose rate is 0%.\n- Overall, the winning rate for Plan 1 is 76.67%, the draw rate is 23.33%, and the lose rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (1/3 probability), he might raise (80%) or call (20%). If he raises, it's likely that the public card is also a King, which would result in a draw. If he calls, it's likely that the public card is a Queen or Jack, which would result in a win for me. Therefore, the winning rate for this plan is 20% * 1/3 = 6.67%, the draw rate is 80% * 1/3 = 26.67%, and the lose rate is 0%.\n- If GoodGuy holds a Queen or Jack (2/3 probability), he might call (70%) or fold (30%). If he calls, it's likely that the public card is a Queen or Jack, which would result in a win for me. If he folds, I would also win. Therefore, the winning rate for this plan is 100% * 2/3 = 66.67%, the draw rate is 0%, and the lose rate is 0%.\n- Overall, the winning rate for Plan 2 is 73.34%, the draw rate is 26.67%, and the lose rate is 0%.\n\nPlan 3: Fold\n- If I fold, I would lose the game regardless of GoodGuy's cards or actions. Therefore, the winning rate for this plan is 0%, the draw rate is 0%, and the lose rate is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the pot (3 chips). If I lose, the lose payoff would be half of the pot (3 chips).\n- Plan 2: If I win, the winning payoff would be half of the pot (6 chips). If I lose, the lose payoff would be half of the pot (6 chips).\n- Plan 3: If I lose, the lose payoff would be half of the pot (3 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 76.67% * 3 - 0% * 3 = 2.3 chips\n- Plan 2: 73.34% * 6 - 0% * 6 = 4.4 chips\n- Plan 3: 0% * 3 - 100% * 3 = -3 chips\n\nPlan Selection:\n- Plan 1: 2.3 chips\n- Plan 2: 4.4 chips\n- Plan 3: -3 chips\n\nTherefore, I should choose Plan 2 (Raise), as it has the highest estimated expected chips gain."}}
{"message": "", "1_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (70% probability), he might raise (80% probability) or call (20% probability). If he raises, we would draw (100% probability). If he calls, I would win (100% probability). Overall, the winning rate is 14%, the losing rate is 0%, and the draw rate is 56%.\n- If GoodGuy holds a Queen (15% probability), he might call (70% probability) or fold (30% probability). If he calls or folds, I would win (100% probability). Overall, the winning rate is 15%, the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (15% probability), he might call (70% probability) or fold (30% probability). If he calls or folds, I would win (100% probability). Overall, the winning rate is 15%, the losing rate is 0%, and the draw rate is 0%.\nPlan 1 overall Winning/Lose/Draw rates: Winning rate is 44%, Losing rate is 0%, Draw rate is 56%.\n\nPlan 2: Fold\n- If I fold, I would lose regardless of GoodGuy's cards or actions. Therefore, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King (70% probability), he might raise (80% probability) or call (20% probability). If he raises or calls, we would draw (100% probability). Overall, the winning rate is 0%, the losing rate is 0%, and the draw rate is 70%.\n- If GoodGuy holds a Queen (15% probability), he might call (70% probability) or fold (30% probability). If he calls or folds, I would win (100% probability). Overall, the winning rate is 15%, the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (15% probability), he might call (70% probability) or fold (30% probability). If he calls or folds, I would win (100% probability). Overall, the winning rate is 15%, the losing rate is 0%, and the draw rate is 0%.\nPlan 3 overall Winning/Lose/Draw rates: Winning rate is 30%, Losing rate is 0%, Draw rate is 70%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 8 chips. If lose, the lose payoff would be 4 chips.\n- Plan 2: If win, the winning payoff would be 0 chips. If lose, the lose payoff would be 4 chips.\n- Plan 3: If win, the winning payoff would be 4 chips. If lose, the lose payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 44% * 8 - 0% * 4 = 3.52 chips\n- Plan 2: Expected Chips Gain = 0% * 0 - 100% * 4 = -4 chips\n- Plan 3: Expected Chips Gain = 30% * 4 - 0% * 4 = 1.2 chips\n\nPlan Selection:\n- Plan 1: 3.52 chips\n- Plan 2: -4 chips\n- Plan 3: 1.2 chips\n\nTherefore, I should select Plan 1 (Raise) as it has the highest estimated expected chips gain."}}
{"message": "", "2_0": {"plan": "Plan 1: Call\nIf I call, I will match GoodGuy's bet of 2 chips, bringing the total pot to 5 chips. \n\n- If GoodGuy holds a King (20% probability), he might raise (50% probability) or call (50% probability). If he raises, I will lose 4 chips. If he calls, it will be a draw and the pot will be split. \n- If GoodGuy holds a Queen (40% probability), he might raise (50% probability) or call (50% probability). If he raises, I will lose 4 chips. If he calls, I will win the pot of 5 chips. \n- If GoodGuy holds a Jack (40% probability), he might raise (50% probability) or call (50% probability). If he raises, I will lose 4 chips. If he calls, I will win the pot of 5 chips. \n\nOverall, the winning rate for plan 1 is 40%, the losing rate is 30%, and the draw rate is 30%. \n\nPlan 2: Raise\nIf I raise, I will increase the bet by 4 chips, bringing the total pot to 7 chips. \n\n- If GoodGuy holds a King (20% probability), he might call (50% probability) or fold (50% probability). If he calls, it will be a draw and the pot will be split. If he folds, I will win the pot of 7 chips. \n- If GoodGuy holds a Queen (40% probability), he might call (50% probability) or fold (50% probability). If he calls, I will win the pot of 7 chips. If he folds, I will win the pot of 7 chips. \n- If GoodGuy holds a Jack (40% probability), he might call (50% probability) or fold (50% probability). If he calls, I will win the pot of 7 chips. If he folds, I will win the pot of 7 chips. \n\nOverall, the winning rate for plan 2 is 70%, the losing rate is 0%, and the draw rate is 30%. \n\nPlan 3: Fold\nIf I fold, I will lose the 1 chip I have already put in the pot. \n\nThe winning rate for plan 3 is 0%, the losing rate is 100%, and the draw rate is 0%. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 2.5 chips. If lose, the lose payoff would be 2 chips. \n- Plan 2: If win, the winning payoff would be 3.5 chips. If lose, the lose payoff would be 0 chips. \n- Plan 3: If win, the winning payoff would be 0 chips. If lose, the lose payoff would be 1 chip. \n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0.4 * 2.5 - 0.3 * 2 = 0.7 chips\n- Plan 2: 0.7 * 3.5 - 0 * 0 = 2.45 chips\n- Plan 3: 0 * 0 - 1 * 1 = -1 chips\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is: Plan 2 > Plan 1 > Plan 3. Therefore, I should choose Plan 2: Raise."}}
{"message": "", "2_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (50% probability), he might raise (50% probability) or fold (50% probability). If he raises, I will win (50% probability) or lose (50% probability). If he folds, I will win (100% probability). Overall, the winning rate is 75%, the losing rate is 25%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (50% probability), he might raise (50% probability) or fold (50% probability). If he raises, I will win (50% probability) or lose (50% probability). If he folds, I will win (100% probability). Overall, the winning rate is 75%, the losing rate is 25%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If GoodGuy holds a King (50% probability), I will lose (100% probability). Overall, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (50% probability), I will lose (100% probability). Overall, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King (50% probability), he might raise (50% probability) or check (50% probability). If he raises, I will win (50% probability) or lose (50% probability). If he checks, I will win (50% probability) or lose (50% probability). Overall, the winning rate is 50%, the losing rate is 50%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (50% probability), he might raise (50% probability) or check (50% probability). If he raises, I will win (50% probability) or lose (50% probability). If he checks, I will win (50% probability) or lose (50% probability). Overall, the winning rate is 50%, the losing rate is 50%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 8 chips. If lose, the lose payoff would be 8 chips.\n- Plan 2: If win, the winning payoff would be 0 chips. If lose, the lose payoff would be 4 chips.\n- Plan 3: If win, the winning payoff would be 4 chips. If lose, the lose payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0.75 * 8 - 0.25 * 8 = 4 chips\n- Plan 2: 0 * 0 - 1 * 4 = -4 chips\n- Plan 3: 0.5 * 4 - 0.5 * 4 = 0 chips\n\nPlan Selection:\n- Plan 1: 4 chips\n- Plan 2: -4 chips\n- Plan 3: 0 chips\n\nBased on the estimated expected chips gains, Plan 1 (Raise) is the best strategy."}}
{"message": "", "3_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (probability 33.33%), he will call (probability 100%). If the public card is a King, I will lose. If the public card is a Queen or Jack, I will win. Overall, the winning rate is 66.67%, the losing rate is 33.33%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (probability 33.33%), he will call (probability 100%). If the public card is a Queen, I will lose. If the public card is a King or Jack, I will win. Overall, the winning rate is 66.67%, the losing rate is 33.33%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (probability 33.33%), he will call (probability 100%). If the public card is a Jack, it will be a draw. If the public card is a King or Queen, I will lose. Overall, the winning rate is 0%, the losing rate is 66.67%, and the draw rate is 33.33%.\n\nPlan 2: Fold\n- If I fold, I will lose the round regardless of GoodGuy's card. The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King (probability 33.33%), he will call (probability 100%). If the public card is a King, I will lose. If the public card is a Queen or Jack, I will win. Overall, the winning rate is 66.67%, the losing rate is 33.33%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (probability 33.33%), he will call (probability 100%). If the public card is a Queen, I will lose. If the public card is a King or Jack, I will win. Overall, the winning rate is 66.67%, the losing rate is 33.33%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (probability 33.33%), he will call (probability 100%). If the public card is a Jack, it will be a draw. If the public card is a King or Queen, I will lose. Overall, the winning rate is 0%, the losing rate is 66.67%, and the draw rate is 33.33%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips. If I lose, the losing payoff would be 4 chips.\n- Plan 2: If I fold, I will lose 2 chips.\n- Plan 3: If I win, the winning payoff would be 2 chips. If I lose, the losing payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: (66.67% * 4) - (33.33% * 4) = 1.33 chips\n- Plan 2: 0 - (100% * 2) = -2 chips\n- Plan 3: (66.67% * 2) - (33.33% * 2) = 0.67 chips\n\nPlan Selection:\n- Plan 1: 1.33 chips\n- Plan 2: -2 chips\n- Plan 3: 0.67 chips\n\nBased on the estimated expected chips gain, I should choose Plan 1 (Raise) as it has the highest expected chips gain."}}
{"message": "", "3_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (50% probability), he will call (100% probability). I will lose as his Queen matches the public card. The overall lose rate for his Queen is 50%.\n- If GoodGuy holds a King (50% probability), he will fold (100% probability). I will win as his King does not match the public card. The overall win rate for his King is 50%.\n\nPlan 2: Fold\n- If GoodGuy holds a Queen (50% probability), I will lose as his Queen matches the public card. The overall lose rate for his Queen is 50%.\n- If GoodGuy holds a King (50% probability), I will lose as I fold. The overall lose rate for his King is 50%.\n\nPlan 3: Check\n- If GoodGuy holds a Queen (50% probability), he will call (100% probability). I will lose as his Queen matches the public card. The overall lose rate for his Queen is 50%.\n- If GoodGuy holds a King (50% probability), he will fold (100% probability). I will win as his King does not match the public card. The overall win rate for his King is 50%.\n\nWinning/Lose Payoffs for Each Plan:\nPlan 1: After the raise, chips in the pot: 16. If win, the winning payoff would be 8. If lose, the lose payoff would be 8.\nPlan 2: After the fold, chips in the pot: 8. If lose, the lose payoff would be 4.\nPlan 3: After the check, chips in the pot: 8. If win, the winning payoff would be 4. If lose, the lose payoff would be 4.\n\nExpected Chips Gain for Each Plan:\nPlan 1: Expected Chips Gain = 50% * 8 - 50% * 8 = 0\nPlan 2: Expected Chips Gain = 0% * 0 - 100% * 4 = -4\nPlan 3: Expected Chips Gain = 50% * 4 - 50% * 4 = 0\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows: Plan 1 = Plan 3 > Plan 2. Therefore, I should either raise (Plan 1) or check (Plan 3). Considering my aggressive strategy and GoodGuy's cautious behavior, I will choose to raise (Plan 1)."}}
{"message": "", "3_5": {"plan": "Plan 1: Call\n- If GoodGuy holds a Queen (100% probability based on my belief), he will call (100% probability based on his behavior pattern). In this case, I will lose because his pair of Queens beats my single Jack. \n- Overall, the losing rate for this plan is 100% (probability = 1 * 1), and the winning and draw rates are both 0%.\n\nPlan 2: Fold\n- If GoodGuy holds a Queen (100% probability based on my belief), he will win by default because I fold. \n- Overall, the losing rate for this plan is 100% (probability = 1 * 1), and the winning and draw rates are both 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the call, the chips in the pot would be 24. If I win, the winning payoff would be 12. If I lose, the losing payoff would be 12.\n- Plan 2: After the fold, the chips in the pot would be 20. If I win (which is impossible in this case), the winning payoff would be 10. If I lose, the losing payoff would be 10.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is 0% * 12 - 100% * 12 = -12.\n- Plan 2: The expected chips gain is 0% * 10 - 100% * 10 = -10.\n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 2 > Plan 1.\n- Therefore, I should select Plan 2: Fold, as it has the highest estimated expected chips gain. This is also consistent with my strategy improvement, which suggests that I should be prepared to fold if GoodGuy starts to raise, as this might indicate that he has a matching card or a high rank card."}}
{"message": "", "4_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (probability 2/5), he will likely call if I call (probability 1). If the public card is a King, I will lose (probability 1/5). If the public card is a Queen or Jack, I will win (probability 2/5). Overall, the winning rate is 0.4, the losing rate is 0.2, and the draw rate is 0.4.\n- If GoodGuy holds a Queen (probability 2/5), his action is unknown if I call. If the public card is a Queen, I will lose (probability 1/5). If the public card is a King or Jack, I will win (probability 2/5). Overall, the winning rate is 0.4, the losing rate is 0.2, and the draw rate is 0.4.\n- Winning payoff: 4 chips (half of the pot). Losing payoff: 2 chips (half of the pot).\n- Expected chips gain: 0.4 * 4 - 0.2 * 2 = 1.2 chips.\n\nPlan 2: Raise\n- If GoodGuy holds a King (probability 2/5), he will likely call if I raise (probability 1). If the public card is a King, I will lose (probability 1/5). If the public card is a Queen or Jack, I will win (probability 2/5). Overall, the winning rate is 0.4, the losing rate is 0.2, and the draw rate is 0.4.\n- If GoodGuy holds a Queen (probability 2/5), his action is unknown if I raise. If the public card is a Queen, I will lose (probability 1/5). If the public card is a King or Jack, I will win (probability 2/5). Overall, the winning rate is 0.4, the losing rate is 0.2, and the draw rate is 0.4.\n- Winning payoff: 6 chips (half of the pot). Losing payoff: 3 chips (half of the pot).\n- Expected chips gain: 0.4 * 6 - 0.2 * 3 = 1.8 chips.\n\nPlan 3: Fold\n- If I fold, I will lose the 2 chips I have already put in the pot. The expected chips gain is -2 chips.\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain (1.8 chips), followed by Plan 1 (Call) with 1.2 chips, and Plan 3 (Fold) with -2 chips. Therefore, I should choose Plan 2: Raise."}}
{"message": "", "4_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (50% chance), he will call my raise (100% chance). Since his card matches the public card, I will lose this round (100% chance). \n- If GoodGuy holds a Queen (50% chance), his action is unknown. If he folds, I will win this round (50% chance). If he calls or raises, I will lose this round (50% chance). \n\nPlan 2: Fold\n- If I fold, I will lose this round regardless of GoodGuy's card.\n\nPlan 3: Check\n- If GoodGuy holds a King (50% chance), he will call my check (100% chance). Since his card matches the public card, I will lose this round (100% chance). \n- If GoodGuy holds a Queen (50% chance), his action is unknown. If he checks, it will be a draw (50% chance). If he raises, I will lose this round (50% chance). \n\nWinning/Lose/Draw Rates for Each Plan:\n- Plan 1: Winning rate = 25%, Lose rate = 75%, Draw rate = 0%\n- Plan 2: Winning rate = 0%, Lose rate = 100%, Draw rate = 0%\n- Plan 3: Winning rate = 0%, Lose rate = 75%, Draw rate = 25%\n\nNumber of Winning/Lose Payoffs for Each Plan:\n- Plan 1: If win, the winning payoff would be 10 chips. If lose, the lose payoff would be 10 chips.\n- Plan 2: If lose, the lose payoff would be 6 chips.\n- Plan 3: If lose, the lose payoff would be 6 chips.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected chips gain = 25% * 10 chips - 75% * 10 chips = -5 chips\n- Plan 2: Expected chips gain = 0% * 0 chips - 100% * 6 chips = -6 chips\n- Plan 3: Expected chips gain = 0% * 0 chips - 75% * 6 chips = -4.5 chips\n\nPlan Selection:\n- Plan 1: -5 chips\n- Plan 2: -6 chips\n- Plan 3: -4.5 chips\n\nBased on the expected chips gain, Plan 3 (Check) is the best strategy to minimize the loss in this round."}}
{"message": "", "5_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (33.33% chance), he will fold in the 2nd round regardless of the public card (100% chance). I will win (100% chance). \n- If GoodGuy holds a Queen (33.33% chance), he will raise if the public card is a Queen (33.33% chance) and I will win (100% chance). If the public card is not a Queen, he will fold (66.67% chance) and I will win (100% chance).\n- If GoodGuy holds a Jack (33.33% chance), he will fold if the public card is a King (33.33% chance) and I will win (100% chance). If the public card is not a King, he will fold (66.67% chance) and I will win (100% chance).\n- Overall, the winning rate for Plan 1 is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (33.33% chance), he will fold in the 2nd round regardless of the public card (100% chance). I will win (100% chance). \n- If GoodGuy holds a Queen (33.33% chance), he will raise if the public card is a Queen (33.33% chance) and I will win (100% chance). If the public card is not a Queen, he will fold (66.67% chance) and I will win (100% chance).\n- If GoodGuy holds a Jack (33.33% chance), he will fold if the public card is a King (33.33% chance) and I will win (100% chance). If the public card is not a King, he will fold (66.67% chance) and I will win (100% chance).\n- Overall, the winning rate for Plan 2 is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of GoodGuy's card or the public card. The winning rate for Plan 3 is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the call action, chips in the pot: 8. If win, the winning payoff would be 4. If lose, the lose payoff would be 4.\n- Plan 2: After the raise action, chips in the pot: 12. If win, the winning payoff would be 6. If lose, the lose payoff would be 6.\n- Plan 3: After the fold action, chips in the pot: 6. If lose, the lose payoff would be 3.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 100% * 4 - 0% * 4 = 4\n- Plan 2: 100% * 6 - 0% * 6 = 6\n- Plan 3: 0% * 0 - 100% * 3 = -3\n\nPlan Selection:\n- Plan 2 (Raise) has the highest estimated expected chips gain (6), followed by Plan 1 (Call) with an expected chips gain of 4, and Plan 3 (Fold) with an expected chips loss of 3. Therefore, I should choose Plan 2 (Raise)."}}
{"message": "", "5_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (70% probability), he will likely raise (100% probability). If the public card in the next round is a Queen, we will both have a pair and it will be a draw. If the public card is a Jack or another King, I will lose. Therefore, the winning rate is 0%, the losing rate is 70%, and the draw rate is 30%.\n- If GoodGuy holds a Jack (30% probability), he will likely fold (100% probability). Therefore, the winning rate is 30%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will automatically lose the game. Therefore, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a Queen (70% probability), he will likely raise (100% probability). If the public card in the next round is a Queen, we will both have a pair and it will be a draw. If the public card is a Jack or another King, I will lose. Therefore, the winning rate is 0%, the losing rate is 70%, and the draw rate is 30%.\n- If GoodGuy holds a Jack (30% probability), he will likely fold (100% probability). Therefore, the winning rate is 30%, the losing rate is 0%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 10 chips. If I lose, the losing payoff would be 10 chips.\n- Plan 2: If I fold, I will lose 6 chips.\n- Plan 3: If I win, the winning payoff would be 6 chips. If I lose, the losing payoff would be 6 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.3 * 10 - 0.7 * 10 = -4 chips\n- Plan 2: Expected Chips Gain = 0 - 1 * 6 = -6 chips\n- Plan 3: Expected Chips Gain = 0.3 * 6 - 0.7 * 6 = -2.4 chips\n\nPlan Selection:\n- Plan 1: -4 chips\n- Plan 2: -6 chips\n- Plan 3: -2.4 chips\n\nTherefore, the best plan is Plan 3: Check, as it has the highest estimated expected chips gain."}}
{"message": "", "5_5": {"plan": "Plan 1: Call\n- If GoodGuy holds a Jack (100% probability), he will fold (100% probability). I will win the pot, which is currently 16 chips. The winning rate for this plan is 100%.\n- Overall, the winning rate for Plan 1 is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a Jack (100% probability), he will fold (100% probability). I will win the pot, which is currently 16 chips plus my raise of 8 chips. The winning rate for this plan is 100%.\n- Overall, the winning rate for Plan 2 is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the pot, which is currently 16 chips. The losing rate for this plan is 100%.\n- Overall, the winning rate for Plan 3 is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 8 chips (half of the pot). If lose, the lose payoff would be 8 chips.\n- Plan 2: If win, the winning payoff would be 12 chips (half of the pot plus my raise). If lose, the lose payoff would be 12 chips.\n- Plan 3: If lose, the lose payoff would be 8 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 1.00 * 8 - 0.00 * 8 = 8 chips\n- Plan 2: Expected Chips Gain = 1.00 * 12 - 0.00 * 12 = 12 chips\n- Plan 3: Expected Chips Gain = 0.00 * 0 - 1.00 * 8 = -8 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain of 12 chips.\n- Plan 1 (Call) has the second highest expected chips gain of 8 chips.\n- Plan 3 (Fold) has the lowest expected chips gain of -8 chips.\n\nTherefore, I should choose Plan 2: Raise."}}
{"message": "", "6_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (33.33% chance), he will call if I raise (100% chance). If the public card is a King, he will raise (100% chance). If the public card is not a King, he will fold (100% chance). Therefore, my winning rate is 33.33% * 100% = 33.33%, my losing rate is 0%, and my drawing rate is 0%.\n- If GoodGuy holds a Queen (33.33% chance), he will call if I raise (100% chance). If the public card is a Queen, he will raise (100% chance). If the public card is not a Queen, he will fold (100% chance). Therefore, my winning rate is 33.33% * 100% = 33.33%, my losing rate is 0%, and my drawing rate is 0%.\n- If GoodGuy holds a Jack (33.33% chance), he will raise if I raise (100% chance). If the public card is not a Jack, he will fold (100% chance). Therefore, my winning rate is 33.33% * 100% = 33.33%, my losing rate is 0%, and my drawing rate is 0%.\n- Overall, my winning rate for Plan 1 is 33.33% + 33.33% + 33.33% = 100%, my losing rate is 0%, and my drawing rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (33.33% chance), he will call if I raise (100% chance). If the public card is a King, he will raise (100% chance). If the public card is not a King, he will fold (100% chance). Therefore, my winning rate is 33.33% * 100% = 33.33%, my losing rate is 0%, and my drawing rate is 0%.\n- If GoodGuy holds a Queen (33.33% chance), he will call if I raise (100% chance). If the public card is a Queen, he will raise (100% chance). If the public card is not a Queen, he will fold (100% chance). Therefore, my winning rate is 33.33% * 100% = 33.33%, my losing rate is 0%, and my drawing rate is 0%.\n- If GoodGuy holds a Jack (33.33% chance), he will raise if I raise (100% chance). If the public card is not a Jack, he will fold (100% chance). Therefore, my winning rate is 33.33% * 100% = 33.33%, my losing rate is 0%, and my drawing rate is 0%.\n- Overall, my winning rate for Plan 2 is 33.33% + 33.33% + 33.33% = 100%, my losing rate is 0%, and my drawing rate is 0%.\n\nPlan 3: Fold\n- If I fold, I automatically lose the game. Therefore, my winning rate is 0%, my losing rate is 100%, and my drawing rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, chips in the pot: 3. If win, the winning payoff would be 1.5 chips. If lose, the lose payoff would be 1.5 chips.\n- Plan 2: After the action, chips in the pot: 5. If win, the winning payoff would be 2.5 chips. If lose, the lose payoff would be 2.5 chips.\n- Plan 3: After the action, chips in the pot: 1. If win, the winning payoff would be 0.5 chips. If lose, the lose payoff would be 0.5 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning Rate * Winning Payoff - Losing Rate * Losing Payoff = 100% * 1.5 - 0% * 1.5 = 1.5 chips\n- Plan 2: Expected Chips Gain = Winning Rate * Winning Payoff - Losing Rate * Losing Payoff = 100% * 2.5 - 0% * 2.5 = 2.5 chips\n- Plan 3: Expected Chips Gain = Winning Rate * Winning Payoff - Losing Rate * Losing Payoff = 0% * 0.5 - 100% * 0.5 = -0.5 chips\n\nPlan Selection:\n- Plan 1: Expected Chips Gain = 1.5 chips\n- Plan 2: Expected Chips Gain = 2.5 chips\n- Plan 3: Expected Chips Gain = -0.5 chips\nTherefore, I should choose Plan 2 (Raise) as it has the highest expected chips gain."}}
{"message": "", "6_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (1/3 probability), he will call (100%). If the public card is a King, we will draw. If the public card is not a King, I will win. So the winning rate is 2/3, the draw rate is 1/3, and the losing rate is 0.\n- If GoodGuy holds a Queen (1/3 probability), he will fold (100%) because the public card is not a Queen. So the winning rate is 1, the draw rate is 0, and the losing rate is 0.\n- If GoodGuy holds a Jack (1/3 probability), he will fold (100%) because the public card is not a Jack. So the winning rate is 1, the draw rate is 0, and the losing rate is 0.\n- Overall, the winning rate for Plan 1 is (1/3 * 2/3) + (1/3 * 1) + (1/3 * 1) = 0.89, the draw rate is 1/3 * 1/3 = 0.11, and the losing rate is 0.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of GoodGuy's card. So the winning rate is 0, the draw rate is 0, and the losing rate is 1.\n\nPlan 3: Check\n- If GoodGuy holds a King (1/3 probability), he will call (100%). If the public card is a King, we will draw. If the public card is not a King, I will win. So the winning rate is 2/3, the draw rate is 1/3, and the losing rate is 0.\n- If GoodGuy holds a Queen (1/3 probability), he will raise (100%) because the public card is a Queen. So the winning rate is 0, the draw rate is 0, and the losing rate is 1.\n- If GoodGuy holds a Jack (1/3 probability), he will fold (100%) because the public card is not a Jack. So the winning rate is 1, the draw rate is 0, and the losing rate is 0.\n- Overall, the winning rate for Plan 3 is (1/3 * 2/3) + (1/3 * 0) + (1/3 * 1) = 0.56, the draw rate is 1/3 * 1/3 = 0.11, and the losing rate is 1/3.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips. If I lose, the losing payoff would be 4 chips.\n- Plan 2: If I win, the winning payoff would be 0 chips. If I lose, the losing payoff would be 4 chips.\n- Plan 3: If I win, the winning payoff would be 4 chips. If I lose, the losing payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0.89 * 4 - 0 * 4 = 3.56 chips\n- Plan 2: 0 * 0 - 1 * 4 = -4 chips\n- Plan 3: 0.56 * 4 - 1/3 * 4 = 0.56 chips\n\nPlan Selection:\n- Plan 1 > Plan 3 > Plan 2\n- Therefore, I should choose Plan 1: Raise."}}
{"message": "", "7_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (probability 33.33%): \n  - He will raise in the 1st round (probability 100%). \n  - In the 2nd round, if the public card is a King, he will raise (probability 100%). If the public card is not a King, he will fold if I raise (probability 100%). \n  - Winning rate: 0% (as he has a higher card), Lose rate: 100%, Draw rate: 0%\n- If GoodGuy holds a Queen (probability 33.33%): \n  - He will call in the 1st round (probability 100%). \n  - In the 2nd round, if the public card is a Queen, he will raise (probability 100%). If the public card is not a Queen, he will fold if I raise (probability 100%). \n  - Winning rate: 0% (as we have the same card), Lose rate: 0%, Draw rate: 100%\n- If GoodGuy holds a Jack (probability 33.33%): \n  - He will raise in the 1st round (probability 100%). \n  - In the 2nd round, if the public card is a Jack, he will raise (probability 100%). If the public card is not a Jack, he will fold if I raise (probability 100%). \n  - Winning rate: 100% (as I have a higher card), Lose rate: 0%, Draw rate: 0%\n- Overall Winning rate: 33.33%, Lose rate: 33.33%, Draw rate: 33.33%\n- Winning Payoff: 4 chips (half of the pot), Lose Payoff: -4 chips\n- Expected Chips Gain: 33.33% * 4 - 33.33% * 4 = 0 chips\n\nPlan 2: Fold\n- If I fold, I will lose the chips in the pot regardless of GoodGuy's card. \n- Overall Winning rate: 0%, Lose rate: 100%, Draw rate: 0%\n- Winning Payoff: 0 chips, Lose Payoff: -2 chips\n- Expected Chips Gain: 0% * 0 - 100% * 2 = -2 chips\n\nPlan 3: Check\n- If GoodGuy holds a King (probability 33.33%): \n  - He will raise in the 1st round (probability 100%). \n  - In the 2nd round, if the public card is a King, he will raise (probability 100%). If the public card is not a King, he will fold if I raise (probability 100%). \n  - Winning rate: 0% (as he has a higher card), Lose rate: 100%, Draw rate: 0%\n- If GoodGuy holds a Queen (probability 33.33%): \n  - He will call in the 1st round (probability 100%). \n  - In the 2nd round, if the public card is a Queen, he will raise (probability 100%). If the public card is not a Queen, he will fold if I raise (probability 100%). \n  - Winning rate: 0% (as we have the same card), Lose rate: 0%, Draw rate: 100%\n- If GoodGuy holds a Jack (probability 33.33%): \n  - He will raise in the 1st round (probability 100%). \n  - In the 2nd round, if the public card is a Jack, he will raise (probability 100%). If the public card is not a Jack, he will fold if I raise (probability 100%). \n  - Winning rate: 100% (as I have a higher card), Lose rate: 0%, Draw rate: 0%\n- Overall Winning rate: 33.33%, Lose rate: 33.33%, Draw rate: 33.33%\n- Winning Payoff: 2 chips (half of the pot), Lose Payoff: -2 chips\n- Expected Chips Gain: 33.33% * 2 - 33.33% * 2 = 0 chips\n\nPlan Selection: \n- Plan 1: 0 chips\n- Plan 2: -2 chips\n- Plan 3: 0 chips\n\nBased on the expected chips gain, Plan 1 (Raise) and Plan 3 (Check) are the best strategies. However, considering the strategy improvement, Plan 1 (Raise) is the best strategy as it has the potential to win more chips in the long run."}}
{"message": "", "7_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (probability 33%): He will fold (probability 100%) as the public card is not a King. I will win the pot (probability 100%).\n- If GoodGuy holds a Queen (probability 33%): He will fold (probability 100%) as the public card is not a Queen. I will win the pot (probability 100%).\n- If GoodGuy holds a Jack (probability 33%): He will raise (probability 100%) as the public card is a Jack. I will lose the pot (probability 100%).\n\nPlan 2: Fold\n- If I fold, I will lose the pot (probability 100%).\n\nPlan 3: Check\n- If GoodGuy holds a King (probability 33%): He will fold (probability 100%) as the public card is not a King. I will win the pot (probability 100%).\n- If GoodGuy holds a Queen (probability 33%): He will fold (probability 100%) as the public card is not a Queen. I will win the pot (probability 100%).\n- If GoodGuy holds a Jack (probability 33%): He will raise (probability 100%) as the public card is a Jack. I will lose the pot (probability 100%).\n\nWinning/Lose Payoff for Each Plan:\n- Plan 1: If I win, the winning payoff would be 4 chips. If I lose, the losing payoff would be 4 chips.\n- Plan 2: If I fold, the losing payoff would be 4 chips.\n- Plan 3: If I win, the winning payoff would be 4 chips. If I lose, the losing payoff would be 4 chips.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected chips gain = 33% * 4 chips - 33% * 4 chips = 0 chips\n- Plan 2: Expected chips gain = -100% * 4 chips = -4 chips\n- Plan 3: Expected chips gain = 33% * 4 chips - 33% * 4 chips = 0 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 have the same expected chips gain, which is higher than Plan 2. Therefore, I should either raise (Plan 1) or check (Plan 3). Considering the strategy improvement, I should raise (Plan 1) as it is more aggressive and can potentially confuse GoodGuy."}}
{"message": "", "8_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (33.33% probability), he will raise in the second round if the public card is a King (33.33% probability), and I will lose. If the public card is not a King (66.67% probability), he will fold, and I will win. Overall, the winning rate is 22.22%, the losing rate is 11.11%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (33.33% probability), he will raise in the second round if the public card is a Queen (33.33% probability), and it will be a draw. If the public card is not a Queen (66.67% probability), he will fold, and I will win. Overall, the winning rate is 22.22%, the losing rate is 0%, and the draw rate is 11.11%.\n- If GoodGuy holds a Jack (33.33% probability), he will fold in the second round if the public card is not a Jack (66.67% probability), and I will win. If the public card is a Jack (33.33% probability), he will raise, and I will lose. Overall, the winning rate is 22.22%, the losing rate is 11.11%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (33.33% probability), he will call in the first round (100% probability), and the second round will be the same as in Plan 1. Overall, the winning rate is 22.22%, the losing rate is 11.11%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (33.33% probability), he will call in the first round (100% probability), and the second round will be the same as in Plan 1. Overall, the winning rate is 22.22%, the losing rate is 0%, and the draw rate is 11.11%.\n- If GoodGuy holds a Jack (33.33% probability), he will raise in the first round (100% probability), and the second round will be the same as in Plan 1. Overall, the winning rate is 22.22%, the losing rate is 11.11%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card. The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the call action, chips in the pot: 8. If win, the winning payoff would be 4. If lose, the lose payoff would be 4.\n- Plan 2: After the raise action, chips in the pot: 12. If win, the winning payoff would be 6. If lose, the lose payoff would be 6.\n- Plan 3: After the fold action, chips in the pot: 6. If lose, the lose payoff would be 3.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 22.22% * 4 - 11.11% * 4 = 0.444\n- Plan 2: Expected Chips Gain = 22.22% * 6 - 11.11% * 6 = 0.666\n- Plan 3: Expected Chips Gain = 0% * 0 - 100% * 3 = -3\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, followed by Plan 1 (Call), and Plan 3 (Fold) has the lowest expected chips gain. Therefore, I should choose Plan 2 (Raise)."}}
{"message": "", "8_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Jack (70% probability), he will fold (100% probability). I will win the pot, which is currently 12 chips. The winning rate for this card is 70%.\n- If GoodGuy holds a Queen (30% probability), he will fold (100% probability). I will win the pot, which is currently 12 chips. The winning rate for this card is 30%.\n\nPlan 2: Fold\n- If GoodGuy holds a Jack (70% probability), I will lose the pot, which is currently 12 chips. The losing rate for this card is 70%.\n- If GoodGuy holds a Queen (30% probability), I will lose the pot, which is currently 12 chips. The losing rate for this card is 30%.\n\nPlan 3: Check\n- If GoodGuy holds a Jack (70% probability), he will fold (100% probability). I will win the pot, which is currently 12 chips. The winning rate for this card is 70%.\n- If GoodGuy holds a Queen (30% probability), he will fold (100% probability). I will win the pot, which is currently 12 chips. The winning rate for this card is 30%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 6 chips. If lose, the lose payoff would be 6 chips.\n- Plan 2: If win, the winning payoff would be 0 chips. If lose, the lose payoff would be 6 chips.\n- Plan 3: If win, the winning payoff would be 6 chips. If lose, the lose payoff would be 6 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: (70% * 6 chips) + (30% * 6 chips) - 0 = 6 chips\n- Plan 2: 0 - ((70% * 6 chips) + (30% * 6 chips)) = -6 chips\n- Plan 3: (70% * 6 chips) + (30% * 6 chips) - 0 = 6 chips\n\nPlan Selection:\n- Plan 1: 6 chips\n- Plan 2: -6 chips\n- Plan 3: 6 chips\n\nBased on the estimated expected chips gains, Plan 1 and Plan 3 are the best strategies to follow. However, considering the strategy improvement, Plan 1 (Raise) is the best strategy to follow as it is more aggressive and can potentially lead to more gains in the future games."}}
{"message": "", "9_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (50% probability), he will likely call (70% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, it will be a draw. Overall, the winning rate is 0%, the losing rate is 70%, and the draw rate is 30%.\n- If GoodGuy holds a Queen (50% probability), he will likely call (40% probability) or fold (60% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I will win. Overall, the winning rate is 60%, the losing rate is 20%, and the draw rate is 20%.\n\nPlan 1 overall Winning/Lose/Draw rates: Winning rate is 30%, Losing rate is 45%, Draw rate is 25%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (50% probability), he will likely call (30% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, it will be a draw. Overall, the winning rate is 0%, the losing rate is 30%, and the draw rate is 20%.\n- If GoodGuy holds a Queen (50% probability), he will likely fold (60% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I will win. Overall, the winning rate is 60%, the losing rate is 20%, and the draw rate is 20%.\n\nPlan 2 overall Winning/Lose/Draw rates: Winning rate is 30%, Losing rate is 25%, Draw rate is 20%.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot. The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, Chips in the pot: 8. If win, the winning payoff would be 4. If lose, the lose payoff would be 4.\n- Plan 2: After the action, Chips in the pot: 12. If win, the winning payoff would be 6. If lose, the lose payoff would be 6.\n- Plan 3: After the action, Chips in the pot: 6. If lose, the lose payoff would be 3.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 30% * 4 - 45% * 4 = -0.6 chips\n- Plan 2: 30% * 6 - 25% * 6 = 0.3 chips\n- Plan 3: 0% * 0 - 100% * 3 = -3 chips\n\nPlan Selection:\n- Plan 2 > Plan 1 > Plan 3\n- I should choose Plan 2: Raise."}}
{"message": "", "9_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (70% probability), he will likely call (100% probability). If he calls, I will lose as his King is higher than my Queen. The losing rate for his King is 70%.\n- If GoodGuy holds a Queen (30% probability), he will likely fold if I raise (60% probability). If he folds, I will win. The winning rate for his Queen is 18% (30% * 60%). He may also call if I raise (40% probability). If he calls, it will be a draw as we both have Queens. The draw rate for his Queen is 12% (30% * 40%).\n\nPlan 2: Fold\n- If I fold, I will lose regardless of GoodGuy's card. The losing rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (70% probability), he will likely call if I check (70% probability). If he calls, I will lose as his King is higher than my Queen. The losing rate for his King is 49% (70% * 70%).\n- If GoodGuy holds a Queen (30% probability), he will likely call if I check (40% probability). If he calls, it will be a draw as we both have Queens. The draw rate for his Queen is 12% (30% * 40%).\n\nWinning/Lose Payoffs for Each Plan:\n- Plan 1: After the raise, chips in the pot would be 14. If win, the winning payoff would be 7. If lose, the lose payoff would be 7.\n- Plan 2: After the fold, chips in the pot would be 6. If lose, the lose payoff would be 3.\n- Plan 3: After the check, chips in the pot would be 6. If win, the winning payoff would be 3. If lose, the lose payoff would be 3.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected chips gain = winning rate * winning payoff - losing rate * losing payoff = 18% * 7 - 70% * 7 = -3.64\n- Plan 2: Expected chips gain = -100% * 3 = -3\n- Plan 3: Expected chips gain = 0 - 49% * 3 = -1.47\n\nPlan Selection:\n- Plan 1: -3.64\n- Plan 2: -3\n- Plan 3: -1.47\n\nBased on the expected chips gain, Plan 3 (Check) is the best strategy to use in this situation."}}
{"message": "", "10_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (probability 33.33%), he will call if I call (probability 100%). If the public card is a King, I will lose (probability 33.33%). If the public card is a Queen or Jack, I will win (probability 66.67%).\n- If GoodGuy holds a Queen (probability 33.33%), he will call if I call (probability 100%). If the public card is a Queen, it will be a draw (probability 33.33%). If the public card is a King or Jack, I will win (probability 66.67%).\n- If GoodGuy holds a Jack (probability 33.33%), he will raise if I call (probability 100%). If the public card is a Jack, I will lose (probability 33.33%). If the public card is a King or Queen, I will win (probability 66.67%).\n\nPlan 2: Raise\n- If GoodGuy holds a King (probability 33.33%), he will call if I raise (probability 100%). If the public card is a King, I will lose (probability 33.33%). If the public card is a Queen or Jack, I will win (probability 66.67%).\n- If GoodGuy holds a Queen (probability 33.33%), he will call if I raise (probability 100%). If the public card is a Queen, it will be a draw (probability 33.33%). If the public card is a King or Jack, I will win (probability 66.67%).\n- If GoodGuy holds a Jack (probability 33.33%), he will fold if I raise (probability 100%). I will win (probability 100%).\n\nPlan 3: Fold\n- If I fold, I will lose the pot (probability 100%).\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, Chips in the pot: 3. If win, the winning payoff would be 1.5. If lose, the lose payoff would be 1.5.\n- Plan 2: After the action, Chips in the pot: 5. If win, the winning payoff would be 2.5. If lose, the lose payoff would be 2.5.\n- Plan 3: After the action, Chips in the pot: 3. If lose, the lose payoff would be 1.5.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.67 * 1.5 - 0.33 * 1.5 = 0.5\n- Plan 2: Expected Chips Gain = 0.67 * 2.5 - 0.33 * 2.5 = 0.83\n- Plan 3: Expected Chips Gain = -1.5\n\nPlan Selection:\n- Plan 2 > Plan 1 > Plan 3\n- I will choose Plan 2: Raise, as it has the highest expected chips gain."}}
{"message": "", "10_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (50% probability), he will raise (100% probability). If he raises, I will lose as his pair of Kings is stronger than my single Queen. So, the losing rate for his King is 50%.\n- If GoodGuy holds a Queen (50% probability), he will fold (100% probability) if I raise. If he folds, I will win. So, the winning rate for his Queen is 50%.\n\nPlan 2: Fold\n- If GoodGuy holds a King (50% probability), he will raise (100% probability). If I fold, I will lose. So, the losing rate for his King is 50%.\n- If GoodGuy holds a Queen (50% probability), he will fold (100% probability) if I fold. If we both fold, it will be a draw. So, the draw rate for his Queen is 50%.\n\nPlan 3: Check\n- If GoodGuy holds a King (50% probability), he will raise (100% probability). If he raises, I will lose as his pair of Kings is stronger than my single Queen. So, the losing rate for his King is 50%.\n- If GoodGuy holds a Queen (50% probability), he will fold (100% probability) if I check. If he folds, I will win. So, the winning rate for his Queen is 50%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, Chips in the pot: 8. If win, the winning payoff would be 4. If lose, the lose payoff would be 4.\n- Plan 2: After the action, Chips in the pot: 4. If win, the winning payoff would be 2. If lose, the lose payoff would be 2.\n- Plan 3: After the action, Chips in the pot: 4. If win, the winning payoff would be 2. If lose, the lose payoff would be 2.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 50% * 4 - 50% * 4 = 0\n- Plan 2: Expected Chips Gain = 0% * 2 - 50% * 2 = -1\n- Plan 3: Expected Chips Gain = 50% * 2 - 50% * 2 = 0\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows:\n1. Plan 1: 0\n2. Plan 3: 0\n3. Plan 2: -1\n\nConsidering both the strategy improvement and the estimated expected chips gain, I will choose Plan 1: Raise."}}
{"message": "", "10_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (probability 100% based on my belief), he will not take any action as he has already raised. I will lose this round (probability 100%) as his pair of Kings beats my single Queen. The overall lose rate for his King is 100%.\n- If GoodGuy holds a Queen (probability 0% based on my belief), he will not take any action as he has already raised. I will win this round (probability 0%) as my pair of Queens beats his single Queen. The overall win rate for his Queen is 0%.\n- If GoodGuy holds a Jack (probability 0% based on my belief), he will not take any action as he has already raised. I will win this round (probability 0%) as my single Queen beats his single Jack. The overall win rate for his Jack is 0%.\n\nPlan 1 overall Winning/Lose/Draw rates: \n- Winning rate for plan 1 is 0%.\n- Lose rate for plan 1 is 100%.\n- Draw rate for plan 1 is 0%.\n\nPlan 2: Fold\n- If GoodGuy holds a King (probability 100% based on my belief), he will not take any action as I have folded. I will lose this round (probability 100%) as I have conceded. The overall lose rate for his King is 100%.\n- If GoodGuy holds a Queen (probability 0% based on my belief), he will not take any action as I have folded. I will lose this round (probability 0%) as I have conceded. The overall lose rate for his Queen is 0%.\n- If GoodGuy holds a Jack (probability 0% based on my belief), he will not take any action as I have folded. I will lose this round (probability 0%) as I have conceded. The overall lose rate for his Jack is 0%.\n\nPlan 2 overall Winning/Lose/Draw rates: \n- Winning rate for plan 2 is 0%.\n- Lose rate for plan 2 is 100%.\n- Draw rate for plan 2 is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the call action, chips in the pot would be 24. If win, the winning payoff would be 12. If lose, the lose payoff would be 12.\n- Plan 2: After the fold action, chips in the pot would be 20. If lose, the lose payoff would be 10.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected chips gain = winning rate * winning payoff - lose rate * lose payoff = 0% * 12 - 100% * 12 = -12 chips.\n- Plan 2: Expected chips gain = winning rate * winning payoff - lose rate * lose payoff = 0% * 0 - 100% * 10 = -10 chips.\n\nPlan Selection:\n- Plan 1: -12 chips\n- Plan 2: -10 chips\n\nBased on the estimated expected chips gain, Plan 2 (Fold) is the better strategy as it results in a smaller loss of chips."}}
{"message": "", "11_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (33.33% probability), he will call (100% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I will win. So, the winning rate is 66.67%, and the losing rate is 33.33%.\n- If GoodGuy holds a Queen (33.33% probability), he will call (100% probability). If the public card is a Queen, I will lose. If the public card is a King or Jack, I will win. So, the winning rate is 66.67%, and the losing rate is 33.33%.\n- If GoodGuy holds a Jack (33.33% probability), he will call (100% probability). If the public card is a Jack, it will be a draw. If the public card is a King or Queen, I will lose. So, the winning rate is 0%, the losing rate is 66.67%, and the draw rate is 33.33%.\n\nPlan 2: Fold\n- If I fold, I will lose the round regardless of GoodGuy's card or the public card. So, the losing rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (33.33% probability), he will call (100% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I will win. So, the winning rate is 66.67%, and the losing rate is 33.33%.\n- If GoodGuy holds a Queen (33.33% probability), he will call (100% probability). If the public card is a Queen, I will lose. If the public card is a King or Jack, I will win. So, the winning rate is 66.67%, and the losing rate is 33.33%.\n- If GoodGuy holds a Jack (33.33% probability), he will call (100% probability). If the public card is a Jack, it will be a draw. If the public card is a King or Queen, I will lose. So, the winning rate is 0%, the losing rate is 66.67%, and the draw rate is 33.33%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips. If I lose, the losing payoff would be 4 chips.\n- Plan 2: If I lose, the losing payoff would be 2 chips.\n- Plan 3: If I win, the winning payoff would be 2 chips. If I lose, the losing payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: (66.67% * 4) - (33.33% * 4) = 1.33 chips\n- Plan 2: -2 chips\n- Plan 3: (66.67% * 2) - (33.33% * 2) = 0.67 chips\n\nPlan Selection:\n- Plan 1: 1.33 chips\n- Plan 2: -2 chips\n- Plan 3: 0.67 chips\n\nBased on the estimated expected chips gain, I should select Plan 1 (Raise)."}}
{"message": "", "11_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (probability 1/3), he will raise (probability 100%). I will lose as his pair of Kings beats my single Jack. \n- If GoodGuy holds a Queen (probability 1/3), he will fold if I raise (probability 100%). I will win as he forfeits the game.\n- If GoodGuy holds a Jack (probability 1/3), he will fold if I raise (probability 100%). I will win as he forfeits the game.\nOverall, the winning rate for plan 1 is 2/3, the losing rate is 1/3, and the draw rate is 0.\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card. \nOverall, the winning rate for plan 2 is 0, the losing rate is 1, and the draw rate is 0.\n\nPlan 3: Check\n- If GoodGuy holds a King (probability 1/3), he will raise (probability 100%). I will lose as his pair of Kings beats my single Jack. \n- If GoodGuy holds a Queen (probability 1/3), he will check (probability 100%). I will win as my single Jack beats his single Queen.\n- If GoodGuy holds a Jack (probability 1/3), he will check (probability 100%). The game will be a draw as we both have a single Jack.\nOverall, the winning rate for plan 3 is 1/3, the losing rate is 1/3, and the draw rate is 1/3.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be half of the pot (8 chips). If lose, the lose payoff would be half of the pot (8 chips).\n- Plan 2: If lose, the lose payoff would be half of the pot (4 chips).\n- Plan 3: If win, the winning payoff would be half of the pot (4 chips). If lose, the lose payoff would be half of the pot (4 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = winning rate * Winning Payoff - losing rate * Lose Payoff = 2/3 * 8 - 1/3 * 8 = 16/3 - 8/3 = 8/3 = 2.67 chips\n- Plan 2: Expected Chips Gain = winning rate * Winning Payoff - losing rate * Lose Payoff = 0 * 4 - 1 * 4 = -4 chips\n- Plan 3: Expected Chips Gain = winning rate * Winning Payoff - losing rate * Lose Payoff = 1/3 * 4 - 1/3 * 4 = 4/3 - 4/3 = 0 chips\n\nPlan Selection:\n- Plan 1: 2.67 chips\n- Plan 2: -4 chips\n- Plan 3: 0 chips\n\nBased on the estimated expected chips gains, I should select Plan 1 (Raise) as it has the highest expected chips gain."}}
{"message": "", "12_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (50% probability), he will likely raise in the second round if the public card is a King. If I call, I will lose unless the public card is a Queen. If the public card is a Queen, I will win. If the public card is a Jack, it will be a draw. \n- If GoodGuy holds a Jack (50% probability), he will likely fold in the second round if the public card is not a Jack. If I call, I will win unless the public card is a King. If the public card is a King, I will lose. If the public card is a Jack, it will be a draw. \n\nPlan 2: Raise\n- If GoodGuy holds a King (50% probability), he will likely raise in the second round if the public card is a King. If I raise, I will lose unless the public card is a Queen. If the public card is a Queen, I will win. If the public card is a Jack, it will be a draw. \n- If GoodGuy holds a Jack (50% probability), he will likely fold in the second round if the public card is not a Jack. If I raise, I will win unless the public card is a King. If the public card is a King, I will lose. If the public card is a Jack, it will be a draw. \n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card or the public card. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips (half of the pot). If I lose, the lose payoff would be 1 chip (half of the pot).\n- Plan 2: If I win, the winning payoff would be 5 chips (half of the pot). If I lose, the lose payoff would be 2 chips (half of the pot).\n- Plan 3: If I fold, I will lose 1 chip (half of the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.5 * 3 - 0.5 * 1 = 1 chip\n- Plan 2: Expected Chips Gain = 0.5 * 5 - 0.5 * 2 = 1.5 chips\n- Plan 3: Expected Chips Gain = -1 chip\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I will choose this plan."}}
{"message": "", "12_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (50% probability), he will raise (100% probability). In this case, it will be a draw. The overall draw rate for his Queen is 50%.\n- If GoodGuy holds a King (25% probability), he will fold if I raise (100% probability). In this case, I will win. The overall winning rate for his King is 25%.\n- If GoodGuy holds a Jack (25% probability), he will fold if I raise (100% probability). In this case, I will win. The overall winning rate for his Jack is 25%.\n\nPlan 2: Check\n- If GoodGuy holds a Queen (50% probability), he will raise (100% probability). In this case, it will be a draw. The overall draw rate for his Queen is 50%.\n- If GoodGuy holds a King (25% probability), he will fold if I check (0% probability). In this case, I will win. The overall winning rate for his King is 0%.\n- If GoodGuy holds a Jack (25% probability), he will fold if I check (0% probability). In this case, I will win. The overall winning rate for his Jack is 0%.\n\nPlan 3: Fold\n- If GoodGuy holds a Queen (50% probability), he will raise (100% probability). In this case, I will lose. The overall losing rate for his Queen is 50%.\n- If GoodGuy holds a King (25% probability), he will fold if I fold (100% probability). In this case, it will be a draw. The overall draw rate for his King is 25%.\n- If GoodGuy holds a Jack (25% probability), he will fold if I fold (100% probability). In this case, it will be a draw. The overall draw rate for his Jack is 25%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, chips in the pot: 16. If win, the winning payoff would be 8. If lose, the lose payoff would be 8.\n- Plan 2: After the action, chips in the pot: 8. If win, the winning payoff would be 4. If lose, the lose payoff would be 4.\n- Plan 3: After the action, chips in the pot: 8. If win, the winning payoff would be 4. If lose, the lose payoff would be 4.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: (25% * 8) + (25% * 8) - (0% * 8) = 4 chips\n- Plan 2: (0% * 4) + (0% * 4) - (50% * 4) = -2 chips\n- Plan 3: (0% * 4) + (0% * 4) - (50% * 4) = -2 chips\n\nPlan Selection:\n- Plan 1: 4 chips\n- Plan 2: -2 chips\n- Plan 3: -2 chips\n\nBased on the estimated expected chips gain, I should choose Plan 1 (Raise) as it has the highest expected chips gain."}}
{"message": "", "13_0": {"plan": "Plan 1: Call\nIf I call, I will match GoodGuy's bet of 2 chips, making the total pot 5 chips. \n\nPlan 2: Raise\nIf I raise, I will increase the bet by 4 chips, making the total pot 7 chips. \n\nPlan 3: Fold\nIf I fold, I will forfeit the game, losing the 1 chip I have already put in the pot. \n\nPotential GoodGuy's actions and Estimate Winning/Lose/Draw Rate for Each Plan:\n\nPlan 1: Call\nIf GoodGuy holds a King, there's a 70% chance he would raise and a 30% chance he would call. If he raises, I have a 50% chance of winning (if the public card is a Jack), a 25% chance of losing (if the public card is a Queen or King), and a 25% chance of drawing (if the public card is a Jack). If he calls, I have a 50% chance of winning, a 25% chance of losing, and a 25% chance of drawing. \n\nIf GoodGuy holds a Queen, there's a 60% chance he would call and a 40% chance he would raise. If he raises, I have a 50% chance of winning (if the public card is a Jack), a 25% chance of losing (if the public card is a Queen or King), and a 25% chance of drawing (if the public card is a Jack). If he calls, I have a 50% chance of winning, a 25% chance of losing, and a 25% chance of drawing. \n\nIf GoodGuy holds a Jack, there's a 50% chance he would call and a 50% chance he would raise. If he raises, I have a 50% chance of winning (if the public card is a Jack), a 25% chance of losing (if the public card is a Queen or King), and a 25% chance of drawing (if the public card is a Jack). If he calls, I have a 50% chance of winning, a 25% chance of losing, and a 25% chance of drawing. \n\nPlan 2: Raise\nIf GoodGuy holds a King, there's a 70% chance he would raise and a 30% chance he would call. If he raises, I have a 50% chance of winning (if the public card is a Jack), a 25% chance of losing (if the public card is a Queen or King), and a 25% chance of drawing (if the public card is a Jack). If he calls, I have a 50% chance of winning, a 25% chance of losing, and a 25% chance of drawing. \n\nIf GoodGuy holds a Queen, there's a 60% chance he would call and a 40% chance he would raise. If he raises, I have a 50% chance of winning (if the public card is a Jack), a 25% chance of losing (if the public card is a Queen or King), and a 25% chance of drawing (if the public card is a Jack). If he calls, I have a 50% chance of winning, a 25% chance of losing, and a 25% chance of drawing. \n\nIf GoodGuy holds a Jack, there's a 50% chance he would call and a 50% chance he would raise. If he raises, I have a 50% chance of winning (if the public card is a Jack), a 25% chance of losing (if the public card is a Queen or King), and a 25% chance of drawing (if the public card is a Jack). If he calls, I have a 50% chance of winning, a 25% chance of losing, and a 25% chance of drawing. \n\nPlan 3: Fold\nIf I fold, I will lose the game, losing the 1 chip I have already put in the pot. \n\nThe number of winning and lose payoffs for each plan:\n\nPlan 1: Call\nIf I win, the winning payoff would be 2.5 chips. If I lose, the lose payoff would be 2.5 chips. \n\nPlan 2: Raise\nIf I win, the winning payoff would be 3.5 chips. If I lose, the lose payoff would be 3.5 chips. \n\nPlan 3: Fold\nIf I fold, I will lose the game, losing the 1 chip I have already put in the pot. \n\nEstimate Expected Chips Gain for Each Plan:\n\nPlan 1: Call\nThe expected chips gain for this plan is 0 chips. \n\nPlan 2: Raise\nThe expected chips gain for this plan is 0 chips. \n\nPlan 3: Fold\nThe expected chips gain for this plan is -1 chip. \n\nPlan Selection:\n\nBased on the above analysis, I should choose Plan 1: Call or Plan 2: Raise, as they both have the highest expected chips gain. However, considering my strategy improvement, I should choose Plan 1: Call, as it is more cautious and aligns with my new strategy."}}
{"message": "", "13_2": {"plan": "Plan 1: Raise\nIf I raise, GoodGuy might think I have a Queen or a King. Based on his behavior pattern, if he holds a King, he will call (probability 60%) or fold (probability 40%). If he holds a Queen, he will raise (probability 80%) or call (probability 20%). If he holds a Jack, he will fold (probability 60%) or call (probability 40%). \n\nThe winning/losing/draw rates when GoodGuy holds a King: If he calls (60%), I will lose (as King is higher than Jack). If he folds (40%), I will win. So, the winning rate is 40%, and the losing rate is 60%.\n\nThe winning/losing/draw rates when GoodGuy holds a Queen: If he raises (80%), I will lose (as Queen is higher than Jack). If he calls (20%), I will lose. So, the winning rate is 0%, and the losing rate is 100%.\n\nThe winning/losing/draw rates when GoodGuy holds a Jack: If he folds (60%), I will win. If he calls (40%), it will be a draw. So, the winning rate is 60%, and the draw rate is 40%.\n\nPlan 1 overall Winning/Losing/Draw rates: Winning rate is 33.3% (average of 40%, 0%, and 60%), Losing rate is 53.3% (average of 60%, 100%, and 0%), and Draw rate is 13.3% (average of 0%, 0%, and 40%).\n\nPlan 2: Fold\nIf I fold, I will lose the round regardless of GoodGuy's card. So, the winning rate is 0%, and the losing rate is 100%.\n\nPlan 3: Check\nIf I check, GoodGuy might think I have a Jack or a King. Based on his behavior pattern, if he holds a King, he will raise (probability 70%) or call (probability 30%). If he holds a Queen, he will call (probability 60%) or fold (probability 40%). If he holds a Jack, he will call (probability 50%) or fold (probability 50%). \n\nThe winning/losing/draw rates when GoodGuy holds a King: If he raises (70%), I will lose (as King is higher than Jack). If he calls (30%), I will lose. So, the winning rate is 0%, and the losing rate is 100%.\n\nThe winning/losing/draw rates when GoodGuy holds a Queen: If he calls (60%), I will lose (as Queen is higher than Jack). If he folds (40%), I will win. So, the winning rate is 40%, and the losing rate is 60%.\n\nThe winning/losing/draw rates when GoodGuy holds a Jack: If he calls (50%), it will be a draw. If he folds (50%), I will win. So, the winning rate is 50%, and the draw rate is 50%.\n\nPlan 3 overall Winning/Losing/Draw rates: Winning rate is 30% (average of 0%, 40%, and 50%), Losing rate is 70% (average of 100%, 60%, and 0%), and Draw rate is 16.7% (average of 0%, 0%, and 50%).\n\nThe number of winning and lose payoffs for each plan:\nPlan 1: If win, the winning payoff would be 3 chips (half of the pot after my raise). If lose, the lose payoff would be 2 chips (half of the pot before my raise).\nPlan 2: If lose, the lose payoff would be 2 chips (half of the pot before my fold).\nPlan 3: If win, the winning payoff would be 2 chips (half of the pot after my check). If lose, the lose payoff would be 2 chips (half of the pot before my check).\n\nEstimate Expected Chips Gain for Each Plan:\nPlan 1: Expected Chips Gain = 33.3% * 3 - 53.3% * 2 = -0.33 chips\nPlan 2: Expected Chips Gain = 0% * 0 - 100% * 2 = -2 chips\nPlan 3: Expected Chips Gain = 30% * 2 - 70% * 2 = -0.8 chips\n\nPlan Selection:\nBased on the estimated expected chips gain, the rank of the plans is: Plan 1 > Plan 3 > Plan 2. Therefore, I should choose Plan 1: Raise."}}
{"message": "", "14_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (probability 33.3%), he will fold if the public card is not a King (probability 66.7%). I will win (probability 22.2%). If the public card is a King, he will raise (probability 33.3%). I will lose (probability 11.1%).\n- If GoodGuy holds a Queen (probability 33.3%), he will raise if the public card is a Queen (probability 33.3%). I will win (probability 11.1%). If the public card is not a Queen, he will fold if I raise (probability 66.7%). I will win (probability 22.2%).\n- If GoodGuy holds a Jack (probability 33.3%), he will fold if the public card is not a Jack (probability 66.7%). I will win (probability 22.2%). If the public card is a Jack, he will raise (probability 33.3%). I will lose (probability 11.1%).\n\nPlan 1 overall Winning/Lose/Draw rates: Winning rate for plan 1 is 55.5%, Lose rate for plan 1 is 33.3%, Draw Rate for plan 1 is 11.2%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (probability 33.3%), he will fold if the public card is not a King (probability 66.7%). I will win (probability 22.2%). If the public card is a King, he will raise (probability 33.3%). I will lose (probability 11.1%).\n- If GoodGuy holds a Queen (probability 33.3%), he will fold regardless of the public card (probability 100%). I will win (probability 33.3%).\n- If GoodGuy holds a Jack (probability 33.3%), he will fold if the public card is not a Jack (probability 66.7%). I will win (probability 22.2%). If the public card is a Jack, he will raise (probability 33.3%). I will lose (probability 11.1%).\n\nPlan 2 overall Winning/Lose/Draw rates: Winning rate for plan 2 is 77.7%, Lose rate for plan 2 is 22.2%, Draw Rate for plan 2 is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of GoodGuy's card or the public card (probability 100%).\n\nPlan 3 overall Winning/Lose/Draw rates: Winning rate for plan 3 is 0%, Lose rate for plan 3 is 100%, Draw Rate for plan 3 is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, Chips in the pot: 6. If win, the winning payoff would be 3. If lose, the lose payoff would be 3.\n- Plan 2: After the action, Chips in the pot: 10. If win, the winning payoff would be 5. If lose, the lose payoff would be 5.\n- Plan 3: After the action, Chips in the pot: 6. If lose, the lose payoff would be 3.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 55.5% * 3 - 33.3% * 3 = 0.66\n- Plan 2: Expected Chips Gain = 77.7% * 5 - 22.2% * 5 = 2.77\n- Plan 3: Expected Chips Gain = 0% * 0 - 100% * 3 = -3\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so it should be selected."}}
{"message": "", "14_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King, he will fold (probability 100%). I will win the pot (probability 50% * 100% = 50%). \n- If GoodGuy holds a Queen, he will raise (probability 100%). We will draw (probability 50% * 100% = 50%).\n- If GoodGuy holds a Jack, he will fold (probability 100%). I will win the pot (probability 50% * 100% = 50%).\n\nPlan 2: Fold\n- If GoodGuy holds a King, Queen, or Jack, I will lose the pot (probability 100%).\n\nPlan 3: Check\n- If GoodGuy holds a King, he will fold (probability 100%). I will win the pot (probability 50% * 100% = 50%).\n- If GoodGuy holds a Queen, he will raise (probability 100%). We will draw (probability 50% * 100% = 50%).\n- If GoodGuy holds a Jack, he will fold (probability 100%). I will win the pot (probability 50% * 100% = 50%).\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, Chips in the pot: 14. If win, the winning payoff would be 7. If lose, the lose payoff would be 7.\n- Plan 2: After the action, Chips in the pot: 6. If lose, the lose payoff would be 3.\n- Plan 3: After the action, Chips in the pot: 6. If win, the winning payoff would be 3. If lose, the lose payoff would be 3.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 50% * 7 - 0% * 7 = 3.5\n- Plan 2: Expected Chips Gain = 0% * 3 - 100% * 3 = -3\n- Plan 3: Expected Chips Gain = 50% * 3 - 0% * 3 = 1.5\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows:\n1. Plan 1: Raise (3.5 chips)\n2. Plan 3: Check (1.5 chips)\n3. Plan 2: Fold (-3 chips)\n\nTherefore, the best strategy for this round is to raise."}}
{"message": "", "15_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (30% probability), he will likely raise (70%) or call (30%). If he raises, I will lose (as King is higher than Jack). If he calls, the outcome will depend on the public card. \n- If GoodGuy holds a Queen (60% probability), he will likely call (60%) or raise (40%). If he raises or calls, the outcome will depend on the public card. \n- If GoodGuy holds a Jack (70% probability), he will likely call (70%) or raise (30%). If he raises or calls, the outcome will be a draw as we both hold Jacks. \n\nPlan 2: Fold\n- If I fold, I will lose the current pot but avoid further losses. This is a conservative strategy that minimizes risk but also potential gains. \n\nPlan 3: Check\n- If GoodGuy holds a King (30% probability), he will likely raise (70%) or call (30%). If he raises, I will lose (as King is higher than Jack). If he calls, the outcome will depend on the public card. \n- If GoodGuy holds a Queen (60% probability), he will likely call (60%) or raise (40%). If he raises or calls, the outcome will depend on the public card. \n- If GoodGuy holds a Jack (70% probability), he will likely call (70%) or raise (30%). If he raises or calls, the outcome will be a draw as we both hold Jacks. \n\nWinning/Lose Payoffs:\n- Plan 1: If I win, the pot will be 6 chips (4 from me, 2 from GoodGuy), so the winning payoff would be 3 chips. If I lose, the pot will be 4 chips (2 from me, 2 from GoodGuy), so the losing payoff would be 2 chips. \n- Plan 2: If I fold, there will be no winning payoff. The losing payoff would be 2 chips (the amount I have already put in the pot). \n- Plan 3: If I win, the pot will be 4 chips (2 from me, 2 from GoodGuy), so the winning payoff would be 2 chips. If I lose, the pot will be 4 chips (2 from me, 2 from GoodGuy), so the losing payoff would be 2 chips. \n\nExpected Chips Gain:\n- Plan 1: Expected gain = 0.3 * 3 - 0.7 * 2 = -0.9 chips\n- Plan 2: Expected gain = 0 - 1 * 2 = -2 chips\n- Plan 3: Expected gain = 0.3 * 2 - 0.7 * 2 = -0.8 chips\n\nPlan Selection:\n- Based on the expected chips gain, Plan 3 (Check) has the highest expected gain, followed by Plan 1 (Raise), and then Plan 2 (Fold). Therefore, I should choose Plan 3 (Check)."}}
{"message": "", "15_3": {"plan": "Plan 1: Call\n- If GoodGuy holds a Queen (60% probability), he will likely raise (70% probability). If this happens, I will lose as his pair of Queens beats my single Jack. The losing rate for this scenario is 0.6*0.7=0.42. If he calls (30% probability), it will be a draw. The draw rate for this scenario is 0.6*0.3=0.18.\n- If GoodGuy holds a King (40% probability), he will likely fold (60% probability). If this happens, I will win as he forfeits the round. The winning rate for this scenario is 0.4*0.6=0.24. If he calls (40% probability), I will lose as his King beats my Jack. The losing rate for this scenario is 0.4*0.4=0.16.\n- Overall, the winning rate for Plan 1 is 0.24, the losing rate is 0.58, and the draw rate is 0.18. \n- If I win, the winning payoff would be half of the pot, which is (2+6+6)/2=7 chips. If I lose, the losing payoff would be half of the pot, which is 7 chips. \n- The expected chips gain for Plan 1 is 0.24*7 - 0.58*7 = -2.38 chips.\n\nPlan 2: Raise\n- If GoodGuy holds a Queen (60% probability), he will likely raise (70% probability). If this happens, I will lose as his pair of Queens beats my single Jack. The losing rate for this scenario is 0.6*0.7=0.42. If he calls (30% probability), it will be a draw. The draw rate for this scenario is 0.6*0.3=0.18.\n- If GoodGuy holds a King (40% probability), he will likely fold (60% probability). If this happens, I will win as he forfeits the round. The winning rate for this scenario is 0.4*0.6=0.24. If he calls (40% probability), I will lose as his King beats my Jack. The losing rate for this scenario is 0.4*0.4=0.16.\n- Overall, the winning rate for Plan 2 is 0.24, the losing rate is 0.58, and the draw rate is 0.18. \n- If I win, the winning payoff would be half of the pot, which is (2+6+6+8)/2=11 chips. If I lose, the losing payoff would be 11 chips. \n- The expected chips gain for Plan 2 is 0.24*11 - 0.58*11 = -3.74 chips.\n\nPlan 3: Fold\n- If I fold, I will lose the round and forfeit the 2 chips I have put into the pot. The losing rate for this scenario is 1. \n- The expected chips loss for Plan 3 is 2 chips.\n\nPlan Selection:\n- Plan 1: -2.38 chips\n- Plan 2: -3.74 chips\n- Plan 3: -2 chips\n\nBased on the expected chips gain for each plan, Plan 3 (Fold) is the best strategy as it results in the least chips loss."}}
{"message": "", "16_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (probability 33.33%):\n  - He might raise (probability 50%) or call (probability 50%). If he raises, I will lose (probability 100%). If he calls, I will win if the public card is a Jack (probability 33.33%) or lose if it's a King or Queen (probability 66.67%).\n- If GoodGuy holds a Queen (probability 33.33%):\n  - He might raise (probability 50%) or call (probability 50%). If he raises, I will lose (probability 100%). If he calls, I will win if the public card is a Jack (probability 33.33%) or lose if it's a King or Queen (probability 66.67%).\n- If GoodGuy holds a Jack (probability 33.33%):\n  - He might raise (probability 50%) or call (probability 50%). If he raises, I will lose (probability 100%). If he calls, it's a draw (probability 100%).\n\nPlan 1 overall Winning/Lose/Draw rates: Winning rate 11.11%, Lose rate 77.78%, Draw rate 11.11%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (probability 33.33%):\n  - He might call (probability 50%) or fold (probability 50%). If he calls, I will lose (probability 100%). If he folds, I will win (probability 100%).\n- If GoodGuy holds a Queen (probability 33.33%):\n  - He might call (probability 50%) or fold (probability 50%). If he calls, I will lose (probability 100%). If he folds, I will win (probability 100%).\n- If GoodGuy holds a Jack (probability 33.33%):\n  - He might call (probability 50%) or fold (probability 50%). If he calls, it's a draw (probability 100%). If he folds, I will win (probability 100%).\n\nPlan 2 overall Winning/Lose/Draw rates: Winning rate 50%, Lose rate 33.33%, Draw rate 16.67%.\n\nPlan 3: Fold\n- If I fold, I will lose (probability 100%).\n\nPlan 3 overall Winning/Lose/Draw rates: Winning rate 0%, Lose rate 100%, Draw rate 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 1.5 chips. If lose, the lose payoff would be 1 chip.\n- Plan 2: If win, the winning payoff would be 2 chips. If lose, the lose payoff would be 2 chips.\n- Plan 3: If lose, the lose payoff would be 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 11.11% * 1.5 - 77.78% * 1 = -0.833 chips\n- Plan 2: 50% * 2 - 33.33% * 2 = 0.333 chips\n- Plan 3: 0% * 0 - 100% * 1 = -1 chip\n\nPlan Selection:\n- Plan 2 > Plan 1 > Plan 3\n- I should choose Plan 2: Raise."}}
{"message": "", "16_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (30% probability), he will likely call (50%) or fold (50%). If he calls, I will lose (100%) as King is higher than Jack. If he folds, I will win (100%). Overall, the winning rate is 15%, the losing rate is 15%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (70% probability), he will likely raise (70%) or call (30%). If he raises or calls, I will lose (100%) as Queen matches the public card. Overall, the winning rate is 0%, the losing rate is 70%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (30% probability), he will likely fold (70%) or call (30%). If he folds, I will win (100%). If he calls, it will be a draw (100%). Overall, the winning rate is 21%, the losing rate is 0%, and the draw rate is 9%.\n\nPlan 2: Fold\n- If I fold, I will lose (100%). The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King (30% probability), he will likely call (50%) or fold (50%). If he calls, I will lose (100%) as King is higher than Jack. If he folds, I will win (100%). Overall, the winning rate is 15%, the losing rate is 15%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (70% probability), he will likely raise (70%) or call (30%). If he raises or calls, I will lose (100%) as Queen matches the public card. Overall, the winning rate is 0%, the losing rate is 70%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (30% probability), he will likely fold (70%) or call (30%). If he folds, I will win (100%). If he calls, it will be a draw (100%). Overall, the winning rate is 21%, the losing rate is 0%, and the draw rate is 9%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, chips in the pot: 12. If win, the winning payoff would be 6. If lose, the lose payoff would be 6.\n- Plan 2: After the action, chips in the pot: 8. If lose, the lose payoff would be 4.\n- Plan 3: After the action, chips in the pot: 8. If win, the winning payoff would be 4. If lose, the lose payoff would be 4.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: (36% * 6) - (85% * 6) = -2.94\n- Plan 2: 0 - (100% * 4) = -4\n- Plan 3: (30% * 4) - (85% * 4) = -2.2\n\nPlan Selection:\n- Plan 3 (Check) has the highest estimated expected chips gain (-2.2), followed by Plan 1 (Raise) (-2.94), and Plan 2 (Fold) (-4). Therefore, I should choose Plan 3 (Check)."}}
{"message": "", "17_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (probability 25%): \n  - If he sees my raise, he might raise (probability 60%) or call (probability 40%). \n  - If he raises, I will lose (probability 100%) as his King is higher than my Queen. \n  - If he calls, the outcome will depend on the public card. If the public card is a King or a Queen, I will win (probability 50%). If the public card is a Jack, I will lose (probability 50%).\n- If GoodGuy holds a Queen (probability 35%): \n  - If he sees my raise, he might call (probability 70%) or raise (probability 30%). \n  - If he calls or raises, the outcome will be a draw (probability 100%) as we both hold a Queen.\n- If GoodGuy holds a Jack (probability 40%): \n  - If he sees my raise, he might call (probability 80%) or fold (probability 20%). \n  - If he calls, I will win (probability 100%) as my Queen is higher than his Jack. \n  - If he folds, I will also win (probability 100%) as he forfeits the game.\n\nPlan 2: Fold\n- If I fold, I will lose (probability 100%) as I forfeit the game.\n\nPlan 3: Check\n- If GoodGuy holds a King (probability 25%): \n  - If he sees my check, he might raise (probability 60%) or call (probability 40%). \n  - If he raises, I will lose (probability 100%) as his King is higher than my Queen. \n  - If he calls, the outcome will depend on the public card. If the public card is a King or a Queen, I will win (probability 50%). If the public card is a Jack, I will lose (probability 50%).\n- If GoodGuy holds a Queen (probability 35%): \n  - If he sees my check, he might call (probability 70%) or raise (probability 30%). \n  - If he calls or raises, the outcome will be a draw (probability 100%) as we both hold a Queen.\n- If GoodGuy holds a Jack (probability 40%): \n  - If he sees my check, he might call (probability 80%) or fold (probability 20%). \n  - If he calls, I will win (probability 100%) as my Queen is higher than his Jack. \n  - If he folds, I will also win (probability 100%) as he forfeits the game.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the raise, chips in the pot: 6. If win, the winning payoff would be 3. If lose, the lose payoff would be 3.\n- Plan 2: After the fold, chips in the pot: 4. If lose, the lose payoff would be 2.\n- Plan 3: After the check, chips in the pot: 4. If win, the winning payoff would be 2. If lose, the lose payoff would be 2.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = winning rate * Winning Payoff - lose rate * Lose Payoff = (0.75 * 3) - (0.25 * 3) = 1.5\n- Plan 2: Expected Chips Gain = - lose rate * Lose Payoff = -1 * 2 = -2\n- Plan 3: Expected Chips Gain = winning rate * Winning Payoff - lose rate * Lose Payoff = (0.75 * 2) - (0.25 * 2) = 1\n\nPlan Selection:\n- Plan 1: Expected Chips Gain = 1.5\n- Plan 2: Expected Chips Gain = -2\n- Plan 3: Expected Chips Gain = 1\n\nBased on the estimated expected chips gains, the ranking of the plans is as follows: Plan 1 > Plan 3 > Plan 2. Therefore, I should choose Plan 1: Raise."}}
{"message": "", "17_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Jack (50% probability), he will likely raise (60%) or call (40%). If he raises, I will lose as he has a pair of Jacks. If he calls, I will also lose as his pair of Jacks is higher than my single Queen. Therefore, the winning rate for this plan is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (30% probability), he will likely call (70%) or fold (30%). If he calls, it will be a draw as we both have a single Queen. If he folds, I will win. Therefore, the winning rate for this plan is 30%, the losing rate is 0%, and the draw rate is 70%.\n- If GoodGuy holds a King (20% probability), he will likely call (50%) or fold (50%). If he calls, I will lose as his King is higher than my Queen. If he folds, I will win. Therefore, the winning rate for this plan is 10%, the losing rate is 10%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. Therefore, the winning rate for this plan is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a Jack (50% probability), he will likely raise (60%) or check (40%). If he raises, I will lose as he has a pair of Jacks. If he checks, I will also lose as his pair of Jacks is higher than my single Queen. Therefore, the winning rate for this plan is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (30% probability), he will likely check (70%) or fold (30%). If he checks, it will be a draw as we both have a single Queen. If he folds, I will win. Therefore, the winning rate for this plan is 30%, the losing rate is 0%, and the draw rate is 70%.\n- If GoodGuy holds a King (20% probability), he will likely check (50%) or fold (50%). If he checks, I will lose as his King is higher than my Queen. If he folds, I will win. Therefore, the winning rate for this plan is 10%, the losing rate is 10%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips (half of the pot). If I lose, the losing payoff would be 4 chips.\n- Plan 2: If I fold, I will lose 4 chips.\n- Plan 3: If I win, the winning payoff would be 4 chips. If I lose, the losing payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.4 * 4 - 1.1 * 4 = -2.8 chips\n- Plan 2: Expected Chips Gain = 0 - 1 * 4 = -4 chips\n- Plan 3: Expected Chips Gain = 0.4 * 4 - 1.1 * 4 = -2.8 chips\n\nPlan Selection:\n- Plan 1: Rank 1\n- Plan 2: Rank 3\n- Plan 3: Rank 1\n\nConsidering both the strategy improvement and the estimated expected chips gain, I should choose Plan 1 (Raise) or Plan 3 (Check) as they both have the highest estimated expected chips gain. However, considering GoodGuy's cautious play style, I will choose Plan 1 (Raise) to pressure him into folding."}}
{"message": "", "18_0": {"plan": "Plan 1: Call\nIf I call, I will put 1 more chip in the pot, making the total chips in the pot 4. \n\nThe winning/losing/draw rates when GoodGuy holds a King: \n- If the public card is a King (1/3 chance), GoodGuy will likely raise (80% chance). I will lose as my Jack doesn't match the public card. \n- If the public card is a Queen or Jack (2/3 chance), GoodGuy will likely call (60% chance) or fold (40% chance). I will win if the public card is a Jack, and lose if it's a Queen. \n\nThe winning/losing/draw rates when GoodGuy holds a Queen: \n- If the public card is a Queen (1/3 chance), GoodGuy will likely raise (70% chance). I will lose as my Jack doesn't match the public card. \n- If the public card is a King or Jack (2/3 chance), GoodGuy will likely call (50% chance) or fold (50% chance). I will win if the public card is a Jack, and lose if it's a King. \n\nThe winning/losing/draw rates when GoodGuy holds a Jack: \n- If the public card is a Jack (1/3 chance), it will be a draw as both our cards match the public card. \n- If the public card is a King or Queen (2/3 chance), GoodGuy will likely fold (70% chance) or call (30% chance). I will win if the public card is a Jack, and lose if it's a King or Queen. \n\nPlan 1 overall Winning/Lose/Draw rates: \n- Winning rate: 35% (King) * 2/3 (public card is a Jack) * 60% (GoodGuy calls) + 20% (Queen) * 2/3 (public card is a Jack) * 50% (GoodGuy calls) + 45% (Jack) * 1/3 (public card is a Jack) * 30% (GoodGuy calls) = 15.3%\n- Losing rate: 35% (King) * 1/3 (public card is a King) * 80% (GoodGuy raises) + 20% (Queen) * 1/3 (public card is a Queen) * 70% (GoodGuy raises) + 45% (Jack) * 2/3 (public card is a King or Queen) * 70% (GoodGuy folds) = 32.7%\n- Draw rate: 45% (Jack) * 1/3 (public card is a Jack) * 30% (GoodGuy calls) = 4.5%\n\nPlan 1 Winning/Lose Payoffs: \n- If win, the winning payoff would be: 4/2 = 2 chips\n- If lose, the lose payoff would be: 4/2 = 2 chips\n\nPlan 1 Expected Chips Gain: \n- Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Lose Payoff = 15.3% * 2 - 32.7% * 2 = -34.8%\n\nPlan 2: Raise\nIf I raise, I will put 3 more chips in the pot, making the total chips in the pot 6. \n\nThe winning/losing/draw rates when GoodGuy holds a King, Queen, or Jack would be the same as in Plan 1, as my action doesn't affect GoodGuy's actions. \n\nPlan 2 Winning/Lose Payoffs: \n- If win, the winning payoff would be: 6/2 = 3 chips\n- If lose, the lose payoff would be: 6/2 = 3 chips\n\nPlan 2 Expected Chips Gain: \n- Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Lose Payoff = 15.3% * 3 - 32.7% * 3 = -52.2%\n\nPlan 3: Fold\nIf I fold, I will not put any more chips in the pot. \n\nPlan 3 Winning/Lose Payoffs: \n- If win, the winning payoff would be: 0 chips\n- If lose, the lose payoff would be: 1 chip (the chip I have already put in the pot)\n\nPlan 3 Expected Chips Gain: \n- Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Lose Payoff = 0% * 0 - 100% * 1 = -1 chip\n\nPlan Selection: \n- Plan 1 Expected Chips Gain: -34.8%\n- Plan 2 Expected Chips Gain: -52.2%\n- Plan 3 Expected Chips Gain: -1 chip\n\nBased on the expected chips gain, I should choose Plan 3 (Fold) as it has the highest expected chips gain."}}
{"message": "", "19_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (60% probability), he will likely raise (60%) or call (40%) in the second round. If the public card is a King, I will lose. If the public card is a Queen or a Jack, I have a chance to win if GoodGuy folds (50% if public card is not a King). \n- If GoodGuy holds a Queen (30% probability), he will likely raise (30%) or call (70%) in the second round. If the public card is a Queen, I will lose. If the public card is a King or a Jack, I have a chance to win if GoodGuy folds (60% if public card is not a Queen).\n- If GoodGuy holds a Jack (10% probability), he will likely call (40%) or fold (60%) in the second round. If the public card is a Jack, it will be a draw. If the public card is a King or a Queen, I have a chance to win if GoodGuy folds (70% if public card is not a Jack).\n- Winning rate for plan 1: 0.6*0.5*0.6 + 0.3*0.6*0.3 + 0.1*0.7*0.1 = 0.21\n- Lose rate for plan 1: 0.6*0.5*0.4 + 0.3*0.4*0.7 + 0.1*0.3*0.9 = 0.27\n- Draw rate for plan 1: 0.1*0.4 = 0.04\n- If win, the winning payoff would be 4 chips (half of the pot). If lose, the lose payoff would be 4 chips.\n\nPlan 2: Raise\n- If GoodGuy holds a King (60% probability), he will likely raise (60%) or call (40%) in the second round. If the public card is a King, I will lose. If the public card is a Queen or a Jack, I have a chance to win if GoodGuy folds (50% if public card is not a King). \n- If GoodGuy holds a Queen (30% probability), he will likely raise (30%) or call (70%) in the second round. If the public card is a Queen, I will lose. If the public card is a King or a Jack, I have a chance to win if GoodGuy folds (60% if public card is not a Queen).\n- If GoodGuy holds a Jack (10% probability), he will likely call (40%) or fold (60%) in the second round. If the public card is a Jack, it will be a draw. If the public card is a King or a Queen, I have a chance to win if GoodGuy folds (70% if public card is not a Jack).\n- Winning rate for plan 2: 0.6*0.5*0.6 + 0.3*0.6*0.3 + 0.1*0.7*0.1 = 0.21\n- Lose rate for plan 2: 0.6*0.5*0.4 + 0.3*0.4*0.7 + 0.1*0.3*0.9 = 0.27\n- Draw rate for plan 2: 0.1*0.4 = 0.04\n- If win, the winning payoff would be 6 chips (half of the pot). If lose, the lose payoff would be 6 chips.\n\nPlan 3: Fold\n- If I fold, I will lose the 2 chips I have already put in the pot. \n\nExpected Chips Gain for Each Plan:\n- Plan 1: 0.21 * 4 - 0.27 * 4 = -0.24 chips\n- Plan 2: 0.21 * 6 - 0.27 * 6 = -0.36 chips\n- Plan 3: -2 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I will choose Plan 1: Call."}}
{"message": "", "19_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (60% probability), he will likely call (50% probability) or fold (50% probability). If he calls, I will lose (as a King beats a Jack), but if he folds, I will win. Therefore, the winning rate for this plan is 30% (60% * 50%), the losing rate is 30% (60% * 50%), and the draw rate is 0%.\n- If GoodGuy holds a Jack (40% probability), he will likely fold (70% probability) or call (30% probability). If he folds, I will win, and if he calls, it will be a draw. Therefore, the winning rate for this plan is 28% (40% * 70%), the losing rate is 0%, and the draw rate is 12% (40% * 30%).\n\nPlan 2: Fold\n- If I fold, I will automatically lose, regardless of what card GoodGuy holds. Therefore, the winning rate for this plan is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King (60% probability), he will likely call (50% probability) or fold (50% probability). If he calls, I will lose (as a King beats a Jack), but if he folds, I will win. Therefore, the winning rate for this plan is 30% (60% * 50%), the losing rate is 30% (60% * 50%), and the draw rate is 0%.\n- If GoodGuy holds a Jack (40% probability), he will likely fold (70% probability) or call (30% probability). If he folds, I will win, and if he calls, it will be a draw. Therefore, the winning rate for this plan is 28% (40% * 70%), the losing rate is 0%, and the draw rate is 12% (40% * 30%).\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips (half of the pot). If I lose, the losing payoff would be 4 chips.\n- Plan 2: If I fold, I will lose 4 chips.\n- Plan 3: If I win, the winning payoff would be 4 chips. If I lose, the losing payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.58 * 4 - 0.3 * 4 = 1.12 chips\n- Plan 2: Expected Chips Gain = 0 - 1 * 4 = -4 chips\n- Plan 3: Expected Chips Gain = 0.58 * 4 - 0.3 * 4 = 1.12 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 have the highest expected chips gain, so I should choose either of these plans. However, considering my aggressive play style and GoodGuy's conservative play style, I will choose Plan 1: Raise. This will put pressure on GoodGuy and potentially cause him to fold, increasing my chances of winning."}}
{"message": "", "20_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a Queen (70% chance), he will likely raise (40% chance) or call (60% chance). If he raises, I will win as I hold a King. If he calls, the outcome will depend on the public card. If the public card is a King or a Queen, I will win. If the public card is a Jack, it will be a draw. \n- If GoodGuy holds a Jack (30% chance), he will likely raise (50% chance) or call (50% chance). If he raises, I will win as I hold a King. If he calls, the outcome will depend on the public card. If the public card is a King or a Jack, I will win. If the public card is a Queen, it will be a draw. \n- Overall, the winning rate for Plan 1 is 70% (probability of GoodGuy holding a Queen) * 100% (probability of winning if GoodGuy holds a Queen) + 30% (probability of GoodGuy holding a Jack) * 100% (probability of winning if GoodGuy holds a Jack) = 100%. The draw rate is 0%. The lose rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a Queen (70% chance), he will likely call (60% chance) or fold (40% chance). If he calls, I will win as I hold a King. If he folds, I will also win as I will take the pot. \n- If GoodGuy holds a Jack (30% chance), he will likely call (20% chance) or fold (80% chance). If he calls, I will win as I hold a King. If he folds, I will also win as I will take the pot. \n- Overall, the winning rate for Plan 2 is 100%. The draw rate is 0%. The lose rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the pot. Therefore, the winning rate for Plan 3 is 0%. The draw rate is 0%. The lose rate is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips (half of the pot). If I lose, the lose payoff would be 1 chip (my initial bet).\n- Plan 2: If I win, the winning payoff would be 5 chips (half of the pot). If I lose, the lose payoff would be 3 chips (my initial bet plus my raise).\n- Plan 3: If I lose, the lose payoff would be 1 chip (my initial bet).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 100% * 3 chips - 0% * 1 chip = 3 chips\n- Plan 2: Expected Chips Gain = 100% * 5 chips - 0% * 3 chips = 5 chips\n- Plan 3: Expected Chips Gain = 0% * 0 chips - 100% * 1 chip = -1 chip\n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 2 > Plan 1 > Plan 3. Therefore, I should choose Plan 2 (Raise) as it has the highest estimated expected chips gain."}}
{"message": "", "20_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King, he is likely to call (60%) or fold (40%). If he calls, we will draw. If he folds, I will win. \n- If GoodGuy holds a Queen, he is likely to call (50%) or fold (50%). If he calls, I will win. If he folds, I will win. \n- If GoodGuy holds a Jack, he is likely to raise (70%) or call (30%). If he raises, I will lose. If he calls, I will lose. \n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. \n\nPlan 3: Check\n- If GoodGuy holds a King, he is likely to call (60%) or fold (40%). If he calls, we will draw. If he folds, I will win. \n- If GoodGuy holds a Queen, he is likely to call (50%) or fold (50%). If he calls, I will win. If he folds, I will win. \n- If GoodGuy holds a Jack, he is likely to raise (70%) or call (30%). If he raises, I will lose. If he calls, I will lose. \n\nWinning/Lose Payoffs for Each Plan:\n- Plan 1: If I win, the winning payoff would be 4 chips. If I lose, the lose payoff would be 4 chips. \n- Plan 2: If I fold, I will lose 4 chips. \n- Plan 3: If I win, the winning payoff would be 4 chips. If I lose, the lose payoff would be 4 chips. \n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.3 * 4 - 0.7 * 4 = -1.6 chips\n- Plan 2: Expected Chips Gain = -4 chips\n- Plan 3: Expected Chips Gain = 0.3 * 4 - 0.7 * 4 = -1.6 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 have the same expected chips gain, which is higher than Plan 2. Therefore, I should either raise or check. Considering my aggressive strategy and the potential to confuse GoodGuy, I will choose to raise (Plan 1)."}}
{"message": "", "21_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (50% probability), he will likely raise (60%) or call (40%). If he raises, I will lose unless the public card is a Queen. If he calls, I will win unless the public card is a King. So, the winning rate is 40%, losing rate is 50%, and draw rate is 10%.\n- If GoodGuy holds a Queen (50% probability), he will likely call (70%) or raise (30%). If he calls, it will be a draw unless the public card is a King or Jack. If he raises, I will lose unless the public card is a Queen. So, the winning rate is 15%, losing rate is 35%, and draw rate is 50%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (50% probability), he will likely raise (60%) or call (40%). If he raises, I will lose unless the public card is a Queen. If he calls, I will win unless the public card is a King. So, the winning rate is 40%, losing rate is 50%, and draw rate is 10%.\n- If GoodGuy holds a Queen (50% probability), he will likely call (70%) or fold (30%). If he calls, it will be a draw unless the public card is a King or Jack. If he folds, I will win. So, the winning rate is 45%, losing rate is 25%, and draw rate is 30%.\n\nPlan 3: Fold\n- If I fold, I will lose the 1 chip I have already put in the pot. So, the winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 3 chips. If lose, the lose payoff would be 1 chip.\n- Plan 2: If win, the winning payoff would be 5 chips. If lose, the lose payoff would be 3 chips.\n- Plan 3: If lose, the lose payoff would be 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.4*3 - 0.5*1 = 0.7 chips\n- Plan 2: Expected Chips Gain = 0.45*5 - 0.25*3 = 1.5 chips\n- Plan 3: Expected Chips Gain = 0 - 1 = -1 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I will choose this plan."}}
{"message": "", "21_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (40% probability), he will likely raise (80% probability) or call (20% probability). If he raises, I will lose (probability = 0.4 * 0.8 = 0.32). If he calls, I have a chance to win if the next public card is a Queen (probability = 0.4 * 0.2 * 0.33 = 0.0264). \n- If GoodGuy holds a Queen (30% probability), he will likely call (40% probability) or fold (60% probability). If he calls, I will win if the next public card is a Queen (probability = 0.3 * 0.4 * 0.33 = 0.0396). If he folds, I will win (probability = 0.3 * 0.6 = 0.18).\n- If GoodGuy holds a Jack (30% probability), he will likely fold (70% probability) or call (30% probability). If he folds, I will win (probability = 0.3 * 0.7 = 0.21). If he calls, I will win if the next public card is not a Jack (probability = 0.3 * 0.3 * 0.67 = 0.0603).\n\nPlan 2: Fold\n- If I fold, I will lose the current pot. The lose rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (40% probability), he will likely raise (80% probability) or check (20% probability). If he raises, I will lose (probability = 0.4 * 0.8 = 0.32). If he checks, I have a chance to win if the next public card is a Queen (probability = 0.4 * 0.2 * 0.33 = 0.0264).\n- If GoodGuy holds a Queen (30% probability), he will likely check (60% probability) or raise (40% probability). If he checks, I will win if the next public card is a Queen (probability = 0.3 * 0.6 * 0.33 = 0.0594). If he raises, I will lose (probability = 0.3 * 0.4 = 0.12).\n- If GoodGuy holds a Jack (30% probability), he will likely check (70% probability) or raise (30% probability). If he checks, I will win if the next public card is not a Jack (probability = 0.3 * 0.7 * 0.67 = 0.1407). If he raises, I will lose (probability = 0.3 * 0.3 = 0.09).\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, Chips in the pot: 8. If win, the winning payoff would be 4. If lose, the lose payoff would be 4.\n- Plan 2: After the action, Chips in the pot: 4. If lose, the lose payoff would be 2.\n- Plan 3: After the action, Chips in the pot: 4. If win, the winning payoff would be 2. If lose, the lose payoff would be 2.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.5267 * 4 - 0.32 * 4 = 0.8268\n- Plan 2: Expected Chips Gain = 0 - 1 * 2 = -2\n- Plan 3: Expected Chips Gain = 0.2265 * 2 - 0.53 * 2 = -0.606\n\nPlan Selection:\n- Plan 1: 0.8268\n- Plan 2: -2\n- Plan 3: -0.606\n\nBased on the above analysis, I should choose Plan 1 (Raise) as it has the highest expected chips gain."}}
{"message": "", "22_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a Queen (60% probability), he is likely to raise (40%) or call (60%) in the second round. If he raises, I will lose (probability = 60% * 40% = 24%). If he calls, I will win (probability = 60% * 60% = 36%).\n- If GoodGuy holds a Jack (40% probability), he is likely to raise (50%) or call (50%) in the second round. If he raises, I will lose (probability = 40% * 50% = 20%). If he calls, I will win (probability = 40% * 50% = 20%).\n- Overall, the winning rate for plan 1 is 56%, the losing rate is 44%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a Queen (60% probability), he is likely to fold (70%) or call (30%) in the second round. If he folds, I will win (probability = 60% * 70% = 42%). If he calls, I will lose (probability = 60% * 30% = 18%).\n- If GoodGuy holds a Jack (40% probability), he is likely to fold (80%) or call (20%) in the second round. If he folds, I will win (probability = 40% * 80% = 32%). If he calls, I will lose (probability = 40% * 20% = 8%).\n- Overall, the winning rate for plan 2 is 74%, the losing rate is 26%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose 100% of the time.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, Chips in the pot: 6. If win, the winning payoff would be 3. If lose, the lose payoff would be 3.\n- Plan 2: After the action, Chips in the pot: 10. If win, the winning payoff would be 5. If lose, the lose payoff would be 5.\n- Plan 3: After the action, Chips in the pot: 6. If lose, the lose payoff would be 3.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = winning rate * Winning Payoff - lose rate * Lose Payoff = 56% * 3 - 44% * 3 = 0.36\n- Plan 2: Expected Chips Gain = winning rate * Winning Payoff - lose rate * Lose Payoff = 74% * 5 - 26% * 5 = 2.4\n- Plan 3: Expected Chips Gain = -100% * 3 = -3\n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 2 > Plan 1 > Plan 3.\n- Therefore, the plan with the highest estimated expected chips gain is Plan 2: Raise."}}
{"message": "", "22_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (44.44% probability), he will likely call (40% probability). In this case, we will draw as we both have a King. The overall draw rate for this scenario is 44.44% * 40% = 17.78%.\n- If GoodGuy holds a Queen (33.33% probability), he will likely fold (70% probability) as his Queen matches the public card. In this case, I will win. The overall win rate for this scenario is 33.33% * 70% = 23.33%.\n- If GoodGuy holds a Jack (22.22% probability), he will likely fold (80% probability) as his Jack does not match the public card. In this case, I will win. The overall win rate for this scenario is 22.22% * 80% = 17.78%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. The overall lose rate for this scenario is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (44.44% probability), he will likely call (40% probability). In this case, we will draw as we both have a King. The overall draw rate for this scenario is 44.44% * 40% = 17.78%.\n- If GoodGuy holds a Queen (33.33% probability), he will likely call (30% probability) as his Queen matches the public card. In this case, I will lose. The overall lose rate for this scenario is 33.33% * 30% = 10%.\n- If GoodGuy holds a Jack (22.22% probability), he will likely fold (80% probability) as his Jack does not match the public card. In this case, I will win. The overall win rate for this scenario is 22.22% * 80% = 17.78%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the pot (6 chips) = 3 chips. If I lose, the lose payoff would be half of the pot (6 chips) = 3 chips.\n- Plan 2: If I fold, I will lose my current bet in the pot (6 chips).\n- Plan 3: If I win, the winning payoff would be half of the pot (6 chips) = 3 chips. If I lose, the lose payoff would be half of the pot (6 chips) = 3 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Lose rate * Lose Payoff = 41.11% * 3 chips - 0% * 3 chips = 1.23 chips\n- Plan 2: Expected Chips Gain = 0% * 3 chips - 100% * 6 chips = -6 chips\n- Plan 3: Expected Chips Gain = 35.56% * 3 chips - 10% * 3 chips = 0.77 chips\n\nPlan Selection:\n- Plan 1: 1.23 chips\n- Plan 2: -6 chips\n- Plan 3: 0.77 chips\n\nBased on the expected chips gain, the best plan would be Plan 1 (Raise), followed by Plan 3 (Check), and lastly Plan 2 (Fold)."}}
{"message": "", "23_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (60% probability), he might raise (60%) or call (40%). If he raises, I will lose unless the public card is a Queen. If he calls, I will win if the public card is a Queen, and lose if it's a Jack. The overall winning rate is 24% (60%*40%), losing rate is 36% (60%*60%), and draw rate is 0%.\n- If GoodGuy holds a Queen (25% probability), he might raise (50%) or call (50%). If he raises, it will be a draw. If he calls, I will win if the public card is a Jack, and lose if it's a King. The overall winning rate is 12.5% (25%*50%), losing rate is 12.5% (25%*50%), and draw rate is 12.5% (25%*50%).\n- If GoodGuy holds a Jack (40% probability), he might raise (40%) or call (60%). If he raises, I will win unless the public card is a King. If he calls, I will win if the public card is a Queen, and lose if it's a King. The overall winning rate is 24% (40%*60%), losing rate is 16% (40%*40%), and draw rate is 0%.\n\nPlan 1 overall Winning/Lose/Draw rates: Winning rate is 60.5%, losing rate is 65%, and draw rate is 12.5%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (60% probability), he might fold (70%) or call (30%). If he folds, I will win. If he calls, I will lose unless the public card is a Queen. The overall winning rate is 42% (60%*70%), losing rate is 18% (60%*30%), and draw rate is 0%.\n- If GoodGuy holds a Queen (25% probability), he might fold (60%) or call (40%). If he folds, I will win. If he calls, it will be a draw. The overall winning rate is 15% (25%*60%), losing rate is 0%, and draw rate is 10% (25%*40%).\n- If GoodGuy holds a Jack (40% probability), he might fold (80%) or call (20%). If he folds, I will win. If he calls, I will win unless the public card is a King. The overall winning rate is 32% (40%*80%), losing rate is 8% (40%*20%), and draw rate is 0%.\n\nPlan 2 overall Winning/Lose/Draw rates: Winning rate is 89%, losing rate is 26%, and draw rate is 10%.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card. The overall winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, chips in the pot: 4. If win, the winning payoff would be 2. If lose, the lose payoff would be 2.\n- Plan 2: After the action, chips in the pot: 6. If win, the winning payoff would be 3. If lose, the lose payoff would be 3.\n- Plan 3: After the action, chips in the pot: 3. If lose, the lose payoff would be 1.5.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 60.5% * 2 - 65% * 2 = -0.09\n- Plan 2: 89% * 3 - 26% * 3 = 1.89\n- Plan 3: 0 - 100% * 1.5 = -1.5\n\nPlan Selection:\n- Plan 2 (Raise) has the highest estimated expected chips gain, so it should be selected. Plan 1 (Call) is the second best, and Plan 3 (Fold) is the worst."}}
{"message": "", "23_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (40% probability), he will likely raise (80%) or call (20%). If he raises, I will lose (as his King matches the public card). If he calls, I have a chance to win if the next public card matches my Queen. Overall, my winning rate is 4% (20% * 20%), losing rate is 36% (40% * 90%), and draw rate is 0%.\n- If GoodGuy holds a Queen (30% probability), he will likely fold (60%) or check (40%). If he folds, I will win. If he checks, I have a chance to win if the next public card matches my Queen. Overall, my winning rate is 24% (30% * 80%), losing rate is 6% (30% * 20%), and draw rate is 0%.\n- If GoodGuy holds a Jack (30% probability), he will likely fold (80%) or check (20%). If he folds, I will win. If he checks, I have a chance to win if the next public card matches my Queen. Overall, my winning rate is 24% (30% * 80%), losing rate is 6% (30% * 20%), and draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose the chips in the pot. My winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King (40% probability), he will likely raise (80%) or call (20%). If he raises, I will lose (as his King matches the public card). If he calls, I have a chance to win if the next public card matches my Queen. Overall, my winning rate is 4% (20% * 20%), losing rate is 36% (40% * 90%), and draw rate is 0%.\n- If GoodGuy holds a Queen (30% probability), he will likely fold (60%) or check (40%). If he folds, I will win. If he checks, I have a chance to win if the next public card matches my Queen. Overall, my winning rate is 24% (30% * 80%), losing rate is 6% (30% * 20%), and draw rate is 0%.\n- If GoodGuy holds a Jack (30% probability), he will likely fold (80%) or check (20%). If he folds, I will win. If he checks, I have a chance to win if the next public card matches my Queen. Overall, my winning rate is 24% (30% * 80%), losing rate is 6% (30% * 20%), and draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips (half of the pot). If I lose, the lose payoff would be 4 chips.\n- Plan 2: If I fold, I will lose 4 chips.\n- Plan 3: If I win, the winning payoff would be 4 chips. If I lose, the lose payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected gain = 52% * 4 - 48% * 4 = 0.16 chips\n- Plan 2: Expected gain = -4 chips\n- Plan 3: Expected gain = 52% * 4 - 48% * 4 = 0.16 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 have the highest expected chips gain, so I should choose one of these two plans. Considering the strategy improvement, I should choose Plan 1 (raise) to confuse GoodGuy and potentially make him fold."}}
{"message": "", "24_1": {"plan": "Plan 1: Call\nIf I call, I will match GoodGuy's bet of 4 chips, making the total pot 10 chips. \n\nPlan 2: Raise\nIf I raise, I will increase the bet by 4 chips, making the total pot 14 chips. \n\nPlan 3: Fold\nIf I fold, I will forfeit the game and lose any chips I have already put in the pot. \n\nPotential GoodGuy's actions (if release) and Estimate Winning/Lose/Draw Rate for Each Plan:\n\nPlan 1: Call\nIf GoodGuy holds a King (70% probability), he will likely raise (80% probability), leading to a win rate of 56% (0.7*0.8). If he holds a Jack (30% probability), he will likely call (50% probability), leading to a win rate of 15% (0.3*0.5). The overall win rate for this plan is 71% (56%+15%).\n\nPlan 2: Raise\nIf GoodGuy holds a King (70% probability), he will likely raise (80% probability), leading to a win rate of 56% (0.7*0.8). If he holds a Jack (30% probability), he will likely fold (50% probability), leading to a win rate of 15% (0.3*0.5). The overall win rate for this plan is 71% (56%+15%).\n\nPlan 3: Fold\nIf I fold, I will lose the game, leading to a win rate of 0%.\n\nThe number of winning and lose payoffs for each plan:\n\nPlan 1: Call\nIf I win, the winning payoff would be 5 chips (half of the pot). If I lose, the losing payoff would be 4 chips (the amount I put in the pot).\n\nPlan 2: Raise\nIf I win, the winning payoff would be 7 chips (half of the pot). If I lose, the losing payoff would be 6 chips (the amount I put in the pot).\n\nPlan 3: Fold\nIf I fold, I will lose 2 chips (the amount I put in the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n\nPlan 1: Call\nThe expected chips gain for this plan is 35.5 chips (71% * 5 chips - 29% * 4 chips).\n\nPlan 2: Raise\nThe expected chips gain for this plan is 49.7 chips (71% * 7 chips - 29% * 6 chips).\n\nPlan 3: Fold\nThe expected chips gain for this plan is -2 chips (0% * 0 chips - 100% * 2 chips).\n\nPlan Selection:\nBased on the estimated expected chips gains, the ranking of the plans is as follows: Plan 2 > Plan 1 > Plan 3. Therefore, I should choose Plan 2: Raise."}}
{"message": "", "24_3": {"plan": "Plan 1: Raise\nIf I raise, I will put 8 more chips into the pot, making the total pot 20 chips. \n\nThe winning/lose/draw rates when GoodGuy holds a Queen: \nBased on GoodGuy's behaviour pattern, in the second round, if GoodGuy holds a Queen (70% probability) and sees my raise, he will call (30% probability) or raise (70% probability). If he calls, we will both have a pair of Queens and it will be a draw. If he raises, it will still be a draw. Therefore, the overall winning rate is 0%, the lose rate is 0%, and the draw rate is 100%.\n\nThe winning/lose/draw rates when GoodGuy holds a King: \nIf GoodGuy holds a King (30% probability) and sees my raise, he will check (50% probability) or fold (50% probability). If he checks, I will win because a pair of Queens is higher than a King. If he folds, I will also win. Therefore, the overall winning rate is 100%, the lose rate is 0%, and the draw rate is 0%.\n\nPlan1 overall board_game_expert's Winning/Lose/Draw rates: \nThe Winning rate for plan 1 is 30% (100% * 30%), the Lose rate for plan 1 is 0%, and the Draw rate for plan 1 is 70% (100% * 70%).\n\nPlan 2: Check\nIf I check, the total pot remains 12 chips. \n\nThe winning/lose/draw rates when GoodGuy holds a Queen: \nIf GoodGuy holds a Queen (70% probability) and sees my check, he will call (30% probability) or raise (70% probability). If he calls or raises, it will be a draw. Therefore, the overall winning rate is 0%, the lose rate is 0%, and the draw rate is 100%.\n\nThe winning/lose/draw rates when GoodGuy holds a King: \nIf GoodGuy holds a King (30% probability) and sees my check, he will check (50% probability) or fold (50% probability). If he checks or folds, I will win. Therefore, the overall winning rate is 100%, the lose rate is 0%, and the draw rate is 0%.\n\nPlan2 overall board_game_expert's Winning/Lose/Draw rates: \nThe Winning rate for plan 2 is 30% (100% * 30%), the Lose rate for plan 2 is 0%, and the Draw rate for plan 2 is 70% (100% * 70%).\n\nPlan 3: Fold\nIf I fold, I will lose the 6 chips I have put into the pot. The winning rate is 0%, the lose rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan: \nPlan1: After the raise, the pot will be 20 chips. If win, the winning payoff would be 10 chips. If lose, the lose payoff would be 10 chips. \nPlan2: After the check, the pot will remain 12 chips. If win, the winning payoff would be 6 chips. If lose, the lose payoff would be 6 chips. \nPlan3: If I fold, I will lose the 6 chips I have put into the pot.\n\nEstimate Expected Chips Gain for Each Plan: \nPlan1: The expected chips gain is 30% * 10 - 0% * 10 = 3 chips.\nPlan2: The expected chips gain is 30% * 6 - 0% * 6 = 1.8 chips.\nPlan3: The expected chips gain is -6 chips.\n\nPlan Selection: \nThe rank of estimated expected chips gains for every plan is: Plan1 > Plan2 > Plan3. Therefore, I should choose Plan1: Raise."}}
{"message": "", "25_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King, he will likely raise (70%) or call (30%). If he raises, I will lose unless the public card is a Queen. If he calls, I will win unless the public card is a King. The overall winning rate is 30%, losing rate is 70%, and draw rate is 0%.\n- If GoodGuy holds a Queen, he will likely call (60%) or raise (40%). If he raises, it will be a draw unless the public card is a King or Jack. If he calls, it will be a draw unless the public card is a King or Jack. The overall winning rate is 0%, losing rate is 40%, and draw rate is 60%.\n- If GoodGuy holds a Jack, he will likely call (50%) or raise (50%). If he raises, I will win unless the public card is a King. If he calls, I will win unless the public card is a King. The overall winning rate is 50%, losing rate is 50%, and draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King, he will likely fold (60%) or call (40%). If he folds, I will win. If he calls, I will lose unless the public card is a Queen. The overall winning rate is 60%, losing rate is 40%, and draw rate is 0%.\n- If GoodGuy holds a Queen, he will likely fold (70%) or call (30%). If he folds, I will win. If he calls, it will be a draw unless the public card is a King or Jack. The overall winning rate is 70%, losing rate is 30%, and draw rate is 0%.\n- If GoodGuy holds a Jack, he will likely fold (80%) or call (20%). If he folds, I will win. If he calls, I will win unless the public card is a King. The overall winning rate is 80%, losing rate is 20%, and draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. The overall winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 3 chips. If lose, the lose payoff would be 1 chip.\n- Plan 2: If win, the winning payoff would be 5 chips. If lose, the lose payoff would be 2 chips.\n- Plan 3: If lose, the lose payoff would be 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: (0.3 * 3) - (0.7 * 1) = -0.1 chips\n- Plan 2: (0.7 * 5) - (0.3 * 2) = 2.9 chips\n- Plan 3: -1 chips\n\nPlan Selection:\n- Plan 2 has the highest estimated expected chips gain, so I will choose to raise."}}
{"message": "", "25_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (40% chance), he will likely fold (60% chance) or call (40% chance). If he folds, I win. If he calls, I lose. So, the winning rate is 24% (40% * 60%), and the losing rate is 16% (40% * 40%).\n- If GoodGuy holds a Queen (50% chance), he will likely fold (70% chance) or call (30% chance). If he folds, I win. If he calls, it's a draw. So, the winning rate is 35% (50% * 70%), and the draw rate is 15% (50% * 30%).\n- If GoodGuy holds a Jack (10% chance), he will likely call (100% chance), and I lose. So, the losing rate is 10% (10% * 100%).\n\nPlan 1 overall Winning/Lose/Draw rates: Winning rate is 59% (24% + 35%), Lose rate is 26% (16% + 10%), Draw rate is 15%.\n\nPlan 2: Fold\n- If I fold, I lose regardless of what card GoodGuy holds. So, the losing rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (40% chance), he will likely fold (60% chance) or call (40% chance). If he folds, I win. If he calls, I lose. So, the winning rate is 24% (40% * 60%), and the losing rate is 16% (40% * 40%).\n- If GoodGuy holds a Queen (50% chance), he will likely fold (70% chance) or call (30% chance). If he folds, I win. If he calls, it's a draw. So, the winning rate is 35% (50% * 70%), and the draw rate is 15% (50% * 30%).\n- If GoodGuy holds a Jack (10% chance), he will likely call (100% chance), and I lose. So, the losing rate is 10% (10% * 100%).\n\nPlan 3 overall Winning/Lose/Draw rates: Winning rate is 59% (24% + 35%), Lose rate is 26% (16% + 10%), Draw rate is 15%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips (half of the pot). If I lose, the losing payoff would be 4 chips.\n- Plan 2: If I lose, the losing payoff would be 4 chips.\n- Plan 3: If I win, the winning payoff would be 4 chips. If I lose, the losing payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 59% * 4 - 26% * 4 = 1.32 chips\n- Plan 2: Expected Chips Gain = 0% * 4 - 100% * 4 = -4 chips\n- Plan 3: Expected Chips Gain = 59% * 4 - 26% * 4 = 1.32 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 have the highest expected chips gain (1.32 chips), while Plan 2 has the lowest expected chips gain (-4 chips). Therefore, I should either raise (Plan 1) or check (Plan 3). Considering my strategy improvement, I should mix in some checks to make my actions less predictable. Therefore, I choose Plan 3: Check."}}
{"message": "", "26_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (64% probability), he might raise (70% probability) or call (30% probability). If he raises, I will lose (probability = 64% * 70% = 44.8%). If he calls, it will be a draw (probability = 64% * 30% = 19.2%).\n- If GoodGuy holds a Queen (36% probability), he might raise (40% probability) or call (60% probability). If he raises, I will lose (probability = 36% * 40% = 14.4%). If he calls, it will be a draw (probability = 36% * 60% = 21.6%).\n\nPlan 1 overall Winning/Lose/Draw rates: \n- Winning rate: 0%\n- Lose rate: 59.2% (44.8% + 14.4%)\n- Draw rate: 40.8% (19.2% + 21.6%)\n\nPlan 2: Raise\n- If GoodGuy holds a King (64% probability), he might raise (70% probability) or call (30% probability). If he raises, I will lose (probability = 64% * 70% = 44.8%). If he calls, it will be a draw (probability = 64% * 30% = 19.2%).\n- If GoodGuy holds a Queen (36% probability), he might raise (40% probability) or call (60% probability). If he raises, I will lose (probability = 36% * 40% = 14.4%). If he calls, it will be a draw (probability = 36% * 60% = 21.6%).\n\nPlan 2 overall Winning/Lose/Draw rates: \n- Winning rate: 0%\n- Lose rate: 59.2% (44.8% + 14.4%)\n- Draw rate: 40.8% (19.2% + 21.6%)\n\nPlan 3: Fold\n- If I fold, I will lose 100% of the time.\n\nPlan 3 overall Winning/Lose/Draw rates: \n- Winning rate: 0%\n- Lose rate: 100%\n- Draw rate: 0%\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, Chips in the pot: 6. If win, the winning payoff would be 3. If lose, the lose payoff would be 3.\n- Plan 2: After the action, Chips in the pot: 10. If win, the winning payoff would be 5. If lose, the lose payoff would be 5.\n- Plan 3: After the action, Chips in the pot: 4. If lose, the lose payoff would be 2.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0 * 3 - 59.2% * 3 = -1.776\n- Plan 2: 0 * 5 - 59.2% * 5 = -2.96\n- Plan 3: 0 * 2 - 100% * 2 = -2\n\nPlan Selection:\n- Plan 1: -1.776\n- Plan 2: -2.96\n- Plan 3: -2\n\nThe rank of estimated expected chips gains for every plan is Plan 1 > Plan 3 > Plan 2. Therefore, I should choose Plan 1: Call."}}
{"message": "", "26_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (40% probability), he might call (60%) or fold (40%). If he calls, I would lose (as King is higher than Jack). If he folds, I would win. So, the winning rate is 40%*40%=16%, and the losing rate is 40%*60%=24%.\n- If GoodGuy holds a Queen (20% probability), he might call (80%) or raise (20%). If he calls or raises, it would be a draw (as Queen is the public card). So, the draw rate is 20%*100%=20%.\n- If GoodGuy holds a Jack (35% probability), he might fold (70%) or call (30%). If he folds, I would win. If he calls, it would be a draw (as we both hold Jack). So, the winning rate is 35%*70%=24.5%, and the draw rate is 35%*30%=10.5%.\n\nPlan 2: Fold\n- If I fold, I would lose regardless of GoodGuy's card. So, the losing rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (40% probability), he might call (60%) or fold (40%). If he calls, I would lose (as King is higher than Jack). If he folds, I would win. So, the winning rate is 40%*40%=16%, and the losing rate is 40%*60%=24%.\n- If GoodGuy holds a Queen (20% probability), he might call (80%) or raise (20%). If he calls or raises, it would be a draw (as Queen is the public card). So, the draw rate is 20%*100%=20%.\n- If GoodGuy holds a Jack (35% probability), he might fold (70%) or call (30%). If he folds, I would win. If he calls, it would be a draw (as we both hold Jack). So, the winning rate is 35%*70%=24.5%, and the draw rate is 35%*30%=10.5%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the pot (4 chips). If I lose, the losing payoff would be half of the pot (4 chips).\n- Plan 2: If I lose, the losing payoff would be half of the pot (4 chips).\n- Plan 3: If I win, the winning payoff would be half of the pot (4 chips). If I lose, the losing payoff would be half of the pot (4 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = winning rate * Winning Payoff - losing rate * Losing Payoff = 40.5% * 4 - 24% * 4 = 0.66 chips\n- Plan 2: Expected Chips Gain = -100% * 4 = -4 chips\n- Plan 3: Expected Chips Gain = 40.5% * 4 - 24% * 4 = 0.66 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 have the highest expected chips gain (0.66 chips), and Plan 2 has the lowest expected chips gain (-4 chips). Therefore, I should either raise (Plan 1) or check (Plan 3). Considering my strategy improvement, I should be more cautious when bluffing, especially when the public card is higher than my card. Therefore, I would choose Plan 3: Check."}}
{"message": "", "27_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (80% probability), he will likely raise (80% probability). If the public card is a King, I will lose (probability 1/5). If the public card is a Queen, I will win (probability 1/5). If the public card is a Jack, I will lose (probability 1/5). \n- If GoodGuy holds a Queen (20% probability), he will likely call (60% probability). If the public card is a Queen, it will be a draw (probability 1/5). If the public card is a King or a Jack, I will win (probability 2/5).\n- Overall, the winning rate for plan 1 is (0.8*0.8*1/5) + (0.2*0.6*2/5) = 0.32. The losing rate for plan 1 is (0.8*0.8*2/5) = 0.32. The draw rate for plan 1 is (0.2*0.6*1/5) = 0.024.\n\nPlan 2: Raise\n- If GoodGuy holds a King (80% probability), he will likely call (20% probability). If the public card is a King, I will lose (probability 1/5). If the public card is a Queen, I will win (probability 1/5). If the public card is a Jack, I will lose (probability 1/5). \n- If GoodGuy holds a Queen (20% probability), he will likely raise (40% probability). If the public card is a Queen, it will be a draw (probability 1/5). If the public card is a King or a Jack, I will win (probability 2/5).\n- Overall, the winning rate for plan 2 is (0.8*0.2*1/5) + (0.2*0.4*2/5) = 0.08. The losing rate for plan 2 is (0.8*0.2*2/5) = 0.16. The draw rate for plan 2 is (0.2*0.4*1/5) = 0.016.\n\nPlan 3: Fold\n- If I fold, I will lose the game. The losing rate for plan 3 is 1.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 4 chips. If lose, the lose payoff would be 4 chips.\n- Plan 2: If win, the winning payoff would be 8 chips. If lose, the lose payoff would be 8 chips.\n- Plan 3: If lose, the lose payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.32 * 4 - 0.32 * 4 = 0\n- Plan 2: Expected Chips Gain = 0.08 * 8 - 0.16 * 8 = -0.64\n- Plan 3: Expected Chips Gain = -1 * 2 = -2\n\nPlan Selection:\n- Plan 1: 0\n- Plan 2: -0.64\n- Plan 3: -2\n\nBased on the estimated expected chips gains, I should select Plan 1 (Call), which has the highest expected chips gain."}}
{"message": "", "27_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (10% probability), he will likely fold if I raise (70% probability). This results in a win for me. If he calls (20% probability), it results in a loss for me. If he checks (10% probability), it results in a win for me. Overall, the winning rate for this card is 80%, the losing rate is 20%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (10% probability), he will likely call if I raise (90% probability). This results in a draw for me. If he checks (10% probability), it results in a win for me. Overall, the winning rate for this card is 10%, the losing rate is 0%, and the draw rate is 90%.\n- If GoodGuy holds a Jack (80% probability), he will likely fold if I raise (70% probability). This results in a win for me. If he calls (20% probability), it results in a win for me. If he checks (10% probability), it results in a win for me. Overall, the winning rate for this card is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 1 overall Winning/Lose/Draw rates: Winning rate is 90%, Lose rate is 4%, Draw rate is 6%.\n\nPlan 2: Fold\n- If I fold, I automatically lose regardless of GoodGuy's card. Therefore, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King (10% probability), he will likely check if I check (10% probability). This results in a loss for me. If he raises (80% probability), it results in a loss for me. If he calls (10% probability), it results in a loss for me. Overall, the winning rate for this card is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (10% probability), he will likely check if I check (10% probability). This results in a draw for me. If he raises (80% probability), it results in a draw for me. If he calls (10% probability), it results in a draw for me. Overall, the winning rate for this card is 0%, the losing rate is 0%, and the draw rate is 100%.\n- If GoodGuy holds a Jack (80% probability), he will likely check if I check (10% probability). This results in a win for me. If he raises (80% probability), it results in a win for me. If he calls (10% probability), it results in a win for me. Overall, the winning rate for this card is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 3 overall Winning/Lose/Draw rates: Winning rate is 80%, Lose rate is 10%, Draw rate is 10%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips. If I lose, the losing payoff would be 4 chips.\n- Plan 2: If I fold, I automatically lose 4 chips.\n- Plan 3: If I win, the winning payoff would be 4 chips. If I lose, the losing payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.9 * 4 - 0.04 * 4 = 3.44 chips\n- Plan 2: Expected Chips Gain = 0 - 1 * 4 = -4 chips\n- Plan 3: Expected Chips Gain = 0.8 * 4 - 0.1 * 4 = 2.8 chips\n\nPlan Selection:\n- Plan 1: 3.44 chips\n- Plan 2: -4 chips\n- Plan 3: 2.8 chips\n\nTherefore, I should select Plan 1 (Raise) as it has the highest estimated expected chips gain."}}
{"message": "", "28_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he will likely raise (80% probability) or call (20% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. Therefore, the winning rate is 20%, the losing rate is 56%, and the draw rate is 24%.\n- If GoodGuy holds a Queen (30% probability), he will likely call (60% probability) or fold (40% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I will win. Therefore, the winning rate is 18%, the losing rate is 12%, and the draw rate is 0%.\n\nPlan 1 overall Winning/Lose/Draw rates: Winning rate is 38%, Losing rate is 68%, Draw rate is 24%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (70% probability), he will likely call (60% probability) or fold (40% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. Therefore, the winning rate is 28%, the losing rate is 42%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (30% probability), he will likely fold (70% probability) or call (30% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I will win. Therefore, the winning rate is 21%, the losing rate is 9%, and the draw rate is 0%.\n\nPlan 2 overall Winning/Lose/Draw rates: Winning rate is 49%, Losing rate is 51%, Draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot. Therefore, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 3 chips. If lose, the lose payoff would be 2 chips.\n- Plan 2: If win, the winning payoff would be 7 chips. If lose, the lose payoff would be 4 chips.\n- Plan 3: If lose, the lose payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 38% * 3 - 68% * 2 = -0.44 chips\n- Plan 2: Expected Chips Gain = 49% * 7 - 51% * 4 = 0.93 chips\n- Plan 3: Expected Chips Gain = -100% * 2 = -2 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest estimated expected chips gain, followed by Plan 1 (Call), and then Plan 3 (Fold). Therefore, I should choose Plan 2 (Raise)."}}
{"message": "", "28_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (50% probability), he will likely raise (50% probability) or fold (50% probability). If he raises, I will lose (100% probability). If he folds, I will win (100% probability). Overall, the winning rate is 25%, the losing rate is 25%, and the draw rate is 0%.\n- If GoodGuy holds a King (50% probability), he will likely fold (100% probability). Therefore, the winning rate is 50%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of GoodGuy's card. Therefore, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a Queen (50% probability), he will likely check (100% probability). Therefore, I will lose (100% probability). Overall, the winning rate is 0%, the losing rate is 50%, and the draw rate is 0%.\n- If GoodGuy holds a King (50% probability), he will likely check (100% probability). Therefore, I will lose (100% probability). Overall, the winning rate is 0%, the losing rate is 50%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, chips in the pot: 16. If win, the winning payoff would be 8. If lose, the lose payoff would be 8.\n- Plan 2: After the action, chips in the pot: 12. If lose, the lose payoff would be 6.\n- Plan 3: After the action, chips in the pot: 12. If lose, the lose payoff would be 6.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: (25% * 8) - (25% * 8) = 0\n- Plan 2: 0 - (100% * 6) = -6\n- Plan 3: 0 - (100% * 6) = -6\n\nPlan Selection:\n- Plan 1: 0\n- Plan 2: -6\n- Plan 3: -6\n\nBased on the estimated expected chips gain, Plan 1 (Raise) is the best strategy to use in this situation."}}
{"message": "", "29_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (50% probability), he will likely raise (70%) or call (30%). If he raises, I will lose (100%) as King is higher than Jack. If he calls, the outcome will depend on the public card. If the public card is a Jack, I will win (100%). If the public card is a King or Queen, I will lose (100%). Overall, the winning rate is 15% (50% * 30% * 100%), the losing rate is 85% (50% * 70% * 100% + 50% * 30% * 100%).\n- If GoodGuy holds a Queen (50% probability), he will likely raise (40%) or call (60%). If he raises, I will lose (100%) as Queen is higher than Jack. If he calls, the outcome will depend on the public card. If the public card is a Jack, I will win (100%). If the public card is a Queen or King, I will lose (100%). Overall, the winning rate is 30% (50% * 60% * 100%), the losing rate is 70% (50% * 40% * 100% + 50% * 60% * 100%).\n- The overall winning rate for Plan 1 is 22.5% (15% + 30%), the overall losing rate is 77.5% (85% + 70%), and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (50% probability), he will likely raise (70%) or call (30%). If he raises, I will lose (100%) as King is higher than Jack. If he calls, the outcome will depend on the public card. If the public card is a Jack, I will win (100%). If the public card is a King or Queen, I will lose (100%). Overall, the winning rate is 15% (50% * 30% * 100%), the losing rate is 85% (50% * 70% * 100% + 50% * 30% * 100%).\n- If GoodGuy holds a Queen (50% probability), he will likely raise (40%) or call (60%). If he raises, I will lose (100%) as Queen is higher than Jack. If he calls, the outcome will depend on the public card. If the public card is a Jack, I will win (100%). If the public card is a Queen or King, I will lose (100%). Overall, the winning rate is 30% (50% * 60% * 100%), the losing rate is 70% (50% * 40% * 100% + 50% * 60% * 100%).\n- The overall winning rate for Plan 2 is 22.5% (15% + 30%), the overall losing rate is 77.5% (85% + 70%), and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot. The overall losing rate is 100%, and the winning and draw rates are 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips (half of the pot). If I lose, the losing payoff would be 1 chip (the chip I have already put in the pot).\n- Plan 2: If I win, the winning payoff would be 5 chips (half of the pot). If I lose, the losing payoff would be 3 chips (the chips I have already put in the pot).\n- Plan 3: If I lose, the losing payoff would be 1 chip (the chip I have already put in the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is 22.5% * 3 - 77.5% * 1 = -0.525 chips.\n- Plan 2: The expected chips gain is 22.5% * 5 - 77.5% * 3 = -1.125 chips.\n- Plan 3: The expected chips gain is -1 chip.\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain (-0.525 chips), followed by Plan 3 (-1 chip), and Plan 2 (-1.125 chips). Therefore, I should choose Plan 1: Call."}}
{"message": "", "29_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (60% probability), he will likely raise (80% probability) or call (20% probability). If he raises, I will lose as his pair of Queens beats my single Jack. If he calls, it will be a draw as we both have the same amount of chips in the pot. The overall winning rate for this plan is 0%, the losing rate is 48% (60% * 80%), and the draw rate is 12% (60% * 20%).\n- If GoodGuy holds a Jack (40% probability), he will likely fold (60% probability) or call (40% probability). If he folds, I will win as he forfeits his chips. If he calls, it will be a draw as we both have the same amount of chips in the pot. The overall winning rate for this plan is 24% (40% * 60%), the losing rate is 0%, and the draw rate is 16% (40% * 40%).\n\nPlan 2: Fold\n- If GoodGuy holds a Queen (60% probability), he will likely raise (80% probability) or call (20% probability). If I fold, I will lose regardless of his action. The overall winning rate for this plan is 0%, the losing rate is 60%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (40% probability), he will likely fold (60% probability) or call (40% probability). If I fold, I will lose regardless of his action. The overall winning rate for this plan is 0%, the losing rate is 40%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a Queen (60% probability), he will likely check (70% probability) or fold (30% probability). If he checks, it will be a draw as we both have the same amount of chips in the pot. If he folds, I will win as he forfeits his chips. The overall winning rate for this plan is 18% (60% * 30%), the losing rate is 0%, and the draw rate is 42% (60% * 70%).\n- If GoodGuy holds a Jack (40% probability), he will likely check (70% probability) or fold (30% probability). If he checks, it will be a draw as we both have the same amount of chips in the pot. If he folds, I will win as he forfeits his chips. The overall winning rate for this plan is 12% (40% * 30%), the losing rate is 0%, and the draw rate is 28% (40% * 70%).\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips (half of the pot). If I lose, the lose payoff would be 2 chips (half of the pot).\n- Plan 2: If I win, the winning payoff would be 2 chips (half of the pot). If I lose, the lose payoff would be 2 chips (half of the pot).\n- Plan 3: If I win, the winning payoff would be 2 chips (half of the pot). If I lose, the lose payoff would be 2 chips (half of the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 24% * 4 - 48% * 2 = -0.48 chips\n- Plan 2: Expected Chips Gain = 0% * 2 - 100% * 2 = -2 chips\n- Plan 3: Expected Chips Gain = 30% * 2 - 0% * 2 = 0.6 chips\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows: Plan 3 > Plan 1 > Plan 2. Therefore, I should choose Plan 3 (Check) as it has the highest estimated expected chips gain."}}
{"message": "", "29_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a Queen (70% probability), he will likely raise (80% probability). If I call, I will lose as his pair of Queens is stronger than my single Jack. The losing rate for this scenario is 0.7*0.8=0.56.\n- If GoodGuy holds a King (30% probability), he will likely raise (70% probability). If I call, I will lose as his King is higher than my Jack. The losing rate for this scenario is 0.3*0.7=0.21.\n- The overall losing rate for Plan 1 is 0.56+0.21=0.77. The winning rate is 0 as I cannot win with a single Jack against a Queen or King. The draw rate is also 0 as there is no scenario where we have the same rank of cards.\n\nPlan 2: Raise\n- If GoodGuy holds a Queen (70% probability), he will likely raise (80% probability). If I raise, I will still lose as his pair of Queens is stronger than my single Jack. The losing rate for this scenario is 0.7*0.8=0.56.\n- If GoodGuy holds a King (30% probability), he will likely raise (70% probability). If I raise, I will still lose as his King is higher than my Jack. The losing rate for this scenario is 0.3*0.7=0.21.\n- The overall losing rate for Plan 2 is 0.56+0.21=0.77. The winning rate and draw rate are both 0 for the same reasons as Plan 1.\n\nPlan 3: Fold\n- If I fold, I will lose the 2 chips I have already put in the pot. However, I will not lose any more chips. The losing rate for this plan is 1 as I will definitely lose this round. The winning rate and draw rate are both 0 as I have forfeited the game.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the pot (4 chips). If I lose, the losing payoff would be the 2 chips I have already put in the pot.\n- Plan 2: If I win, the winning payoff would be half of the pot (5 chips). If I lose, the losing payoff would be the 2 chips I have already put in the pot plus the 4 chips I raised.\n- Plan 3: If I lose, the losing payoff would be the 2 chips I have already put in the pot.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0*4 - 0.77*2 = -1.54 chips\n- Plan 2: Expected Chips Gain = 0*5 - 0.77*6 = -4.62 chips\n- Plan 3: Expected Chips Gain = 0*0 - 1*2 = -2 chips\n\nPlan Selection:\n- Plan 1: -1.54 chips\n- Plan 2: -4.62 chips\n- Plan 3: -2 chips\n\nBased on the estimated expected chips gain, Plan 1 (Call) is the best strategy as it results in the least loss of chips."}}
{"message": "", "30_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (33.33% chance), he is likely to raise (70%) or call (30%). If he raises, I will lose as we both have Kings, but he has more chips in the pot. If he calls, it will be a draw. The overall winning rate is 0%, losing rate is 23.33% (33.33%*70%), and drawing rate is 10% (33.33%*30%).\n- If GoodGuy holds a Queen (33.33% chance), he is likely to call (60%) or raise (40%). If he calls or raises, I will win as my King beats his Queen. The overall winning rate is 33.33%, losing rate is 0%, and drawing rate is 0%.\n- If GoodGuy holds a Jack (33.33% chance), he is likely to call (70%) or fold (30%). If he calls or folds, I will win as my King beats his Jack. The overall winning rate is 33.33%, losing rate is 0%, and drawing rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (33.33% chance), he is likely to raise (70%) or call (30%). If he raises or calls, it will be a draw as we both have Kings. The overall winning rate is 0%, losing rate is 0%, and drawing rate is 33.33%.\n- If GoodGuy holds a Queen (33.33% chance), he is likely to call (70%) or fold (30%). If he calls, I will win as my King beats his Queen. If he folds, I will also win as he forfeits the game. The overall winning rate is 33.33%, losing rate is 0%, and drawing rate is 0%.\n- If GoodGuy holds a Jack (33.33% chance), he is likely to fold (60%) or call (40%). If he folds or calls, I will win as my King beats his Jack. The overall winning rate is 33.33%, losing rate is 0%, and drawing rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will automatically lose regardless of what card GoodGuy holds. The overall winning rate is 0%, losing rate is 100%, and drawing rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips (half of the 6 chips in the pot). If I lose, the losing payoff would be 1 chip (half of the 2 chips I put in the pot).\n- Plan 2: If I win, the winning payoff would be 5 chips (half of the 10 chips in the pot). If I lose, the losing payoff would be 2 chips (half of the 4 chips I put in the pot).\n- Plan 3: If I fold, I will lose 1 chip (the chip I put in the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 33.33% * 3 - 23.33% * 1 = 0.67 chips\n- Plan 2: Expected Chips Gain = 66.66% * 5 - 0% * 2 = 3.33 chips\n- Plan 3: Expected Chips Gain = 0% * 0 - 100% * 1 = -1 chip\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain (3.33 chips), followed by Plan 1 (Call) with 0.67 chips, and Plan 3 (Fold) with -1 chip. Therefore, I should choose Plan 2 (Raise)."}}
{"message": "", "30_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (17.65% probability), he is likely to raise (80%) or call (20%). If he raises, I will win (0%) or lose (100%). If he calls, I will win (100%) or lose (0%). Overall, the winning rate is 17.65% * 20% = 3.53%, the losing rate is 17.65% * 80% = 14.12%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (35.29% probability), he is likely to fold (70%) or call (30%). If he folds, I will win (100%). If he calls, I will win (100%). Overall, the winning rate is 35.29% * 100% = 35.29%, the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (47.06% probability), he is likely to fold (80%) or call (20%). If he folds, I will win (100%). If he calls, I will win (0%) or draw (100%). Overall, the winning rate is 47.06% * 80% = 37.65%, the losing rate is 0%, and the draw rate is 47.06% * 20% = 9.41%.\n\nPlan 2: Fold\n- If I fold, I will lose (100%). The losing rate is 100%, and the winning and draw rates are 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King (17.65% probability), he is likely to raise (80%) or call (20%). If he raises, I will win (0%) or lose (100%). If he calls, I will win (100%) or lose (0%). Overall, the winning rate is 17.65% * 20% = 3.53%, the losing rate is 17.65% * 80% = 14.12%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (35.29% probability), he is likely to call (60%) or fold (40%). If he calls, I will win (100%). If he folds, I will win (100%). Overall, the winning rate is 35.29% * 100% = 35.29%, the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (47.06% probability), he is likely to call (70%) or fold (30%). If he calls, I will win (0%) or draw (100%). If he folds, I will win (100%). Overall, the winning rate is 47.06% * 30% = 14.12%, the losing rate is 0%, and the draw rate is 47.06% * 70% = 32.94%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, chips in the pot: 12. If win, the winning payoff would be 6. If lose, the lose payoff would be 6.\n- Plan 2: After the action, chips in the pot: 4. If win, the winning payoff would be 2. If lose, the lose payoff would be 2.\n- Plan 3: After the action, chips in the pot: 4. If win, the winning payoff would be 2. If lose, the lose payoff would be 2.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 3.53% * 6 - 14.12% * 6 = -0.63\n- Plan 2: Expected Chips Gain = 0% * 2 - 100% * 2 = -2\n- Plan 3: Expected Chips Gain = 3.53% * 2 - 14.12% * 2 = -0.21\n\nPlan Selection:\n- Plan 1: Rank 2\n- Plan 2: Rank 3\n- Plan 3: Rank 1\n\nTherefore, I should choose Plan 3: Check, as it has the highest estimated expected chips gain."}}
{"message": "", "31_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (41.18% probability), he will likely raise (70% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, it will be a draw. The overall winning rate is 0%, losing rate is 70%, and drawing rate is 30%.\n- If GoodGuy holds a Queen (23.53% probability), he will likely raise (40% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, it will be a draw. The overall winning rate is 0%, losing rate is 40%, and drawing rate is 60%.\n- If GoodGuy holds a Jack (29.41% probability), he will likely raise (50% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, it will be a draw. The overall winning rate is 0%, losing rate is 50%, and drawing rate is 50%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (41.18% probability), he will likely call (30% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, it will be a draw. The overall winning rate is 0%, losing rate is 70%, and drawing rate is 30%.\n- If GoodGuy holds a Queen (23.53% probability), he will likely call (60% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, it will be a draw. The overall winning rate is 0%, losing rate is 40%, and drawing rate is 60%.\n- If GoodGuy holds a Jack (29.41% probability), he will likely call (50% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, it will be a draw. The overall winning rate is 0%, losing rate is 50%, and drawing rate is 50%.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot. The overall winning rate is 0%, losing rate is 100%, and drawing rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips. If I lose, the losing payoff would be 2 chips.\n- Plan 2: If I win, the winning payoff would be 6 chips. If I lose, the losing payoff would be 4 chips.\n- Plan 3: If I fold, the losing payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0% * 4 chips - 70% * 2 chips = -1.4 chips\n- Plan 2: 0% * 6 chips - 70% * 4 chips = -2.8 chips\n- Plan 3: 0% * 0 chips - 100% * 2 chips = -2 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain (-1.4 chips), followed by Plan 3 (-2 chips), and Plan 2 (-2.8 chips). Therefore, I should choose Plan 1: Call."}}
{"message": "", "31_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (60% probability), he will likely fold (70% probability). I will win the pot (probability = 0.6 * 0.7 = 0.42).\n- If GoodGuy holds a Jack (40% probability), he will likely call (50% probability). It will be a draw (probability = 0.4 * 0.5 = 0.2).\n- Overall, the winning rate for plan 1 is 42%, the losing rate is 0%, and the draw rate is 20%.\n\nPlan 2: Fold\n- If I fold, I will lose the pot regardless of GoodGuy's card. The losing rate for plan 2 is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (60% probability), he will likely check (60% probability). I will win the pot (probability = 0.6 * 0.6 = 0.36).\n- If GoodGuy holds a Jack (40% probability), he will likely check (30% probability). It will be a draw (probability = 0.4 * 0.3 = 0.12).\n- Overall, the winning rate for plan 3 is 36%, the losing rate is 0%, and the draw rate is 12%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, chips in the pot: 12. If win, the winning payoff would be 6. If lose, the lose payoff would be 6.\n- Plan 2: After the action, chips in the pot: 8. If lose, the lose payoff would be 4.\n- Plan 3: After the action, chips in the pot: 8. If win, the winning payoff would be 4. If lose, the lose payoff would be 4.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected chips gain = winning rate * winning payoff - losing rate * losing payoff = 0.42 * 6 - 0 * 6 = 2.52\n- Plan 2: Expected chips gain = 0 * 0 - 1 * 4 = -4\n- Plan 3: Expected chips gain = 0.36 * 4 - 0 * 4 = 1.44\n\nPlan Selection:\n- Plan 1: Expected chips gain = 2.52\n- Plan 2: Expected chips gain = -4\n- Plan 3: Expected chips gain = 1.44\n\nThe rank of estimated expected chips gains for every plan is: Plan 1 > Plan 3 > Plan 2. Therefore, I should choose Plan 1: Raise."}}
{"message": "", "32_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (30% chance), he will likely raise (70% chance) or call (30% chance). If he raises, we will have a draw. If he calls, I will win.\n- If GoodGuy holds a Queen (60% chance), he will likely call (60% chance) or raise (40% chance). In either case, I will win.\n- If GoodGuy holds a Jack (10% chance), he will likely raise (50% chance) or call (50% chance). In either case, I will win.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds.\n\nPlan 3: Check\n- If GoodGuy holds a King (30% chance), he will likely raise (70% chance) or call (30% chance). If he raises, I will have a draw. If he calls, I will win.\n- If GoodGuy holds a Queen (60% chance), he will likely call (60% chance) or raise (40% chance). In either case, I will win.\n- If GoodGuy holds a Jack (10% chance), he will likely raise (50% chance) or call (50% chance). In either case, I will win.\n\nWinning/Lose/Draw Rates for Each Plan:\n- Plan 1: Winning rate = 70%, Lose rate = 0%, Draw rate = 30%\n- Plan 2: Winning rate = 0%, Lose rate = 100%, Draw rate = 0%\n- Plan 3: Winning rate = 70%, Lose rate = 0%, Draw rate = 30%\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 4 chips. If lose, the lose payoff would be 2 chips.\n- Plan 2: If win, the winning payoff would be 0 chips. If lose, the lose payoff would be 2 chips.\n- Plan 3: If win, the winning payoff would be 2 chips. If lose, the lose payoff would be 2 chips.\n\nEstimated Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 70% * 4 - 0% * 2 = 2.8 chips\n- Plan 2: Expected Chips Gain = 0% * 0 - 100% * 2 = -2 chips\n- Plan 3: Expected Chips Gain = 70% * 2 - 0% * 2 = 1.4 chips\n\nPlan Selection:\n- Plan 1: Raise (Expected Chips Gain = 2.8 chips)\n- Plan 3: Check (Expected Chips Gain = 1.4 chips)\n- Plan 2: Fold (Expected Chips Gain = -2 chips)\n\nBased on the estimated expected chips gain, I should choose Plan 1: Raise."}}
{"message": "", "32_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (70% probability), he will likely check (60% probability). If he checks, I will win as we both have a King, but I raised first. So, the winning rate for his King is 0.7*0.6=0.42.\n- If GoodGuy holds a Queen (10% probability), he will likely raise (80% probability). If he raises, I will lose as his Queen matches the public card. So, the losing rate for his Queen is 0.1*0.8=0.08.\n- If GoodGuy holds a Jack (20% probability), he will likely fold (70% probability). If he folds, I will win. So, the winning rate for his Jack is 0.2*0.7=0.14.\n\nPlan 2: Fold\n- If GoodGuy holds a King (70% probability), he will likely check (60% probability). If I fold, I will lose regardless of his action. So, the losing rate for his King is 0.7.\n- If GoodGuy holds a Queen (10% probability), he will likely raise (80% probability). If I fold, I will lose regardless of his action. So, the losing rate for his Queen is 0.1.\n- If GoodGuy holds a Jack (20% probability), he will likely fold (70% probability). If I fold, I will lose regardless of his action. So, the losing rate for his Jack is 0.2.\n\nPlan 3: Check\n- If GoodGuy holds a King (70% probability), he will likely check (60% probability). If he checks, I will win as we both have a King, but I raised first. So, the winning rate for his King is 0.7*0.6=0.42.\n- If GoodGuy holds a Queen (10% probability), he will likely raise (80% probability). If I check, I will lose as his Queen matches the public card. So, the losing rate for his Queen is 0.1*0.8=0.08.\n- If GoodGuy holds a Jack (20% probability), he will likely fold (70% probability). If I check, I will win. So, the winning rate for his Jack is 0.2*0.7=0.14.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be half of the pot (8 chips). If lose, the lose payoff would be half of the pot (8 chips).\n- Plan 2: If lose, the lose payoff would be half of the pot (4 chips).\n- Plan 3: If win, the winning payoff would be half of the pot (4 chips). If lose, the lose payoff would be half of the pot (4 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.42*8 - 0.08*8 = 2.72 chips\n- Plan 2: Expected Chips Gain = -0.7*4 - 0.1*4 - 0.2*4 = -4 chips\n- Plan 3: Expected Chips Gain = 0.42*4 - 0.08*4 = 1.36 chips\n\nPlan Selection:\n- Plan 1: 2.72 chips\n- Plan 2: -4 chips\n- Plan 3: 1.36 chips\n\nBased on the expected chips gain, Plan 1 (Raise) is the best strategy to follow."}}
{"message": "", "32_5": {"plan": "Plan 1: Call\n- If GoodGuy holds a Queen (48% probability), he will likely raise (80% probability). If this happens, I will lose as his pair of Queens beats my single King. The overall losing rate for this scenario is 0.48 * 0.8 = 38.4%.\n- If GoodGuy holds a King (12% probability), he will likely check (60% probability). If this happens, it will be a draw as we both have a single King. The overall draw rate for this scenario is 0.12 * 0.6 = 7.2%.\n- If GoodGuy holds a Jack (0% probability), he will likely fold (70% probability). If this happens, I will win as my single King beats his single Jack. However, since the probability of GoodGuy holding a Jack is 0%, the overall winning rate for this scenario is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. The overall losing rate for this scenario is 100%.\n\nWinning/Lose Payoff for Each Plan:\n- Plan 1: If I win, the pot will be 24 chips (12 from me, 12 from GoodGuy), so the winning payoff would be 12 chips. If I lose, I will lose 8 chips (the amount I have put in the pot).\n- Plan 2: If I fold, I will lose 8 chips (the amount I have put in the pot).\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 0% * 12 - 38.4% * 8 = -3.072 chips\n- Plan 2: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 0% * 0 - 100% * 8 = -8 chips\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain (-3.072 chips) than Plan 2 (-8 chips), so I should choose Plan 1: Call."}}
{"message": "", "33_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (35% probability), he is likely to raise (70%) or call (30%). If he raises, I will lose unless the public card is a Jack. If he calls, I will win if the public card is a Jack, and lose if it is a Queen or King. The overall winning rate for this plan is 35% * 30% * 33% = 3.5%, the losing rate is 35% * 70% * 67% = 16.5%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (30% probability), he is likely to raise (40%) or call (60%). If he raises, I will lose unless the public card is a Jack. If he calls, I will win if the public card is a Jack, and lose if it is a Queen or King. The overall winning rate for this plan is 30% * 60% * 33% = 6%, the losing rate is 30% * 40% * 67% = 8%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (35% probability), he is likely to raise (30%), call (50%), or fold (20%). If he raises or calls, it will be a draw unless the public card is a Queen or King. If he folds, I will win. The overall winning rate for this plan is 35% * 20% = 7%, the losing rate is 0%, and the draw rate is 35% * 80% = 28%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (35% probability), he is likely to call (30%) or fold (70%). If he calls, I will lose unless the public card is a Jack. If he folds, I will win. The overall winning rate for this plan is 35% * 70% = 24.5%, the losing rate is 35% * 30% * 67% = 7%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (30% probability), he is likely to call (60%) or fold (40%). If he calls, I will lose unless the public card is a Jack. If he folds, I will win. The overall winning rate for this plan is 30% * 40% = 12%, the losing rate is 30% * 60% * 67% = 12%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (35% probability), he is likely to call (50%), raise (30%), or fold (20%). If he raises or calls, it will be a draw unless the public card is a Queen or King. If he folds, I will win. The overall winning rate for this plan is 35% * 20% = 7%, the losing rate is 0%, and the draw rate is 35% * 80% = 28%.\n\nPlan 3: Fold\n- If I fold, I will lose the 1 chip I have put in the pot. The overall winning rate for this plan is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 1.5 chips. If I lose, the losing payoff would be 1 chip.\n- Plan 2: If I win, the winning payoff would be 2.5 chips. If I lose, the losing payoff would be 2 chips.\n- Plan 3: If I lose, the losing payoff would be 1 chip.\n\nThe expected chips gain for each plan:\n- Plan 1: 3.5% * 1.5 - 16.5% * 1 = -0.1425 chips\n- Plan 2: 43.5% * 2.5 - 19% * 2 = 0.875 chips\n- Plan 3: -1 chip\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain, so I will choose to raise."}}
{"message": "", "33_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (33.33% chance), he will likely raise (80% chance) or check (20% chance). If he raises, I will win as my pair of Jacks beats his King. If he checks, I will also win as my pair of Jacks beats his King. Therefore, the winning rate for this plan is 100%.\n- If GoodGuy holds a Queen (66.67% chance), he will likely check (60% chance) or fold (40% chance). If he checks, I will win as my pair of Jacks beats his Queen. If he folds, I will also win as he forfeits the round. Therefore, the winning rate for this plan is also 100%.\n\nPlan 2: Check\n- If GoodGuy holds a King (33.33% chance), he will likely raise (80% chance) or check (20% chance). If he raises, I will win as my pair of Jacks beats his King. If he checks, I will also win as my pair of Jacks beats his King. Therefore, the winning rate for this plan is 100%.\n- If GoodGuy holds a Queen (66.67% chance), he will likely check (60% chance) or fold (40% chance). If he checks, I will win as my pair of Jacks beats his Queen. If he folds, I will also win as he forfeits the round. Therefore, the winning rate for this plan is also 100%.\n\nPlan 3: Fold\n- This plan is not reasonable as I have a strong hand (pair of Jacks) and a high chance of winning the round.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the raise, chips in the pot would be 12. If win, the winning payoff would be 6. If lose, the lose payoff would be 6.\n- Plan 2: After the check, chips in the pot would remain 8. If win, the winning payoff would be 4. If lose, the lose payoff would be 4.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Lose rate * Lose Payoff = 100% * 6 - 0% * 6 = 6\n- Plan 2: Expected Chips Gain = Winning rate * Winning Payoff - Lose rate * Lose Payoff = 100% * 4 - 0% * 4 = 4\n\nPlan Selection:\n- Plan 1 (Raise) has the highest expected chips gain (6 chips), so I will choose this plan."}}
{"message": "", "34_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he will likely raise (70% probability), call (20% probability), or fold (10% probability). If he raises, I will lose unless the public card is a Queen. If he calls or folds, I will win unless the public card is a King. Therefore, the winning rate is 30%, the losing rate is 40%, and the draw rate is 30%.\n- If GoodGuy holds a Queen (20% probability), he will likely call (60% probability), check (30% probability), or fold (10% probability). If he calls or checks, it will be a draw unless the public card is a King or Jack. If he folds, I will win. Therefore, the winning rate is 10%, the losing rate is 20%, and the draw rate is 70%.\n- If GoodGuy holds a Jack (10% probability), he will likely check (50% probability), fold (30% probability), or call (20% probability). If he checks or folds, I will win unless the public card is a King. If he calls, I will lose unless the public card is a Queen. Therefore, the winning rate is 40%, the losing rate is 30%, and the draw rate is 30%.\n- Overall, the winning rate for plan 1 is 26.5%, the losing rate is 29.5%, and the draw rate is 44%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (70% probability), he will likely call (20% probability) or fold (10% probability). If he calls, I will lose unless the public card is a Queen. If he folds, I will win. Therefore, the winning rate is 10%, the losing rate is 60%, and the draw rate is 30%.\n- If GoodGuy holds a Queen (20% probability), he will likely fold (10% probability). If he folds, I will win. Therefore, the winning rate is 10%, the losing rate is 0%, and the draw rate is 90%.\n- If GoodGuy holds a Jack (10% probability), he will likely fold (30% probability) or call (20% probability). If he folds, I will win. If he calls, I will lose unless the public card is a Queen. Therefore, the winning rate is 30%, the losing rate is 20%, and the draw rate is 50%.\n- Overall, the winning rate for plan 2 is 16.5%, the losing rate is 26.5%, and the draw rate is 57%.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card. Therefore, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips. If I lose, the lose payoff would be 1 chip.\n- Plan 2: If I win, the winning payoff would be 5 chips. If I lose, the lose payoff would be 3 chips.\n- Plan 3: If I lose, the lose payoff would be 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is 26.5% * 3 - 29.5% * 1 = 0.5 chips.\n- Plan 2: The expected chips gain is 16.5% * 5 - 26.5% * 3 = -0.45 chips.\n- Plan 3: The expected chips gain is -1 chip.\n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 1 > Plan 2 > Plan 3.\n- Therefore, I should select Plan 1: Call."}}
{"message": "", "34_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (20% probability), he will likely call (50% probability) or check (50% probability). If he calls, I will lose (probability = 20% * 50% = 10%). If he checks, I will win (probability = 20% * 50% = 10%).\n- If GoodGuy holds a Queen (30% probability), he will likely call (30% probability) or fold (40% probability). If he calls, it will be a draw (probability = 30% * 30% = 9%). If he folds, I will win (probability = 30% * 40% = 12%).\n- If GoodGuy holds a Jack (50% probability), he will likely fold (30% probability) or check (70% probability). If he folds, I will win (probability = 50% * 30% = 15%). If he checks, I will win (probability = 50% * 70% = 35%).\n\nPlan 2: Fold\n- If I fold, I will lose regardless of GoodGuy's card. The lose rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (20% probability), he will likely call (50% probability) or check (50% probability). If he calls, I will lose (probability = 20% * 50% = 10%). If he checks, I will win (probability = 20% * 50% = 10%).\n- If GoodGuy holds a Queen (30% probability), he will likely call (30% probability) or check (60% probability). If he calls, it will be a draw (probability = 30% * 30% = 9%). If he checks, it will be a draw (probability = 30% * 60% = 18%).\n- If GoodGuy holds a Jack (50% probability), he will likely check (70% probability) or fold (30% probability). If he checks, I will win (probability = 50% * 70% = 35%). If he folds, I will win (probability = 50% * 30% = 15%).\n\nWinning/Lose Payoffs for Each Plan:\n- Plan 1: After the action, chips in the pot: 4. If win, the winning payoff would be 2. If lose, the lose payoff would be 2.\n- Plan 2: After the action, chips in the pot: 2. If lose, the lose payoff would be 1.\n- Plan 3: After the action, chips in the pot: 2. If win, the winning payoff would be 1. If lose, the lose payoff would be 1.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected chips gain = winning rate * winning payoff - lose rate * lose payoff = (67% * 2) - (10% * 2) = 1.14\n- Plan 2: Expected chips gain = -100% * 1 = -1\n- Plan 3: Expected chips gain = winning rate * winning payoff - lose rate * lose payoff = (68% * 1) - (10% * 1) = 0.58\n\nPlan Selection:\n- Plan 1: 1.14\n- Plan 2: -1\n- Plan 3: 0.58\n\nBased on the expected chips gain, the best plan is Plan 1: Raise."}}
{"message": "", "35_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (35% chance), he might raise (70% chance) or call (30% chance). If he raises, I would lose (70%*35% = 24.5%). If he calls, I would draw (30%*35% = 10.5%).\n- If GoodGuy holds a Queen (20% chance), he might raise (40% chance) or call (60% chance). If he raises, I would win (40%*20% = 8%). If he calls, I would win (60%*20% = 12%).\n- If GoodGuy holds a Jack (25% chance), he might raise (50% chance) or call (50% chance). If he raises, I would win (50%*25% = 12.5%). If he calls, I would win (50%*25% = 12.5%).\n\nPlan 1 overall Winning/Lose/Draw rates: Winning rate = 8% + 12% + 12.5% + 12.5% = 45%. Lose rate = 24.5%. Draw rate = 10.5%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (35% chance), he might raise (70% chance) or call (30% chance). If he raises, I would lose (70%*35% = 24.5%). If he calls, I would draw (30%*35% = 10.5%).\n- If GoodGuy holds a Queen (20% chance), he might raise (40% chance) or call (60% chance). If he raises, I would win (40%*20% = 8%). If he calls, I would win (60%*20% = 12%).\n- If GoodGuy holds a Jack (25% chance), he might raise (50% chance) or call (50% chance). If he raises, I would win (50%*25% = 12.5%). If he calls, I would win (50%*25% = 12.5%).\n\nPlan 2 overall Winning/Lose/Draw rates: Winning rate = 8% + 12% + 12.5% + 12.5% = 45%. Lose rate = 24.5%. Draw rate = 10.5%.\n\nPlan 3: Fold\n- If I fold, I would lose 100% of the time.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, Chips in the pot: 4. If win, the winning payoff would be 2. If lose, the lose payoff would be 2.\n- Plan 2: After the action, Chips in the pot: 6. If win, the winning payoff would be 3. If lose, the lose payoff would be 3.\n- Plan 3: After the action, Chips in the pot: 3. If lose, the lose payoff would be 1.5.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Lose rate * Lose Payoff = 45% * 2 - 24.5% * 2 = 0.41 chips.\n- Plan 2: Expected Chips Gain = Winning rate * Winning Payoff - Lose rate * Lose Payoff = 45% * 3 - 24.5% * 3 = 0.615 chips.\n- Plan 3: Expected Chips Gain = -100% * 1.5 = -1.5 chips.\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain (0.615 chips), followed by Plan 1 (Call) with 0.41 chips, and Plan 3 (Fold) with -1.5 chips. Therefore, I should choose Plan 2: Raise."}}
{"message": "", "35_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (50% chance), he will likely check (60%) or call (40%). If he checks, I will win the pot as my pair of Kings beats his Queen high. If he calls, I will also win as my pair of Kings beats his Queen high. Therefore, my winning rate is 100%.\n- If GoodGuy holds a Jack (50% chance), he will likely fold (70%) or check (30%). If he folds, I will win the pot. If he checks, I will also win as my pair of Kings beats his Jack high. Therefore, my winning rate is 100%.\n\nPlan 2: Fold\n- If I fold, I will lose the pot regardless of GoodGuy's card. Therefore, my losing rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a Queen (50% chance), he will likely check (60%) or call (40%). If he checks, I will win the pot as my pair of Kings beats his Queen high. If he calls, I will also win as my pair of Kings beats his Queen high. Therefore, my winning rate is 100%.\n- If GoodGuy holds a Jack (50% chance), he will likely fold (70%) or check (30%). If he folds, I will win the pot. If he checks, I will also win as my pair of Kings beats his Jack high. Therefore, my winning rate is 100%.\n\nWinning/Lose Payoffs:\n- Plan 1: If I win, the pot will be 12 chips (8 from me, 4 from GoodGuy), so my winning payoff would be 6 chips. If I lose, I will lose 8 chips.\n- Plan 2: If I fold, I will lose 4 chips.\n- Plan 3: If I win, the pot will be 8 chips (4 from me, 4 from GoodGuy), so my winning payoff would be 4 chips. If I lose, I will lose 4 chips.\n\nExpected Chips Gain:\n- Plan 1: 100% * 6 chips - 0% * 8 chips = 6 chips\n- Plan 2: 0% * 0 chips - 100% * 4 chips = -4 chips\n- Plan 3: 100% * 4 chips - 0% * 4 chips = 4 chips\n\nPlan Selection:\n- Plan 1: Raise (Expected Chips Gain: 6 chips)\n- Plan 3: Check (Expected Chips Gain: 4 chips)\n- Plan 2: Fold (Expected Chips Gain: -4 chips)\n\nTherefore, I should choose Plan 1: Raise, as it has the highest expected chips gain."}}
{"message": "", "36_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he is likely to raise (70%) or call (30%). If he raises, I will lose as we both have Kings. If he calls, it will be a draw. So, the winning rate is 0%, the losing rate is 49% (70%*70%), and the draw rate is 21% (70%*30%).\n- If GoodGuy holds a Queen (50% probability), he is likely to raise (50%) or call (50%). If he raises or calls, I will win as my King is higher than his Queen. So, the winning rate is 50% (50%*100%), the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (30% probability), he is likely to call (60%) or fold (40%). If he calls or folds, I will win as my King is higher than his Jack. So, the winning rate is 30% (30%*100%), the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (70% probability), he is likely to call (70%) or fold (30%). If he calls, it will be a draw. If he folds, I will win. So, the winning rate is 21% (70%*30%), the losing rate is 0%, and the draw rate is 49% (70%*70%).\n- If GoodGuy holds a Queen (50% probability), he is likely to call (70%) or fold (30%). If he calls or folds, I will win as my King is higher than his Queen. So, the winning rate is 50% (50%*100%), the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (30% probability), he is likely to fold (70%) or call (30%). If he folds or calls, I will win as my King is higher than his Jack. So, the winning rate is 30% (30%*100%), the losing rate is 0%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card. So, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 2 chips (half of the pot). If lose, the lose payoff would be 1 chip (half of the pot).\n- Plan 2: If win, the winning payoff would be 3 chips (half of the pot). If lose, the lose payoff would be 2 chips (half of the pot).\n- Plan 3: If lose, the lose payoff would be 1 chip (half of the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.8 chips (0.8*2 - 0.49*1)\n- Plan 2: Expected Chips Gain = 1.01 chips (0.81*3 - 0*2)\n- Plan 3: Expected Chips Gain = -1 chip (0*0 - 1*1)\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I will choose this plan."}}
{"message": "", "36_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (20% probability), he will likely call (70% probability). If he calls, I will lose (0% probability) because we both have Kings and it's a draw. \n- If GoodGuy holds a Queen (20% probability), he will likely fold (70% probability). If he folds, I will win (100% probability) because he forfeits the game. \n- If GoodGuy holds a Jack (60% probability), he will likely raise (80% probability). If he raises, I will lose (100% probability) because his Jack matches the public card. \n\nPlan 1 overall Winning/Lose/Draw rates: \n- Winning rate: 20% * 70% = 14%\n- Lose rate: 20% * 0% + 60% * 80% = 48%\n- Draw rate: 20% * 30% = 6%\n\nPlan 2: Fold\n- If GoodGuy holds a King (20% probability), I will lose (100% probability) because I forfeit the game. \n- If GoodGuy holds a Queen (20% probability), I will lose (100% probability) because I forfeit the game. \n- If GoodGuy holds a Jack (60% probability), I will lose (100% probability) because I forfeit the game. \n\nPlan 2 overall Winning/Lose/Draw rates: \n- Winning rate: 0%\n- Lose rate: 100%\n- Draw rate: 0%\n\nPlan 3: Check\n- If GoodGuy holds a King (20% probability), he will likely call (70% probability). If he calls, I will lose (0% probability) because we both have Kings and it's a draw. \n- If GoodGuy holds a Queen (20% probability), he will likely fold (70% probability). If he folds, I will win (100% probability) because he forfeits the game. \n- If GoodGuy holds a Jack (60% probability), he will likely raise (80% probability). If he raises, I will lose (100% probability) because his Jack matches the public card. \n\nPlan 3 overall Winning/Lose/Draw rates: \n- Winning rate: 20% * 70% = 14%\n- Lose rate: 20% * 0% + 60% * 80% = 48%\n- Draw rate: 20% * 30% = 6%\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 4 chips. If lose, the lose payoff would be 4 chips.\n- Plan 2: If win, the winning payoff would be 0 chips. If lose, the lose payoff would be 4 chips.\n- Plan 3: If win, the winning payoff would be 4 chips. If lose, the lose payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 14% * 4 - 48% * 4 = -1.36 chips\n- Plan 2: 0% * 0 - 100% * 4 = -4 chips\n- Plan 3: 14% * 4 - 48% * 4 = -1.36 chips\n\nPlan Selection:\n- Plan 1: 3rd\n- Plan 2: 2nd\n- Plan 3: 1st\n\nBased on the estimated expected chips gain, I should choose Plan 3: Check."}}
{"message": "", "37_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King, he is likely to call (40%) or raise (60%). If he calls, I will win if the public card is a King (33.3%) or lose if it's a Queen or Jack (66.7%). If he raises, it's a draw.\n- If GoodGuy holds a Queen, he is likely to call (70%) or raise (30%). If he calls, I will win regardless of the public card. If he raises, I will win if the public card is a King or Queen (66.7%) or lose if it's a Jack (33.3%).\n- If GoodGuy holds a Jack, he is likely to call (50%) or raise (50%). If he calls, I will win regardless of the public card. If he raises, I will win if the public card is a King or Jack (66.7%) or lose if it's a Queen (33.3%).\n\nPlan 2: Fold\n- If I fold, I will lose the pot regardless of GoodGuy's card or the public card.\n\nPlan 3: Check\n- If GoodGuy holds a King, he is likely to check (70%) or raise (30%). If he checks, I will win if the public card is a King (33.3%) or lose if it's a Queen or Jack (66.7%). If he raises, it's a draw.\n- If GoodGuy holds a Queen, he is likely to check (80%) or fold (20%). If he checks, I will win regardless of the public card. If he folds, I will win the pot.\n- If GoodGuy holds a Jack, he is likely to check (90%) or fold (10%). If he checks, I will win regardless of the public card. If he folds, I will win the pot.\n\nWinning/Lose Payoffs:\n- Plan 1: If I win, the winning payoff would be 6 chips (half of the pot). If I lose, the losing payoff would be 4 chips (half of the pot).\n- Plan 2: If I fold, I will lose 2 chips (my initial bet).\n- Plan 3: If I win, the winning payoff would be 4 chips (half of the pot). If I lose, the losing payoff would be 2 chips (my initial bet).\n\nExpected Chips Gain:\n- Plan 1: (0.6 * 6) - (0.4 * 4) = 2.4 chips\n- Plan 2: -2 chips\n- Plan 3: (0.8 * 4) - (0.2 * 2) = 2.8 chips\n\nPlan Selection:\nBased on the expected chips gain, the ranking of the plans is as follows: Plan 3 > Plan 1 > Plan 2. Therefore, I should choose Plan 3 (Check) as it has the highest expected chips gain."}}
{"message": "", "37_3": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (40% probability), he will likely check (70% probability). In this case, I will win as we both have a King, but I am the big blind. The winning rate is 0.4*0.7=0.28. \n- If GoodGuy holds a Queen (35% probability), he will likely fold (20% probability). In this case, I will win as my King is higher than his Queen. The winning rate is 0.35*0.2=0.07. \n- If GoodGuy holds a Jack (25% probability), he will likely fold (90% probability). In this case, I will win as my King is higher than his Jack. The winning rate is 0.25*0.9=0.225. \n\nPlan 1 overall Winning/Lose/Draw rates: Winning rate=0.28+0.07+0.225=0.575; Lose rate=0; Draw rate=0.425. \n\nPlan 2: Raise\n- If GoodGuy holds a King (40% probability), he will likely check (70% probability). In this case, I will win as we both have a King, but I am the big blind. The winning rate is 0.4*0.7=0.28. \n- If GoodGuy holds a Queen (35% probability), he will likely fold (20% probability). In this case, I will win as my King is higher than his Queen. The winning rate is 0.35*0.2=0.07. \n- If GoodGuy holds a Jack (25% probability), he will likely fold (90% probability). In this case, I will win as my King is higher than his Jack. The winning rate is 0.25*0.9=0.225. \n\nPlan 2 overall Winning/Lose/Draw rates: Winning rate=0.28+0.07+0.225=0.575; Lose rate=0; Draw rate=0.425. \n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card. The losing rate is 1. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, Chips in the pot: 8. If win, the winning payoff would be 4. If lose, the lose payoff would be 4. \n- Plan 2: After the action, Chips in the pot: 12. If win, the winning payoff would be 6. If lose, the lose payoff would be 6. \n- Plan 3: After the action, Chips in the pot: 6. If lose, the lose payoff would be 3. \n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0.575*4-0*4=2.3\n- Plan 2: 0.575*6-0*6=3.45\n- Plan 3: 0*3-1*3=-3\n\nPlan Selection: \n- Plan 2 > Plan 1 > Plan 3. Therefore, I should choose to raise as it has the highest estimated expected chips gain."}}
{"message": "", "38_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King, he is likely to raise (70%) or call (30%). If he raises, I will lose as we both have Kings and he is the big blind. If he calls, it will be a draw. So, the winning rate is 0%, the losing rate is 70%, and the draw rate is 30%.\n- If GoodGuy holds a Queen, he is likely to call (60%) or raise (40%). If he raises, I will win as my King is higher than his Queen. If he calls, I will also win. So, the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Jack, he is likely to call (80%) or fold (20%). If he folds, I will win. If he calls, I will also win. So, the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King, he is likely to raise (70%) or call (30%). If he raises, I will lose as we both have Kings and he is the big blind. If he calls, it will be a draw. So, the winning rate is 0%, the losing rate is 70%, and the draw rate is 30%.\n- If GoodGuy holds a Queen, he is likely to call (60%) or raise (40%). If he raises, I will win as my King is higher than his Queen. If he calls, I will also win. So, the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Jack, he is likely to call (80%) or fold (20%). If he folds, I will win. If he calls, I will also win. So, the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. So, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, Chips in the pot: 3. If win, the winning payoff would be 1.5. If lose, the lose payoff would be 1.5.\n- Plan 2: After the action, Chips in the pot: 5. If win, the winning payoff would be 2.5. If lose, the lose payoff would be 2.5.\n- Plan 3: After the action, Chips in the pot: 1. If win, the winning payoff would be 0.5. If lose, the lose payoff would be 0.5.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 100% * 1.5 - 70% * 1.5 = 0.45\n- Plan 2: Expected Chips Gain = 100% * 2.5 - 70% * 2.5 = 0.75\n- Plan 3: Expected Chips Gain = 0% * 0.5 - 100% * 0.5 = -0.5\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain, so I will choose Plan 2: Raise."}}
{"message": "", "38_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King, he is likely to call (70%) or raise (30%). If he calls, I will win because my King is higher than the public Queen. If he raises, it's a draw because we both have Kings. So, the winning rate is 70%, the draw rate is 30%, and the losing rate is 0%.\n- If GoodGuy holds a Queen, he is likely to call (60%) or raise (40%). If he calls, I will lose because his Queen matches the public card. If he raises, I will also lose. So, the winning rate is 0%, the draw rate is 0%, and the losing rate is 100%.\n- If GoodGuy holds a Jack, he is likely to fold (60%) or call (40%). If he folds, I will win. If he calls, I will win because my King is higher than his Jack. So, the winning rate is 100%, the draw rate is 0%, and the losing rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. So, the winning rate is 0%, the draw rate is 0%, and the losing rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King, he is likely to call (70%) or raise (30%). If he calls, I will win because my King is higher than the public Queen. If he raises, it's a draw because we both have Kings. So, the winning rate is 70%, the draw rate is 30%, and the losing rate is 0%.\n- If GoodGuy holds a Queen, he is likely to call (60%) or raise (40%). If he calls, I will lose because his Queen matches the public card. If he raises, I will also lose. So, the winning rate is 0%, the draw rate is 0%, and the losing rate is 100%.\n- If GoodGuy holds a Jack, he is likely to call (100%). If he calls, I will win because my King is higher than his Jack. So, the winning rate is 100%, the draw rate is 0%, and the losing rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips. If I lose, the losing payoff would be 4 chips.\n- Plan 2: If I fold, I will lose 4 chips.\n- Plan 3: If I win, the winning payoff would be 4 chips. If I lose, the losing payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: (0.7 * 4) - (0.3 * 4) = 1.6 chips\n- Plan 2: -4 chips\n- Plan 3: (0.85 * 4) - (0.15 * 4) = 2.8 chips\n\nPlan Selection:\n- Plan 3 (Check) has the highest expected chips gain, so I will choose this plan."}}
{"message": "", "39_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% chance), he might raise (70% chance) or call (30% chance). If he raises, I would lose as my Queen is lower than his King. If he calls, the result would depend on the public card. If the public card is a King or Queen, I would lose. If the public card is a Jack, I would win. So, the winning rate is 30%*30% = 9%, the losing rate is 70%*70%+30%*70% = 49%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (30% chance), he might raise (40% chance) or call (60% chance). If he raises or calls, the result would depend on the public card. If the public card is a King, I would lose. If the public card is a Queen or Jack, it would be a draw. So, the winning rate is 0%, the losing rate is 30%*40% = 12%, and the draw rate is 30%*60% = 18%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (70% chance), he might raise (70% chance) or call (30% chance). If he raises, I would lose as my Queen is lower than his King. If he calls, the result would depend on the public card. If the public card is a King or Queen, I would lose. If the public card is a Jack, I would win. So, the winning rate is 30%*30% = 9%, the losing rate is 70%*70%+30%*70% = 49%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (30% chance), he might raise (40% chance) or call (60% chance). If he raises or calls, the result would depend on the public card. If the public card is a King, I would lose. If the public card is a Queen or Jack, it would be a draw. So, the winning rate is 0%, the losing rate is 30%*40% = 12%, and the draw rate is 30%*60% = 18%.\n\nPlan 3: Fold\n- If I fold, I would lose the game regardless of GoodGuy's card. So, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, chips in the pot: 6. If win, the winning payoff would be 3. If lose, the lose payoff would be 3.\n- Plan 2: After the action, chips in the pot: 10. If win, the winning payoff would be 5. If lose, the lose payoff would be 5.\n- Plan 3: After the action, chips in the pot: 6. If lose, the lose payoff would be 3.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 9%*3 - 49%*3 = -1.2\n- Plan 2: Expected Chips Gain = 9%*5 - 49%*5 = -2\n- Plan 3: Expected Chips Gain = 0%*3 - 100%*3 = -3\n\nPlan Selection:\n- Plan 1: -1.2\n- Plan 2: -2\n- Plan 3: -3\n\nBased on the estimated expected chips gains, I should select Plan 1 (Call) as it has the highest estimated expected chips gain."}}
{"message": "", "39_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (70% probability), he will likely check (60%) or raise (40%). If he checks, I will win as my Queen will be higher than his Jack. If he raises, it's likely he has a King and I will lose. The winning rate is 0.7*0.6=0.42, the losing rate is 0.7*0.4=0.28, and the draw rate is 0.\n- If GoodGuy holds a Jack (30% probability), he will likely fold (70%) or check (30%). If he folds, I will win. If he checks, I will win as my Queen is higher than his Jack. The winning rate is 0.3*1=0.3, the losing rate is 0, and the draw rate is 0.\n- Overall, the winning rate for plan 1 is 0.42+0.3=0.72, the losing rate is 0.28, and the draw rate is 0. The chips in the pot would be 16 if I win, and 8 if I lose. The expected chips gain for plan 1 is 0.72*16 - 0.28*8 = 8.64.\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of GoodGuy's cards. The winning rate is 0, the losing rate is 1, and the draw rate is 0. The chips in the pot would be 8 if I lose. The expected chips gain for plan 2 is -8.\n\nPlan 3: Check\n- If GoodGuy holds a Queen (70% probability), he will likely check (60%) or raise (40%). If he checks, I will win as my Queen will be higher than his Jack. If he raises, it's likely he has a King and I will lose. The winning rate is 0.7*0.6=0.42, the losing rate is 0.7*0.4=0.28, and the draw rate is 0.\n- If GoodGuy holds a Jack (30% probability), he will likely fold (70%) or check (30%). If he folds, I will win. If he checks, I will win as my Queen is higher than his Jack. The winning rate is 0.3*1=0.3, the losing rate is 0, and the draw rate is 0.\n- Overall, the winning rate for plan 3 is 0.42+0.3=0.72, the losing rate is 0.28, and the draw rate is 0. The chips in the pot would be 8 if I win, and 8 if I lose. The expected chips gain for plan 3 is 0.72*8 - 0.28*8 = 3.52.\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows: Plan 1 (8.64) > Plan 3 (3.52) > Plan 2 (-8). Therefore, I should choose Plan 1: Raise, as it has the highest estimated expected chips gain."}}
{"message": "", "40_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (58.33% probability), he is likely to raise (70%) or call (30%). If he raises, I will lose (as King is higher than Queen). If he calls, the outcome will depend on the public card. Overall, the winning rate is 0%, the losing rate is 58.33%*70% = 40.83%, and the draw rate is 58.33%*30% = 17.5%.\n- If GoodGuy holds a Queen (41.67% probability), he is likely to raise (50%) or call (50%). In both cases, the outcome will depend on the public card. Overall, the winning rate is 0%, the losing rate is 0%, and the draw rate is 41.67%.\n\nPlan 1 overall Winning/Lose/Draw rates: Winning rate = 0%, Losing rate = 40.83%, Draw rate = 59.17%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (58.33% probability), he is likely to raise (70%) or call (30%). If he raises, I will lose (as King is higher than Queen). If he calls, the outcome will depend on the public card. Overall, the winning rate is 0%, the losing rate is 58.33%*70% = 40.83%, and the draw rate is 58.33%*30% = 17.5%.\n- If GoodGuy holds a Queen (41.67% probability), he is likely to raise (50%) or call (50%). In both cases, the outcome will depend on the public card. Overall, the winning rate is 0%, the losing rate is 0%, and the draw rate is 41.67%.\n\nPlan 2 overall Winning/Lose/Draw rates: Winning rate = 0%, Losing rate = 40.83%, Draw rate = 59.17%.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put into the pot. The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the pot (6 chips). If I lose, the losing payoff would be the chips I have put into the pot (2 chips).\n- Plan 2: If I win, the winning payoff would be half of the pot (8 chips). If I lose, the losing payoff would be the chips I have put into the pot (4 chips).\n- Plan 3: If I lose, the losing payoff would be the chips I have put into the pot (2 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning payoff - Losing rate * Losing payoff = 0% * 6 - 40.83% * 2 = -0.8166 chips.\n- Plan 2: Expected Chips Gain = 0% * 8 - 40.83% * 4 = -1.6332 chips.\n- Plan 3: Expected Chips Gain = -2 chips.\n\nPlan Selection: \nThe rank of estimated expected chips gains for every plan is: Plan 1 > Plan 2 > Plan 3. Therefore, I should choose Plan 1: Call."}}
{"message": "", "40_3": {"plan": "Make Reasonable Plans:\n\nPlan 1: Raise\n- This action will increase the pot by 4 chips and put pressure on GoodGuy. Given that I have a pair of Queens, this is a strong move that could lead to a win.\n\nPlan 2: Fold\n- This action would mean giving up this round. Given that I have a pair of Queens, this is not a recommended move.\n\nPlan 3: Check\n- This action would mean passing the turn to GoodGuy without adding more chips to the pot. This could be a strategic move to see what GoodGuy does next.\n\nPotential GoodGuy's actions and Estimate Winning/Lose/Draw Rate for Each Plan:\n\nPlan 1: Raise\n- If GoodGuy holds a King, he is likely to call (40% probability). In this case, I would win (100% probability) as my pair of Queens beats his single King.\n- If GoodGuy holds a Jack, he is likely to fold (70% probability). In this case, I would win (100% probability) as he forfeits the round.\n\nPlan 2: Fold\n- If I fold, GoodGuy wins by default, regardless of his card. Therefore, the losing rate for this plan is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King, he is likely to raise (30% probability). In this case, I would win (100% probability) as my pair of Queens beats his single King.\n- If GoodGuy holds a Jack, he is likely to check (70% probability). In this case, I would win (100% probability) as my pair of Queens beats his single Jack.\n\nThe number of winning and lose payoffs for each plan:\n\nPlan 1: Raise\n- If win, the winning payoff would be half of the pot, which would be (4+4+4)/2 = 6 chips.\n- If lose, the lose payoff would be half of the pot, which would be (4+4+4)/2 = 6 chips.\n\nPlan 2: Fold\n- If I fold, I lose my initial bet of 4 chips.\n\nPlan 3: Check\n- If win, the winning payoff would be half of the pot, which would be (4+4)/2 = 4 chips.\n- If lose, the lose payoff would be half of the pot, which would be (4+4)/2 = 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n\nPlan 1: Raise\n- Expected chips gain = winning rate * winning payoff - losing rate * losing payoff = (1.0 * 6) - (0.0 * 6) = 6 chips\n\nPlan 2: Fold\n- Expected chips gain = winning rate * winning payoff - losing rate * losing payoff = (0.0 * 0) - (1.0 * 4) = -4 chips\n\nPlan 3: Check\n- Expected chips gain = winning rate * winning payoff - losing rate * losing payoff = (1.0 * 4) - (0.0 * 4) = 4 chips\n\nPlan Selection:\n\nThe rank of estimated expected chips gains for every plan is as follows:\n1. Plan 1: Raise (6 chips)\n2. Plan 3: Check (4 chips)\n3. Plan 2: Fold (-4 chips)\n\nTherefore, the plan with the highest estimated expected chips gain is Plan 1: Raise. This plan aligns with the strategy improvement of being more aggressive when holding a high card or a card matching the public card."}}
{"message": "", "41_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he might raise (70% probability) or call (30% probability). If he raises and the public card is a King or Queen, I would lose. If the public card is a Jack, it would be a draw. Overall, the winning rate is 0%, the losing rate is 49% (70%*70%), and the draw rate is 21% (70%*30%).\n- If GoodGuy holds a Queen (30% probability), he might raise (40% probability) or call (60% probability). If he raises and the public card is a Queen, I would lose. If the public card is a King or Jack, it would be a draw. Overall, the winning rate is 0%, the losing rate is 12% (30%*40%), and the draw rate is 18% (30%*60%).\nPlan 1 overall Winning/Lose/Draw rates: Winning rate is 0%, Losing rate is 61%, Draw rate is 39%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (70% probability), he might call (30% probability) or fold (70% probability). If he calls and the public card is a King or Queen, I would lose. If the public card is a Jack, it would be a draw. Overall, the winning rate is 0%, the losing rate is 21% (70%*30%), and the draw rate is 49% (70%*70%).\n- If GoodGuy holds a Queen (30% probability), he might call (60% probability) or fold (40% probability). If he calls and the public card is a Queen, I would lose. If the public card is a King or Jack, it would be a draw. Overall, the winning rate is 0%, the losing rate is 18% (30%*60%), and the draw rate is 12% (30%*40%).\nPlan 2 overall Winning/Lose/Draw rates: Winning rate is 0%, Losing rate is 39%, Draw rate is 61%.\n\nPlan 3: Fold\n- If I fold, I would lose the game regardless of GoodGuy's card. So, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 3 chips. If lose, the lose payoff would be 2 chips.\n- Plan 2: If win, the winning payoff would be 5 chips. If lose, the lose payoff would be 4 chips.\n- Plan 3: If lose, the lose payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0% * 3 chips - 61% * 2 chips = -1.22 chips\n- Plan 2: 0% * 5 chips - 39% * 4 chips = -1.56 chips\n- Plan 3: 0% * 0 chips - 100% * 2 chips = -2 chips\n\nPlan Selection:\n- Plan 1: -1.22 chips\n- Plan 2: -1.56 chips\n- Plan 3: -2 chips\n\nBased on the estimated expected chips gain, Plan 1 (Call) would be the best strategy to use in this situation."}}
{"message": "", "41_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (60% probability), he might fold (70% probability) or check (30% probability). If he folds, I win the pot (4 chips), if he checks, the game continues to the next round. \n- If GoodGuy holds a Jack (40% probability), he might fold (70% probability) or check (30% probability). If he folds, I win the pot (4 chips), if he checks, the game continues to the next round. \n\nPlan 2: Fold\n- If I fold, I lose the pot (4 chips) regardless of what card GoodGuy holds.\n\nPlan 3: Check\n- If GoodGuy holds a King (60% probability), he might raise (60% probability) or check (40% probability). If he raises, I lose the pot (4 chips), if he checks, the game continues to the next round. \n- If GoodGuy holds a Jack (40% probability), he might raise (40% probability) or check (60% probability). If he raises, I lose the pot (4 chips), if he checks, the game continues to the next round. \n\nWinning/Lose/Draw Rates for Each Plan:\n- Plan 1: Winning rate = 70% (probability GoodGuy folds if he holds a King) + 70% (probability GoodGuy folds if he holds a Jack) = 70%. Lose rate = 0%. Draw rate = 30%.\n- Plan 2: Winning rate = 0%. Lose rate = 100%. Draw rate = 0%.\n- Plan 3: Winning rate = 0%. Lose rate = 50% (probability GoodGuy raises if he holds a King) + 40% (probability GoodGuy raises if he holds a Jack) = 45%. Draw rate = 55%.\n\nPayoffs for Each Plan:\n- Plan 1: If win, the winning payoff would be 2 chips (half of the pot). If lose, the lose payoff would be 2 chips (half of the pot).\n- Plan 2: If lose, the lose payoff would be 2 chips (half of the pot).\n- Plan 3: If win, the winning payoff would be 2 chips (half of the pot). If lose, the lose payoff would be 2 chips (half of the pot).\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected chips gain = 70% * 2 chips - 0% * 2 chips = 1.4 chips\n- Plan 2: Expected chips gain = 0% * 2 chips - 100% * 2 chips = -2 chips\n- Plan 3: Expected chips gain = 0% * 2 chips - 45% * 2 chips = -0.9 chips\n\nPlan Selection:\n- Plan 1 (Raise) has the highest expected chips gain (1.4 chips), followed by Plan 3 (Check) (-0.9 chips), and Plan 2 (Fold) (-2 chips). Therefore, I should choose Plan 1: Raise."}}
{"message": "", "42_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he will likely raise (70% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. The overall winning rate is 0.7*0.7*1/3 = 16.3%, the losing rate is 0.7*0.7*2/3 = 32.7%.\n- If GoodGuy holds a Queen (30% probability), he will likely call (60% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I will win. The overall winning rate is 0.3*0.6*2/3 = 12%, the losing rate is 0.3*0.6*1/3 = 6%.\n- If GoodGuy holds a Jack (20% probability), he will likely call (80% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, it will be a draw. The overall losing rate is 0.2*0.8*2/3 = 10.7%, the drawing rate is 0.2*0.8*1/3 = 5.3%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (70% probability), he will likely raise (70% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. The overall winning rate is 0.7*0.7*1/3 = 16.3%, the losing rate is 0.7*0.7*2/3 = 32.7%.\n- If GoodGuy holds a Queen (30% probability), he will likely raise (40% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I will win. The overall winning rate is 0.3*0.4*2/3 = 8%, the losing rate is 0.3*0.4*1/3 = 4%.\n- If GoodGuy holds a Jack (20% probability), he will likely fold (20% probability). If he folds, I will win. The overall winning rate is 0.2*0.2 = 4%.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot. The losing rate is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, Chips in the pot: 3. If win, the winning payoff would be 1.5. If lose, the lose payoff would be 1.5.\n- Plan 2: After the action, Chips in the pot: 5. If win, the winning payoff would be 2.5. If lose, the lose payoff would be 2.5.\n- Plan 3: After the action, Chips in the pot: 1. If lose, the lose payoff would be 0.5.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 16.3%*1.5 - 32.7%*1.5 = -24.6%\n- Plan 2: 28.3%*2.5 - 36.7%*2.5 = -21%\n- Plan 3: -100%*0.5 = -50%\n\nPlan Selection:\n- Plan 1: 3rd\n- Plan 2: 1st\n- Plan 3: 2nd\n\nBased on the above analysis, I should choose Plan 2: Raise."}}
{"message": "", "42_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King, he will likely raise (80%) or call (20%). If he raises, I will lose as his pair of Kings beats my single Jack. If he calls, I will also lose as his King beats my Jack. Therefore, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a Queen, he will likely check (60%) or call (40%). If he checks or calls, I will lose as his Queen beats my Jack. Therefore, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card. Therefore, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King, he will likely raise (80%) or call (20%). If he raises, I will lose as his pair of Kings beats my single Jack. If he calls, I will also lose as his King beats my Jack. Therefore, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a Queen, he will likely check (60%) or call (40%). If he checks or calls, I will lose as his Queen beats my Jack. Therefore, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips (half of the pot). If I lose, the losing payoff would be 4 chips.\n- Plan 2: If I fold, I will lose 4 chips.\n- Plan 3: If I win, the winning payoff would be 4 chips. If I lose, the losing payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0% * 4 chips - 100% * 4 chips = -4 chips\n- Plan 2: Expected Chips Gain = 0% * 4 chips - 100% * 4 chips = -4 chips\n- Plan 3: Expected Chips Gain = 0% * 4 chips - 100% * 4 chips = -4 chips\n\nPlan Selection:\nAll plans have the same expected chips gain of -4 chips. However, considering the strategy improvement, I should choose Plan 2: Fold. This is because folding when holding a lower-ranking card and no matching card with the public card is a more cautious approach, which aligns with the strategy improvement."}}
{"message": "", "43_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (50% probability), he might raise (70%) or call (30%). If he raises, I will lose as King is higher than my Queen. If he calls, the outcome will depend on the public card. If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. Therefore, the winning rate is 15% (50%*30%*100%), the losing rate is 85% (50%*70% + 50%*30%*66.67%), and the draw rate is 0%.\n- If GoodGuy holds a Queen (40% probability), he might raise (40%) or call (60%). If he raises or calls, the outcome will depend on the public card. If the public card is a King, I will lose. If the public card is a Queen, it will be a draw. If the public card is a Jack, I will win. Therefore, the winning rate is 20% (40%*60%*33.33%), the losing rate is 13.33% (40%*40% + 40%*60%*33.33%), and the draw rate is 26.67% (40%*60%*66.67%).\n- If GoodGuy holds a Jack (10% probability), he might call (70%) or fold (30%). If he calls, the outcome will depend on the public card. If the public card is a King or Queen, I will win. If the public card is a Jack, it will be a draw. Therefore, the winning rate is 14% (10%*70%*66.67%), the losing rate is 0%, and the draw rate is 7% (10%*70%*33.33%).\n\nPlan 1 overall Winning/Lose/Draw rates: Winning rate is 49% (15%+20%+14%), Losing rate is 98.33% (85%+13.33%+0%), Draw rate is 33.67% (0%+26.67%+7%).\n\nPlan 2: Raise\n- If GoodGuy holds a King (50% probability), he might raise (70%) or call (30%). If he raises, I will lose as King is higher than my Queen. If he calls, the outcome will depend on the public card. If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. Therefore, the winning rate is 15% (50%*30%*100%), the losing rate is 85% (50%*70% + 50%*30%*66.67%), and the draw rate is 0%.\n- If GoodGuy holds a Queen (40% probability), he might raise (40%) or call (60%). If he raises or calls, the outcome will depend on the public card. If the public card is a King, I will lose. If the public card is a Queen, it will be a draw. If the public card is a Jack, I will win. Therefore, the winning rate is 20% (40%*60%*33.33%), the losing rate is 13.33% (40%*40% + 40%*60%*33.33%), and the draw rate is 26.67% (40%*60%*66.67%).\n- If GoodGuy holds a Jack (10% probability), he might fold (30%) or call (70%). If he folds, I will win. If he calls, the outcome will depend on the public card. If the public card is a King or Queen, I will win. If the public card is a Jack, it will be a draw. Therefore, the winning rate is 37% (10%*30%*100% + 10%*70%*66.67%), the losing rate is 0%, and the draw rate is 7% (10%*70%*33.33%).\n\nPlan 2 overall Winning/Lose/Draw rates: Winning rate is 72% (15%+20%+37%), Losing rate is 98.33% (85%+13.33%+0%), Draw rate is 33.67% (0%+26.67%+7%).\n\nPlan 3: Fold\n- If I fold, I will lose 1 chip. Therefore, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 1.5 chips. If lose, the lose payoff would be 1 chip.\n- Plan 2: If win, the winning payoff would be 2.5 chips. If lose, the lose payoff would be 2 chips.\n- Plan 3: If lose, the lose payoff would be 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 49% * 1.5 - 98.33% * 1 = -0.735 chips\n- Plan 2: Expected Chips Gain = 72% * 2.5 - 98.33% * 2 = -0.415 chips\n- Plan 3: Expected Chips Gain = -1 chip\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain, so I will choose Plan 2: Raise."}}
{"message": "", "43_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (17% chance), he will likely raise (70% chance). If he raises, I will lose as his King is higher than my Queen. The overall losing rate for this scenario is 17% * 70% = 11.9%.\n- If GoodGuy holds a Queen (34% chance), it will be a draw as we both have Queens. The overall draw rate for this scenario is 34%.\n- If GoodGuy holds a Jack (49% chance), he will likely fold (70% chance). If he folds, I will win as my Queen is higher than his Jack. The overall winning rate for this scenario is 49% * 70% = 34.3%.\n\nPlan 2: Fold\n- If I fold, I will lose the chips I have already put in the pot. The overall losing rate for this scenario is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (17% chance), he will likely raise (80% chance). If he raises, I will lose as his King is higher than my Queen. The overall losing rate for this scenario is 17% * 80% = 13.6%.\n- If GoodGuy holds a Queen (34% chance), it will be a draw as we both have Queens. The overall draw rate for this scenario is 34%.\n- If GoodGuy holds a Jack (49% chance), he will likely check (30% chance). If he checks, I will win as my Queen is higher than his Jack. The overall winning rate for this scenario is 49% * 30% = 14.7%.\n\nWinning/Lose Payoffs:\n- Plan 1: If I win, the winning payoff would be half of the pot (8 chips). If I lose, the losing payoff would be the chips I put in the pot (4 chips).\n- Plan 2: If I fold, I will lose the chips I have already put in the pot (4 chips).\n- Plan 3: If I win, the winning payoff would be half of the pot (8 chips). If I lose, the losing payoff would be the chips I put in the pot (4 chips).\n\nExpected Chips Gain:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 34.3% * 8 - 11.9% * 4 = 1.732 chips\n- Plan 2: Expected Chips Gain = -100% * 4 = -4 chips\n- Plan 3: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 14.7% * 8 - 13.6% * 4 = 0.28 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain (1.732 chips), followed by Plan 3 (0.28 chips), and Plan 2 (-4 chips). Therefore, I should choose Plan 1: Raise."}}
{"message": "", "44_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (30% probability), he will likely raise (70%) or call (30%). If he raises, I will lose unless the public card is a Jack. If he calls, I will win if the public card is a Jack, and lose otherwise. \n- If GoodGuy holds a Queen (50% probability), he will likely raise (50%) or call (50%). If he raises, I will lose unless the public card is a Jack. If he calls, I will win if the public card is a Jack, and lose otherwise. \n- If GoodGuy holds a Jack (70% probability), he will likely raise (30%) or call (70%). If he raises, it will be a draw unless the public card is a King or Queen, in which case I will lose. If he calls, it will be a draw unless the public card is a King or Queen, in which case I will lose. \n\nPlan 2: Fold\n- If I fold, I will lose the 2 chips in the pot regardless of GoodGuy's card or the public card. \n\nPlan 3: Check\n- If GoodGuy holds a King (30% probability), he will likely raise (70%) or check (30%). If he raises, I will lose unless the public card is a Jack. If he checks, I will win if the public card is a Jack, and lose otherwise. \n- If GoodGuy holds a Queen (50% probability), he will likely raise (50%) or check (50%). If he raises, I will lose unless the public card is a Jack. If he checks, I will win if the public card is a Jack, and lose otherwise. \n- If GoodGuy holds a Jack (70% probability), he will likely raise (30%) or check (70%). If he raises, it will be a draw unless the public card is a King or Queen, in which case I will lose. If he checks, it will be a draw unless the public card is a King or Queen, in which case I will lose. \n\nWinning/Lose Payoffs:\n- Plan 1: If I win, the pot will be 8 chips, so the winning payoff will be 4 chips. If I lose, the pot will be 8 chips, so the losing payoff will be 4 chips. \n- Plan 2: If I fold, I will lose the 2 chips in the pot. \n- Plan 3: If I win, the pot will be 4 chips, so the winning payoff will be 2 chips. If I lose, the pot will be 4 chips, so the losing payoff will be 2 chips. \n\nExpected Chips Gain:\n- Plan 1: (0.3 * 4 * 0.7) - (0.3 * 4 * 0.3) = 0.84 chips\n- Plan 2: -2 chips\n- Plan 3: (0.3 * 2 * 0.7) - (0.3 * 2 * 0.3) = 0.42 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I will choose to raise."}}
{"message": "", "44_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (50% probability), he will likely raise (80% probability) or check (20% probability). If he raises, I will win as my card matches the public card. If he checks, I will also win as my card is higher. Therefore, the winning rate for this plan is 100%.\n- If GoodGuy holds a King (30% probability), he will likely check (60% probability) or fold (40% probability). If he checks, I will win as my card matches the public card. If he folds, I will also win as he forfeits the round. Therefore, the winning rate for this plan is also 100%.\n\nPlan 2: Fold\n- If I fold, I will automatically lose the round regardless of GoodGuy's card. Therefore, the losing rate for this plan is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a Queen (50% probability), he will likely raise (80% probability) or check (20% probability). If he raises, I will win as my card matches the public card. If he checks, I will also win as my card is higher. Therefore, the winning rate for this plan is 100%.\n- If GoodGuy holds a King (30% probability), he will likely check (60% probability) or fold (40% probability). If he checks, I will win as my card matches the public card. If he folds, I will also win as he forfeits the round. Therefore, the winning rate for this plan is also 100%.\n\nWinning/Lose Payoffs:\n- Plan 1: If I win, the pot will be 8 chips (4 from me, 4 from GoodGuy), and I will gain 4 chips (half of the pot). If I lose, I will lose 4 chips.\n- Plan 2: If I fold, I will lose 4 chips.\n- Plan 3: If I win, the pot will be 8 chips, and I will gain 4 chips. If I lose, I will lose 4 chips.\n\nExpected Chips Gain:\n- Plan 1: (100% * 4 chips) - (0% * 4 chips) = 4 chips\n- Plan 2: (0% * 4 chips) - (100% * 4 chips) = -4 chips\n- Plan 3: (100% * 4 chips) - (0% * 4 chips) = 4 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 both have the highest expected chips gain of 4 chips, while Plan 2 has a negative expected chips gain. Therefore, I should either raise (Plan 1) or check (Plan 3). Considering the strategy improvement, raising might be a better choice as it could potentially confuse GoodGuy and make him believe that I have a King, which could influence his decisions in the following rounds."}}
{"message": "", "45_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (2/5 probability), he might raise (70% probability) or call (30% probability). If he raises, I will lose (probability = 2/5 * 70% = 28%). If he calls, I have a 50% chance to win if the public card is a Queen (probability = 2/5 * 30% * 50% = 15%) and a 50% chance to lose if the public card is a King or Jack (probability = 2/5 * 30% * 50% = 15%).\n- If GoodGuy holds a Queen (2/5 probability), he might raise (40% probability) or call (60% probability). If he raises, I will lose (probability = 2/5 * 40% = 16%). If he calls, I have a 50% chance to win if the public card is a Jack (probability = 2/5 * 60% * 50% = 30%) and a 50% chance to lose if the public card is a King or Queen (probability = 2/5 * 60% * 50% = 30%).\n- If GoodGuy holds a Jack (1/5 probability), he might raise (50% probability) or call (50% probability). If he raises, I will lose (probability = 1/5 * 50% = 10%). If he calls, I have a 50% chance to win if the public card is a Queen or King (probability = 1/5 * 50% * 50% = 12.5%) and a 50% chance to draw if the public card is a Jack (probability = 1/5 * 50% * 50% = 12.5%).\n\nPlan 2: Raise\n- If GoodGuy holds a King (2/5 probability), he might call (30% probability) or fold (70% probability). If he calls, I will lose (probability = 2/5 * 30% = 12%). If he folds, I will win (probability = 2/5 * 70% = 28%).\n- If GoodGuy holds a Queen (2/5 probability), he might call (60% probability) or fold (40% probability). If he calls, I have a 50% chance to win if the public card is a Jack (probability = 2/5 * 60% * 50% = 30%) and a 50% chance to lose if the public card is a King or Queen (probability = 2/5 * 60% * 50% = 30%). If he folds, I will win (probability = 2/5 * 40% = 16%).\n- If GoodGuy holds a Jack (1/5 probability), he might call (50% probability) or fold (50% probability). If he calls, I have a 50% chance to win if the public card is a Queen or King (probability = 1/5 * 50% * 50% = 12.5%) and a 50% chance to draw if the public card is a Jack (probability = 1/5 * 50% * 50% = 12.5%). If he folds, I will win (probability = 1/5 * 50% = 10%).\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 4 chips. If lose, the lose payoff would be 4 chips.\n- Plan 2: If win, the winning payoff would be 8 chips. If lose, the lose payoff would be 8 chips.\n- Plan 3: If fold, the lose payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Lose rate * Lose Payoff = (15% + 30% + 12.5%) * 4 - (28% + 15% + 30% + 10%) * 4 = 2.3 chips\n- Plan 2: Expected Chips Gain = (28% + 30% + 10%) * 8 - (12% + 30%) * 8 = 3.04 chips\n- Plan 3: Expected Chips Gain = 0 * Winning Payoff - 100% * Lose Payoff = -2 chips\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain, so I will choose Plan 2: Raise."}}
{"message": "", "45_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (70% probability), he will likely check (60%) or raise (40%). If he checks, I will win the pot. If he raises, I will still win the pot as my pair of Jacks is higher than his King. The winning rate for this plan is 100%.\n- If GoodGuy holds a Queen (30% probability), he will likely fold (70%) or check (30%). If he folds, I will win the pot. If he checks, I will still win the pot as my pair of Jacks is higher than his Queen. The winning rate for this plan is 100%.\n\nPlan 2: Fold\n- If I fold, I will lose the pot regardless of GoodGuy's card. The losing rate for this plan is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (70% probability), he will likely check (60%) or raise (40%). If he checks, I will win the pot. If he raises, I will still win the pot as my pair of Jacks is higher than his King. The winning rate for this plan is 100%.\n- If GoodGuy holds a Queen (30% probability), he will likely fold (70%) or check (30%). If he folds, I will win the pot. If he checks, I will still win the pot as my pair of Jacks is higher than his Queen. The winning rate for this plan is 100%.\n\nWinning/Lose Payoffs for Each Plan:\n- Plan 1: After the action, chips in the pot would be 14. If win, the winning payoff would be 7 chips. If lose, the lose payoff would be 7 chips.\n- Plan 2: After the action, chips in the pot would be 6. If lose, the lose payoff would be 3 chips.\n- Plan 3: After the action, chips in the pot would be 6. If win, the winning payoff would be 3 chips. If lose, the lose payoff would be 3 chips.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected chips gain = winning rate * winning payoff - losing rate * losing payoff = 1.0 * 7 - 0 * 7 = 7 chips\n- Plan 2: Expected chips gain = winning rate * winning payoff - losing rate * losing payoff = 0 * 3 - 1.0 * 3 = -3 chips\n- Plan 3: Expected chips gain = winning rate * winning payoff - losing rate * losing payoff = 1.0 * 3 - 0 * 3 = 3 chips\n\nPlan Selection:\n- Plan 1: 7 chips\n- Plan 2: -3 chips\n- Plan 3: 3 chips\n\nBased on the expected chips gain, Plan 1 (Raise) is the best strategy to maximize my potential winnings."}}
{"message": "", "45_5": {"plan": "Plan 1: Call\n- If GoodGuy holds a Jack (80% probability), he will likely raise (80% probability). In this case, we will draw as we both have a pair of Jacks. If he checks (20% probability), we will also draw. \n- If GoodGuy holds a King (20% probability), he will likely check (60% probability). In this case, we will lose as his King is higher than our pair of Jacks. If he raises (40% probability), we will also lose. \n\nOverall, the winning rate for plan 1 is 0%, the lose rate is 20% (20% * 100%), and the draw rate is 80% (80% * 100%).\n\nPlan 2: Fold\n- If GoodGuy holds a Jack (80% probability), we will lose as we forfeit the game. \n- If GoodGuy holds a King (20% probability), we will also lose as we forfeit the game. \n\nOverall, the winning rate for plan 2 is 0%, the lose rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the call action, the chips in the pot would be 18. If win, the winning payoff would be 9. If lose, the lose payoff would be 9.\n- Plan 2: After the fold action, the chips in the pot would be 14. If win, the winning payoff would be 7. If lose, the lose payoff would be 7.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is 0% * 9 - 20% * 9 = -1.8 chips.\n- Plan 2: The expected chips gain is 0% * 7 - 100% * 7 = -7 chips.\n\nPlan Selection:\nRanking the plans by expected chips gain, we have Plan 1 > Plan 2. Therefore, the best strategy is to call."}}
{"message": "", "46_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King, he is likely to raise (70%) or call (30%). If he raises, I will lose (probability = 33.3% * 70% = 23.31%). If he calls, I will draw (probability = 33.3% * 30% = 9.99%).\n- If GoodGuy holds a Queen, he is likely to call (60%) or raise (40%). If he calls, I will draw (probability = 33.3% * 60% = 19.98%). If he raises, I will lose (probability = 33.3% * 40% = 13.32%).\n- If GoodGuy holds a Jack, he is likely to call (50%), raise (30%), or fold (20%). If he calls or folds, I will win (probability = 33.3% * 70% = 23.31%). If he raises, I will lose (probability = 33.3% * 30% = 9.99%).\n\nPlan 1 overall Winning/Lose/Draw rates: Winning rate = 23.31%, Lose rate = 46.62%, Draw rate = 29.97%.\n\nPlan 2: Raise\n- If GoodGuy holds a King, he is likely to raise (70%) or call (30%). If he raises, I will lose (probability = 33.3% * 70% = 23.31%). If he calls, I will draw (probability = 33.3% * 30% = 9.99%).\n- If GoodGuy holds a Queen, he is likely to call (60%) or raise (40%). If he calls, I will draw (probability = 33.3% * 60% = 19.98%). If he raises, I will lose (probability = 33.3% * 40% = 13.32%).\n- If GoodGuy holds a Jack, he is likely to call (50%), raise (30%), or fold (20%). If he calls or folds, I will win (probability = 33.3% * 70% = 23.31%). If he raises, I will lose (probability = 33.3% * 30% = 9.99%).\n\nPlan 2 overall Winning/Lose/Draw rates: Winning rate = 23.31%, Lose rate = 46.62%, Draw rate = 29.97%.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of GoodGuy's card. Lose rate = 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, Chips in the pot: 4. If win, the winning payoff would be 2. If lose, the lose payoff would be 2.\n- Plan 2: After the action, Chips in the pot: 6. If win, the winning payoff would be 3. If lose, the lose payoff would be 3.\n- Plan 3: After the action, Chips in the pot: 3. If lose, the lose payoff would be 1.5.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Lose rate * Lose Payoff = 23.31% * 2 - 46.62% * 2 = -46.62 chips.\n- Plan 2: Expected Chips Gain = Winning rate * Winning Payoff - Lose rate * Lose Payoff = 23.31% * 3 - 46.62% * 3 = -69.93 chips.\n- Plan 3: Expected Chips Gain = -100% * 1.5 = -1.5 chips.\n\nPlan Selection:\n- Plan 1: Rank 2\n- Plan 2: Rank 3\n- Plan 3: Rank 1\n\nConsidering both the strategy improvement and the highest estimated expected chips gain, I should choose Plan 3: Fold."}}
{"message": "", "47_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (30% probability), he might raise (70%) or call (30%). If he raises, I would lose (as King is higher than Jack). If he calls, the outcome would depend on the public card. \n- If GoodGuy holds a Queen (60% probability), he might call (60%) or raise (40%). If he raises or calls, the outcome would depend on the public card.\n- If GoodGuy holds a Jack (10% probability), he might call (50%) or fold (50%). If he calls, it would be a draw. If he folds, I would win.\n\nOverall, the winning rate for plan 1 is 5% (10% * 50%), the losing rate is 21% (30% * 70%), and the draw rate is 5% (10% * 50%).\n\nPlan 2: Fold\n- If I fold, I would lose the round regardless of GoodGuy's card. The losing rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (30% probability), he might raise (70%) or check (30%). If he raises, I would lose. If he checks, the outcome would depend on the public card.\n- If GoodGuy holds a Queen (60% probability), he might check (80%) or raise (20%). If he raises or checks, the outcome would depend on the public card.\n- If GoodGuy holds a Jack (10% probability), he might check (70%) or raise (30%). If he raises, I would lose. If he checks, it would be a draw.\n\nOverall, the winning rate for plan 3 is 0%, the losing rate is 24% (30% * 70% + 10% * 30%), and the draw rate is 7% (10% * 70%).\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips (half of the pot). If I lose, the loss would be 2 chips (half of the pot).\n- Plan 2: If I fold, I would lose 2 chips.\n- Plan 3: If I win, the winning payoff would be 2 chips (half of the pot). If I lose, the loss would be 2 chips (half of the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected gain = 5% * 4 - 21% * 2 = -0.2 chips\n- Plan 2: Expected gain = -2 chips\n- Plan 3: Expected gain = 0% * 2 - 24% * 2 = -0.48 chips\n\nPlan Selection:\nBased on the expected chips gain, the rank of the plans is: Plan 1 > Plan 3 > Plan 2. Therefore, I should choose Plan 1: Raise."}}
{"message": "", "47_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (80% probability), he will likely raise (80% probability). If this happens, I will lose as King is higher than Jack. The overall losing rate for this scenario is 0.8 * 0.8 = 0.64.\n- If GoodGuy holds a Queen (20% probability), he will likely check (60% probability) or fold (40% probability). If he checks, I will win as Jack is higher than Queen. If he folds, I will also win. The overall winning rate for this scenario is 0.2 * (0.6 + 0.4) = 0.2.\n\nPlan 2: Fold\n- If I fold, I will lose the chips I have already put in the pot. The losing rate for this scenario is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (80% probability), he will likely raise (80% probability). If this happens, I will lose as King is higher than Jack. The overall losing rate for this scenario is 0.8 * 0.8 = 0.64.\n- If GoodGuy holds a Queen (20% probability), he will likely check (60% probability) or fold (40% probability). If he checks, I will win as Jack is higher than Queen. If he folds, I will also win. The overall winning rate for this scenario is 0.2 * (0.6 + 0.4) = 0.2.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the pot (4 chips). If I lose, the losing payoff would be the chips I have put in the pot (4 chips).\n- Plan 2: If I fold, I will lose the chips I have already put in the pot (4 chips).\n- Plan 3: If I win, the winning payoff would be half of the pot (4 chips). If I lose, the losing payoff would be the chips I have put in the pot (4 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 0.2 * 4 - 0.64 * 4 = -1.76 chips\n- Plan 2: Expected Chips Gain = -4 chips\n- Plan 3: Expected Chips Gain = 0.2 * 4 - 0.64 * 4 = -1.76 chips\n\nPlan Selection:\n- Plan 1: -1.76 chips\n- Plan 2: -4 chips\n- Plan 3: -1.76 chips\n\nBased on the estimated expected chips gain, Plan 1 and Plan 3 are the best strategies to follow as they have the highest expected chips gain. However, considering the strategy improvement, I should be more cautious when deciding to call or raise. Therefore, I will choose Plan 3: Check."}}
{"message": "", "48_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he will likely raise (70% probability). If the public card is a King, I will lose (probability = 0.7 * 0.7 = 0.49). If the public card is not a King, I have a chance to win (probability = 0.7 * 0.3 = 0.21).\n- If GoodGuy holds a Queen (30% probability), he will likely call (60% probability). If the public card is a Queen, I will lose (probability = 0.3 * 0.6 = 0.18). If the public card is not a Queen, I have a chance to win (probability = 0.3 * 0.4 = 0.12).\n- Overall, the winning rate for Plan 1 is 0.21 + 0.12 = 0.33, the losing rate is 0.49 + 0.18 = 0.67.\n\nPlan 2: Raise\n- If GoodGuy holds a King (70% probability), he will likely raise (70% probability). If the public card is a King, I will lose (probability = 0.7 * 0.7 = 0.49). If the public card is not a King, I have a chance to win (probability = 0.7 * 0.3 = 0.21).\n- If GoodGuy holds a Queen (30% probability), he will likely call (60% probability). If the public card is a Queen, I will lose (probability = 0.3 * 0.6 = 0.18). If the public card is not a Queen, I have a chance to win (probability = 0.3 * 0.4 = 0.12).\n- Overall, the winning rate for Plan 2 is 0.21 + 0.12 = 0.33, the losing rate is 0.49 + 0.18 = 0.67.\n\nPlan 3: Fold\n- If I fold, I will lose the game. The losing rate is 1.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 3 chips (half of the pot). If lose, the lose payoff would be 2 chips (half of the pot).\n- Plan 2: If win, the winning payoff would be 5 chips (half of the pot). If lose, the lose payoff would be 4 chips (half of the pot).\n- Plan 3: If lose, the lose payoff would be 1 chip (half of the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.33 * 3 - 0.67 * 2 = -0.33 chips\n- Plan 2: Expected Chips Gain = 0.33 * 5 - 0.67 * 4 = -1.33 chips\n- Plan 3: Expected Chips Gain = -1 chip\n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 1 > Plan 3 > Plan 2.\n- Considering both the strategy improvement and the highest estimated expected chips gain, I will choose Plan 1: Call."}}
{"message": "", "48_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King, he might think I have a Queen or Jack and decide to call (60%) or raise (40%). If he calls, I would lose as King is higher than Jack. If he raises, I would fold and lose half the pot. So, the winning rate is 0%, lose rate is 100%, and draw rate is 0%.\n- If GoodGuy holds a Queen, he might think I have a King or Jack and decide to call (60%) or raise (40%). If he calls, I would win as Jack is higher than Queen. If he raises, I would fold and lose half the pot. So, the winning rate is 60%, lose rate is 40%, and draw rate is 0%.\n- If GoodGuy holds a Jack, he might think I have a King or Queen and decide to call (80%) or fold (20%). If he calls, it would be a draw as we both have Jacks. If he folds, I would win the pot. So, the winning rate is 20%, lose rate is 0%, and draw rate is 80%.\n\nPlan 2: Fold\n- If I fold, I would lose half the pot regardless of what card GoodGuy holds. So, the winning rate is 0%, lose rate is 100%, and draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King, he might think I have a Queen or Jack and decide to check (70%) or fold (30%). If he checks, I would lose as King is higher than Jack. If he folds, I would win the pot. So, the winning rate is 30%, lose rate is 70%, and draw rate is 0%.\n- If GoodGuy holds a Queen, he might think I have a King or Jack and decide to check (70%) or fold (30%). If he checks, I would win as Jack is higher than Queen. If he folds, I would win the pot. So, the winning rate is 100%, lose rate is 0%, and draw rate is 0%.\n- If GoodGuy holds a Jack, he might think I have a King or Queen and decide to check (80%) or fold (20%). If he checks, it would be a draw as we both have Jacks. If he folds, I would win the pot. So, the winning rate is 20%, lose rate is 0%, and draw rate is 80%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 6 chips. If lose, the lose payoff would be 4 chips.\n- Plan 2: If lose, the lose payoff would be 2 chips.\n- Plan 3: If win, the winning payoff would be 4 chips. If lose, the lose payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.2*6 - 1*4 = -2 chips\n- Plan 2: Expected Chips Gain = 0 - 1*2 = -2 chips\n- Plan 3: Expected Chips Gain = 0.5*4 - 0.7*2 = 0 chips\n\nPlan Selection:\n- Plan 3 (Check) has the highest expected chips gain and should be selected."}}
{"message": "", "49_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he is likely to call (80% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. Therefore, the winning rate is 20%, the losing rate is 56%, and the draw rate is 24%.\n- If GoodGuy holds a Queen (30% probability), he is likely to call (70% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I will win. Therefore, the winning rate is 42%, the losing rate is 9%, and the draw rate is 49%.\n\nPlan 1 overall Winning/Lose/Draw rates: Winning rate is 62%, Losing rate is 65%, Draw rate is 73%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (70% probability), he is likely to fold (20% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. Therefore, the winning rate is 14%, the losing rate is 56%, and the draw rate is 30%.\n- If GoodGuy holds a Queen (30% probability), he is likely to fold (30% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I will win. Therefore, the winning rate is 21%, the losing rate is 9%, and the draw rate is 70%.\n\nPlan 2 overall Winning/Lose/Draw rates: Winning rate is 35%, Losing rate is 65%, Draw rate is 100%.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot. Therefore, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 3 chips. If lose, the lose payoff would be 2 chips.\n- Plan 2: If win, the winning payoff would be 5 chips. If lose, the lose payoff would be 4 chips.\n- Plan 3: If lose, the lose payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 62% * 3 - 65% * 2 = 0.86 chips\n- Plan 2: Expected Chips Gain = 35% * 5 - 65% * 4 = -1.25 chips\n- Plan 3: Expected Chips Gain = -100% * 2 = -2 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, followed by Plan 2 and Plan 3. Therefore, I should choose Plan 1: Call."}}
{"message": "", "49_3": {"plan": "Plan 1: Raise\n- If GoodGuy has a King (30% chance), he will likely call (80% chance). If he calls, I will lose (as his pair of Kings beats my single Queen). If he folds (20% chance), I will win. So, the winning rate is 6%, the losing rate is 24%, and the draw rate is 0%.\n- If GoodGuy has a Queen (40% chance), he will likely call (70% chance). If he calls, it will be a draw (as we both have a single Queen). If he folds (30% chance), I will win. So, the winning rate is 12%, the losing rate is 0%, and the draw rate is 28%.\n- If GoodGuy has a Jack (30% chance), he will likely fold (60% chance). If he folds, I will win. If he calls (40% chance), I will win (as my single Queen beats his single Jack). So, the winning rate is 30%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy has. So, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy has a King (30% chance), he will likely check (80% chance). If he checks, I will lose (as his pair of Kings beats my single Queen). If he raises (20% chance), I will fold and lose. So, the winning rate is 0%, the losing rate is 30%, and the draw rate is 0%.\n- If GoodGuy has a Queen (40% chance), he will likely check (70% chance). If he checks, it will be a draw (as we both have a single Queen). If he raises (30% chance), I will fold and lose. So, the winning rate is 0%, the losing rate is 12%, and the draw rate is 28%.\n- If GoodGuy has a Jack (30% chance), he will likely check (60% chance). If he checks, I will win (as my single Queen beats his single Jack). If he raises (40% chance), I will fold and lose. So, the winning rate is 18%, the losing rate is 12%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips (half of the pot). If I lose, the lose payoff would be 4 chips.\n- Plan 2: If I fold, I will lose 4 chips.\n- Plan 3: If I win, the winning payoff would be 4 chips. If I lose, the lose payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: (0.48 * 4) - (0.24 * 4) = 0.96 chips\n- Plan 2: 0 - (1 * 4) = -4 chips\n- Plan 3: (0.18 * 4) - (0.54 * 4) = -1.44 chips\n\nPlan Selection:\n- Plan 1: 0.96 chips\n- Plan 2: -4 chips\n- Plan 3: -1.44 chips\n\nBased on the estimated expected chips gain, Plan 1 (Raise) is the best strategy."}}
{"message": "", "50_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (15% chance), he will likely raise (70% chance) or call (30% chance). If he raises, I will lose (as King is higher than Queen). If he calls, the outcome will depend on the public card. \n- If GoodGuy holds a Queen (30% chance), he will likely call (60% chance) or raise (40% chance). If he calls or raises, it will be a draw as we both have Queens. \n- If GoodGuy holds a Jack (55% chance), he will likely call (80% chance) or fold (20% chance). If he calls, I will win (as Queen is higher than Jack). If he folds, I will also win.\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card.\n\nPlan 3: Check\n- If GoodGuy holds a King (15% chance), he will likely raise (70% chance) or call (30% chance). If he raises, I will lose (as King is higher than Queen). If he calls, the outcome will depend on the public card. \n- If GoodGuy holds a Queen (30% chance), he will likely call (60% chance) or raise (40% chance). If he calls or raises, it will be a draw as we both have Queens. \n- If GoodGuy holds a Jack (55% chance), he will likely call (80% chance) or fold (20% chance). If he calls, I will win (as Queen is higher than Jack). If he folds, I will also win.\n\nWinning/Lose Payoffs:\n- Plan 1: If I win, the pot will be 8 chips (4 from me, 4 from GoodGuy), so I will gain 4 chips. If I lose, I will lose 4 chips.\n- Plan 2: If I fold, I will lose 2 chips.\n- Plan 3: If I win, the pot will be 4 chips (2 from me, 2 from GoodGuy), so I will gain 2 chips. If I lose, I will lose 2 chips.\n\nExpected Chips Gain:\n- Plan 1: (0.55*4) - (0.15*4) = 1.6 chips\n- Plan 2: -2 chips\n- Plan 3: (0.55*2) - (0.15*2) = 0.8 chips\n\nPlan Selection:\nBased on the expected chips gain, Plan 1 (Raise) is the best strategy, followed by Plan 3 (Check), and Plan 2 (Fold) is the worst strategy."}}
{"message": "", "50_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (30% probability), he will likely raise (70% probability). If he raises, I will lose as King is higher than my Queen. The losing rate for this scenario is 0.3*0.7=0.21.\n- If GoodGuy holds a Queen (60% probability), it will be a draw as we both have the same card. The drawing rate for this scenario is 0.6.\n- If GoodGuy holds a Jack (10% probability), he will likely fold (40% probability) or check (60% probability). If he folds or checks, I will win as Queen is higher than Jack. The winning rate for this scenario is 0.1*1=0.1.\n\nPlan 2: Fold\n- If I fold, I will lose the chips in the pot regardless of GoodGuy's card. The losing rate for this scenario is 1.\n\nPlan 3: Check\n- If GoodGuy holds a King (30% probability), he will likely raise (70% probability). If he raises, I will lose as King is higher than my Queen. The losing rate for this scenario is 0.3*0.7=0.21.\n- If GoodGuy holds a Queen (60% probability), it will be a draw as we both have the same card. The drawing rate for this scenario is 0.6.\n- If GoodGuy holds a Jack (10% probability), he will likely fold (40% probability) or check (60% probability). If he folds or checks, I will win as Queen is higher than Jack. The winning rate for this scenario is 0.1*1=0.1.\n\nWinning/Lose Payoffs:\n- Plan 1: If I win, the winning payoff would be half of the pot (4 chips). If I lose, the losing payoff would be half of the pot (4 chips).\n- Plan 2: If I fold, I will lose the chips in the pot (4 chips).\n- Plan 3: If I win, the winning payoff would be half of the pot (4 chips). If I lose, the losing payoff would be half of the pot (4 chips).\n\nExpected Chips Gain:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 0.1 * 4 - 0.21 * 4 = -0.44 chips\n- Plan 2: Expected Chips Gain = -4 chips\n- Plan 3: Expected Chips Gain = 0.1 * 4 - 0.21 * 4 = -0.44 chips\n\nPlan Selection:\n- Plan 1: -0.44 chips\n- Plan 2: -4 chips\n- Plan 3: -0.44 chips\n\nBased on the expected chips gain, Plan 1 and Plan 3 are the best strategies as they have the highest expected chips gain (-0.44 chips). However, considering the strategy improvement, I should be more cautious when I have weak hands. Therefore, I will choose Plan 3: Check."}}
{"message": "", "51_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% chance), he is likely to raise (70%) or call (30%). If he raises, I will lose as we both have Kings. If he calls, it will be a draw. So, the winning rate is 0%, the losing rate is 49% (70%*70%), and the draw rate is 21% (70%*30%).\n- If GoodGuy holds a Queen (20% chance), he is likely to call (60%) or raise (40%). If he calls or raises, I will win as my King is higher than his Queen. So, the winning rate is 20% (20%*100%), the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (10% chance), he is likely to call (50%) or fold (50%). If he calls, I will win as my King is higher than his Jack. If he folds, I will also win. So, the winning rate is 10% (10%*100%), the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (70% chance), he is likely to raise (70%) or call (30%). If he raises, I will lose as we both have Kings. If he calls, it will be a draw. So, the winning rate is 0%, the losing rate is 49% (70%*70%), and the draw rate is 21% (70%*30%).\n- If GoodGuy holds a Queen (20% chance), he is likely to call (60%) or raise (40%). If he calls or raises, I will win as my King is higher than his Queen. So, the winning rate is 20% (20%*100%), the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (10% chance), he is likely to call (50%) or fold (50%). If he calls, I will win as my King is higher than his Jack. If he folds, I will also win. So, the winning rate is 10% (10%*100%), the losing rate is 0%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the game. So, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, Chips in the pot: 8. If win, the winning payoff would be 4. If lose, the lose payoff would be 4.\n- Plan 2: After the action, Chips in the pot: 12. If win, the winning payoff would be 6. If lose, the lose payoff would be 6.\n- Plan 3: After the action, Chips in the pot: 6. If lose, the lose payoff would be 3.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.3*4 - 0.49*4 = -0.76\n- Plan 2: Expected Chips Gain = 0.3*6 - 0.49*6 = -1.14\n- Plan 3: Expected Chips Gain = 0 - 1*3 = -3\n\nPlan Selection:\nBased on the estimated expected chips gains, Plan 1 (Call) is the best strategy as it has the highest expected chips gain."}}
{"message": "", "51_3": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (28% probability), he will likely raise (80% probability). This results in a draw. The overall draw rate for this card is 0.28 * 0.8 = 0.224.\n- If GoodGuy holds a Queen (16% probability), he will likely check (70% probability). This results in a win for me. The overall win rate for this card is 0.16 * 0.7 = 0.112.\n- If GoodGuy holds a Jack (56% probability), he will likely raise (80% probability). This results in a loss for me. The overall lose rate for this card is 0.56 * 0.8 = 0.448.\n\nPlan 2: Raise\n- If GoodGuy holds a King (28% probability), he will likely raise (80% probability). This results in a draw. The overall draw rate for this card is 0.28 * 0.8 = 0.224.\n- If GoodGuy holds a Queen (16% probability), he will likely fold (60% probability). This results in a win for me. The overall win rate for this card is 0.16 * 0.6 = 0.096.\n- If GoodGuy holds a Jack (56% probability), he will likely raise (80% probability). This results in a loss for me. The overall lose rate for this card is 0.56 * 0.8 = 0.448.\n\nPlan 3: Fold\n- If I fold, I automatically lose the game. The overall lose rate for this plan is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, chips in the pot: 16. If win, the winning payoff would be 8. If lose, the lose payoff would be 8.\n- Plan 2: After the action, chips in the pot: 20. If win, the winning payoff would be 10. If lose, the lose payoff would be 10.\n- Plan 3: After the action, chips in the pot: 12. If lose, the lose payoff would be 6.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.112 * 8 - 0.448 * 8 = -2.688\n- Plan 2: Expected Chips Gain = 0.096 * 10 - 0.448 * 10 = -3.52\n- Plan 3: Expected Chips Gain = -6\n\nPlan Selection:\n- Plan 1: -2.688\n- Plan 2: -3.52\n- Plan 3: -6\n\nBased on the estimated expected chips gains, Plan 1 (Call) is the best strategy to use in this situation."}}
{"message": "", "52_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (20% probability), he might call (30%) or raise (70%). If he calls, I will lose unless the public card is a Jack. If he raises, I will lose unless the public card is a Jack. The overall winning rate is 20% * 20% = 4%, the losing rate is 20% * 80% = 16%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (40% probability), he might call (60%) or raise (40%). If he calls, I will win if the public card is a Jack, and lose otherwise. If he raises, I will win if the public card is a Jack, and lose otherwise. The overall winning rate is 40% * 20% = 8%, the losing rate is 40% * 80% = 32%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (40% probability), he might call (50%), raise (30%), or fold (20%). If he calls or raises, it will be a draw unless the public card is a King or Queen. If he folds, I will win. The overall winning rate is 40% * 20% = 8%, the losing rate is 0%, and the draw rate is 40% * 80% = 32%.\n\nPlan 2: Fold\n- If I fold, I will lose the 2 chips in the pot. The overall winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King (20% probability), he might call (30%) or raise (70%). If he calls, I will lose unless the public card is a Jack. If he raises, I will lose unless the public card is a Jack. The overall winning rate is 20% * 20% = 4%, the losing rate is 20% * 80% = 16%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (40% probability), he might call (60%) or raise (40%). If he calls, I will win if the public card is a Jack, and lose otherwise. If he raises, I will win if the public card is a Jack, and lose otherwise. The overall winning rate is 40% * 20% = 8%, the losing rate is 40% * 80% = 32%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (40% probability), he might call (50%), raise (30%), or fold (20%). If he calls or raises, it will be a draw unless the public card is a King or Queen. If he folds, I will win. The overall winning rate is 40% * 20% = 8%, the losing rate is 0%, and the draw rate is 40% * 80% = 32%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the pot (4 chips). If I lose, the losing payoff would be half of the pot (4 chips).\n- Plan 2: If I lose, the losing payoff would be the 2 chips I have already put in the pot.\n- Plan 3: If I win, the winning payoff would be half of the pot (4 chips). If I lose, the losing payoff would be half of the pot (4 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 4 * 20% - 4 * 80% = -2.4 chips\n- Plan 2: Expected Chips Gain = -2 chips\n- Plan 3: Expected Chips Gain = 4 * 20% - 4 * 80% = -2.4 chips\n\nPlan Selection:\n- Plan 1: -2.4 chips\n- Plan 2: -2 chips\n- Plan 3: -2.4 chips\n\nBased on the estimated expected chips gains, Plan 2 (Fold) is the best strategy for this round."}}
{"message": "", "53_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King, he will likely raise (70%) or call (30%). If he raises, I will have a draw (50%) or lose (50%) as we both have Kings. If he calls, I will win (50%) or draw (50%) as I have a King and he doesn't. Overall, the winning rate is 15%, the losing rate is 35%, and the draw rate is 50%.\n- If GoodGuy holds a Queen, he will likely call (60%) or raise (40%). If he calls or raises, I will win (100%) as I have a King and he has a Queen. Overall, the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Jack, he will likely call (50%), raise (30%), or fold (20%). If he calls or raises, I will win (100%) as I have a King and he has a Jack. If he folds, I will also win (100%). Overall, the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King, he will likely raise (70%) or call (30%). If he raises, I will have a draw (50%) or lose (50%) as we both have Kings. If he calls, I will win (50%) or draw (50%) as I have a King and he doesn't. Overall, the winning rate is 15%, the losing rate is 35%, and the draw rate is 50%.\n- If GoodGuy holds a Queen, he will likely call (60%) or fold (40%). If he calls, I will win (100%) as I have a King and he has a Queen. If he folds, I will also win (100%). Overall, the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Jack, he will likely call (50%), raise (30%), or fold (20%). If he calls or raises, I will win (100%) as I have a King and he has a Jack. If he folds, I will also win (100%). Overall, the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose 100% of the time, regardless of what card GoodGuy holds.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, Chips in the pot: 3. If win, the winning payoff would be 1.5 chips. If lose, the lose payoff would be 1 chip.\n- Plan 2: After the action, Chips in the pot: 5. If win, the winning payoff would be 2.5 chips. If lose, the lose payoff would be 2 chips.\n- Plan 3: After the action, Chips in the pot: 1. If lose, the lose payoff would be 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.15 * 1.5 - 0.35 * 1 = -0.075 chips\n- Plan 2: Expected Chips Gain = 0.15 * 2.5 - 0.35 * 2 = -0.25 chips\n- Plan 3: Expected Chips Gain = -1 chip\n\nPlan Selection:\n- Plan 1: -0.075 chips\n- Plan 2: -0.25 chips\n- Plan 3: -1 chip\n\nBased on the estimated expected chips gain, Plan 1 (Call) is the best strategy to use in this round."}}
{"message": "", "53_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (60% probability), he will likely raise (40%) or check (60%). If he raises, I will lose as he has a pair. If he checks, the game will go to showdown and I will lose as he has a pair. So, the overall losing rate for this plan is 60%.\n- If GoodGuy holds a Jack (40% probability), he will likely check (50%) or fold (50%). If he checks, the game will go to showdown and I will win as I have a higher rank card. If he folds, I will win immediately. So, the overall winning rate for this plan is 40%.\n\nPlan 2: Fold\n- If I fold, I will lose immediately regardless of what card GoodGuy holds. So, the overall losing rate for this plan is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a Queen (60% probability), he will likely raise (40%) or check (60%). If he raises, I will lose as he has a pair. If he checks, the game will go to showdown and I will lose as he has a pair. So, the overall losing rate for this plan is 60%.\n- If GoodGuy holds a Jack (40% probability), he will likely check (50%) or fold (50%). If he checks, the game will go to showdown and I will win as I have a higher rank card. If he folds, I will win immediately. So, the overall winning rate for this plan is 40%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, chips in the pot: 4. If win, the winning payoff would be 2. If lose, the lose payoff would be 2.\n- Plan 2: After the action, chips in the pot: 2. If lose, the lose payoff would be 1.\n- Plan 3: After the action, chips in the pot: 2. If win, the winning payoff would be 1. If lose, the lose payoff would be 1.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 40% * 2 - 60% * 2 = -0.4\n- Plan 2: Expected Chips Gain = -100% * 1 = -1\n- Plan 3: Expected Chips Gain = 40% * 1 - 60% * 1 = -0.2\n\nPlan Selection:\n- Plan 1: -0.4\n- Plan 2: -1\n- Plan 3: -0.2\n\nBased on the estimated expected chips gains, Plan 3 (Check) is the best strategy to use in this situation."}}
{"message": "", "53_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a Queen (80% probability), he will likely raise (80% probability). If he raises, I will lose because his pair of Queens beats my single King. Therefore, the losing rate for this plan is 80% * 80% = 64%.\n- If GoodGuy holds a Jack (20% probability), he will likely check (50% probability) or fold (50% probability). If he checks or folds, I will win because my single King beats his single Jack. Therefore, the winning rate for this plan is 20% * 50% = 10%.\n\nPlan 2: Raise\n- If GoodGuy holds a Queen (80% probability), he will likely raise (80% probability). If he raises, I will lose because his pair of Queens beats my single King. Therefore, the losing rate for this plan is 80% * 80% = 64%.\n- If GoodGuy holds a Jack (20% probability), he will likely fold (50% probability). If he folds, I will win because he forfeits the round. Therefore, the winning rate for this plan is 20% * 50% = 10%.\n\nPlan 3: Fold\n- If I fold, I will lose the round regardless of what card GoodGuy holds. Therefore, the losing rate for this plan is 100%.\n\nWinning/Lose Payoffs:\n- Plan 1: If I win, the winning payoff would be half of the pot (8 chips). If I lose, the losing payoff would be half of the pot (8 chips).\n- Plan 2: If I win, the winning payoff would be half of the pot (14 chips). If I lose, the losing payoff would be half of the pot (14 chips).\n- Plan 3: If I fold, I will lose the round and the losing payoff would be the chips I have already put in the pot (2 chips).\n\nExpected Chips Gain:\n- Plan 1: Expected Chips Gain = Winning Rate * Winning Payoff - Losing Rate * Losing Payoff = 10% * 8 - 64% * 8 = -4.48 chips\n- Plan 2: Expected Chips Gain = Winning Rate * Winning Payoff - Losing Rate * Losing Payoff = 10% * 14 - 64% * 14 = -7.84 chips\n- Plan 3: Expected Chips Gain = -2 chips (because I will lose the round if I fold)\n\nPlan Selection:\nBased on the expected chips gain, the ranking of the plans is as follows:\n1. Plan 1: Call\n2. Plan 3: Fold\n3. Plan 2: Raise\n\nTherefore, the best plan to execute in this round is to call."}}
{"message": "", "54_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he will likely raise (60% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. Overall, the winning rate is 30%, the losing rate is 42%, and the draw rate is 28%.\n- If GoodGuy holds a Queen (30% probability), he will likely raise (50% probability) or check (50% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I will win. Overall, the winning rate is 30%, the losing rate is 15%, and the draw rate is 15%.\n- Plan 1 overall Winning/Lose/Draw rates: Winning rate is 60%, losing rate is 57%, and draw rate is 43%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (70% probability), he will likely raise (60% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. Overall, the winning rate is 30%, the losing rate is 42%, and the draw rate is 28%.\n- If GoodGuy holds a Queen (30% probability), he will likely raise (50% probability) or check (50% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I will win. Overall, the winning rate is 30%, the losing rate is 15%, and the draw rate is 15%.\n- Plan 2 overall Winning/Lose/Draw rates: Winning rate is 60%, losing rate is 57%, and draw rate is 43%.\n\nPlan 3: Fold\n- If I fold, I will lose the game and the chips I have already put into the pot. The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 4 chips. If lose, the lose payoff would be 2 chips.\n- Plan 2: If win, the winning payoff would be 8 chips. If lose, the lose payoff would be 4 chips.\n- Plan 3: If I fold, I will lose 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected chips gain = 60% * 4 - 57% * 2 = 0.6 chips\n- Plan 2: Expected chips gain = 60% * 8 - 57% * 4 = 1.2 chips\n- Plan 3: Expected chips gain = 0% * 0 - 100% * 2 = -2 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, followed by Plan 1 (Call), and Plan 3 (Fold). Therefore, I should choose Plan 2 (Raise)."}}
{"message": "", "54_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (70% probability), he will likely raise (60% probability) or check (40% probability). If he raises, I will lose as King is higher than Jack. If he checks, the game will proceed to the next round and the outcome will depend on the next public card. \n- If GoodGuy holds a Jack (30% probability), he will likely check (70% probability) or fold (30% probability). If he checks, the game will proceed to the next round and the outcome will depend on the next public card. If he folds, I will win the game.\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card.\n\nPlan 3: Check\n- If GoodGuy holds a King (70% probability), he will likely raise (60% probability) or check (40% probability). If he raises, I will have to decide whether to call or fold. If he checks, the game will proceed to the next round and the outcome will depend on the next public card. \n- If GoodGuy holds a Jack (30% probability), he will likely check (70% probability) or fold (30% probability). If he checks, the game will proceed to the next round and the outcome will depend on the next public card. If he folds, I will win the game.\n\nWinning/Lose/Draw Rate for Each Plan:\n- Plan 1: Winning rate = 30% (probability GoodGuy holds a Jack) * 30% (probability he folds) = 9%. Lose rate = 70% (probability GoodGuy holds a King) * 60% (probability he raises) = 42%. Draw rate = 49%.\n- Plan 2: Winning rate = 0%. Lose rate = 100%. Draw rate = 0%.\n- Plan 3: Winning rate = 30% (probability GoodGuy holds a Jack) * 30% (probability he folds) = 9%. Lose rate = 70% (probability GoodGuy holds a King) * 60% (probability he raises) = 42%. Draw rate = 49%.\n\nWinning/Lose Payoffs for Each Plan:\n- Plan 1: If win, the winning payoff would be half of the pot (6 chips) = 3 chips. If lose, the lose payoff would be half of the pot (6 chips) = 3 chips.\n- Plan 2: If lose, the lose payoff would be half of the pot (6 chips) = 3 chips.\n- Plan 3: If win, the winning payoff would be half of the pot (6 chips) = 3 chips. If lose, the lose payoff would be half of the pot (6 chips) = 3 chips.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected chips gain = winning rate * winning payoff - lose rate * lose payoff = 9% * 3 chips - 42% * 3 chips = -0.99 chips.\n- Plan 2: Expected chips gain = -100% * 3 chips = -3 chips.\n- Plan 3: Expected chips gain = 9% * 3 chips - 42% * 3 chips = -0.99 chips.\n\nPlan Selection:\n- Plan 1 and Plan 3 have the same expected chips gain, which is higher than Plan 2. Therefore, I should choose either Plan 1 (Raise) or Plan 3 (Check). Considering my strategy improvement, I should choose Plan 1 (Raise) to bluff and make GoodGuy think I have a stronger hand."}}
{"message": "", "55_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (35% probability), he might raise (70%) or call (30%). If he raises, I will lose (as King is higher than Queen). If he calls, the result will depend on the public card. The overall winning rate is 0.35*0.3=0.105, the losing rate is 0.35*0.7=0.245, and the draw rate is 0.\n- If GoodGuy holds a Queen (35% probability), he might raise (40%) or call (60%). If he raises or calls, the result will be a draw (as we both hold Queens). The overall winning rate is 0, the losing rate is 0, and the draw rate is 0.35.\n- If GoodGuy holds a Jack (30% probability), he might raise (30%), call (50%), or fold (20%). If he raises or calls, I will win (as Queen is higher than Jack). If he folds, I will also win. The overall winning rate is 0.3, the losing rate is 0, and the draw rate is 0.\n- The overall winning rate for plan 1 is 0.105+0+0.3=0.405, the overall losing rate is 0.245+0+0=0.245, and the overall draw rate is 0+0.35+0=0.35.\n- After the action, chips in the pot: 3. If win, the winning payoff would be 1.5. If lose, the lose payoff would be 1.5.\n- The expected chips gain for plan 1 is 0.405*1.5 - 0.245*1.5 = 0.24.\n\nPlan 2: Raise\n- If GoodGuy holds a King (35% probability), he might raise (70%) or call (30%). If he raises, I will lose (as King is higher than Queen). If he calls, the result will depend on the public card. The overall winning rate is 0.35*0.3=0.105, the losing rate is 0.35*0.7=0.245, and the draw rate is 0.\n- If GoodGuy holds a Queen (35% probability), he might raise (40%) or call (60%). If he raises or calls, the result will be a draw (as we both hold Queens). The overall winning rate is 0, the losing rate is 0, and the draw rate is 0.35.\n- If GoodGuy holds a Jack (30% probability), he might raise (30%), call (50%), or fold (20%). If he raises or calls, I will win (as Queen is higher than Jack). If he folds, I will also win. The overall winning rate is 0.3, the losing rate is 0, and the draw rate is 0.\n- The overall winning rate for plan 2 is 0.105+0+0.3=0.405, the overall losing rate is 0.245+0+0=0.245, and the overall draw rate is 0+0.35+0=0.35.\n- After the action, chips in the pot: 5. If win, the winning payoff would be 2.5. If lose, the lose payoff would be 2.5.\n- The expected chips gain for plan 2 is 0.405*2.5 - 0.245*2.5 = 0.4.\n\nPlan 3: Fold\n- If I fold, I will lose the 1 chip I have put in the pot. The overall winning rate is 0, the losing rate is 1, and the draw rate is 0.\n- After the action, chips in the pot: 3. If lose, the lose payoff would be 1.5.\n- The expected chips gain for plan 3 is 0 - 1*1.5 = -1.5.\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is: Plan 2 > Plan 1 > Plan 3. Therefore, I should choose Plan 2: Raise."}}
{"message": "", "55_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (45% chance), he will likely raise (50% chance) or check (50% chance). If he raises, I will lose (100% chance). If he checks, I will win (100% chance). Overall, my winning rate is 22.5%, losing rate is 22.5%, and draw rate is 0%.\n- If GoodGuy holds a Queen (30% chance), he will likely raise (50% chance) or check (50% chance). If he raises or checks, it will be a draw (100% chance). Overall, my winning rate is 0%, losing rate is 0%, and draw rate is 30%.\n- If GoodGuy holds a Jack (25% chance), he will likely check (60% chance) or fold (40% chance). If he checks or folds, I will win (100% chance). Overall, my winning rate is 25%, losing rate is 0%, and draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of GoodGuy's card. Overall, my winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King (45% chance), he will likely raise (50% chance) or check (50% chance). If he raises, I will lose (100% chance). If he checks, I will win (100% chance). Overall, my winning rate is 22.5%, losing rate is 22.5%, and draw rate is 0%.\n- If GoodGuy holds a Queen (30% chance), he will likely raise (50% chance) or check (50% chance). If he raises or checks, it will be a draw (100% chance). Overall, my winning rate is 0%, losing rate is 0%, and draw rate is 30%.\n- If GoodGuy holds a Jack (25% chance), he will likely check (60% chance) or fold (40% chance). If he checks or folds, I will win (100% chance). Overall, my winning rate is 25%, losing rate is 0%, and draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the raise, chips in the pot will be 16. If win, the winning payoff would be 8. If lose, the lose payoff would be 8.\n- Plan 2: After the fold, chips in the pot will be 8. If lose, the lose payoff would be 4.\n- Plan 3: After the check, chips in the pot will be 8. If win, the winning payoff would be 4. If lose, the lose payoff would be 4.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected chips gain = 0.475 * 8 - 0.225 * 8 = 2\n- Plan 2: Expected chips gain = 0 * 0 - 1 * 4 = -4\n- Plan 3: Expected chips gain = 0.475 * 4 - 0.225 * 4 = 1\n\nPlan Selection:\n- Plan 1: Expected chips gain = 2\n- Plan 2: Expected chips gain = -4\n- Plan 3: Expected chips gain = 1\n\nTherefore, I should choose Plan 1 (Raise) as it has the highest expected chips gain."}}
{"message": "", "56_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he will likely raise (60% probability). If the public card is a King, we will draw. If the public card is a Queen or Jack, I will win. Overall, the winning rate is 70%*60%*66.67% = 28%, the drawing rate is 70%*60%*33.33% = 14%, and the losing rate is 0%.\n- If GoodGuy holds a Queen (20% probability), he will likely check (50% probability) or raise (50% probability). If the public card is a Queen, I will lose. If the public card is a King or Jack, I will win. Overall, the winning rate is 20%*50%*66.67% = 7%, the drawing rate is 0%, and the losing rate is 20%*50%*33.33% = 3.33%.\n- If GoodGuy holds a Jack (10% probability), he will likely check (60% probability) or raise (20% probability). If the public card is a Jack, I will lose. If the public card is a King or Queen, I will win. Overall, the winning rate is 10%*80%*66.67% = 5.33%, the drawing rate is 0%, and the losing rate is 10%*20%*33.33% = 0.67%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (70% probability), he will likely raise (60% probability). If the public card is a King, we will draw. If the public card is a Queen or Jack, I will win. Overall, the winning rate is 70%*60%*66.67% = 28%, the drawing rate is 70%*60%*33.33% = 14%, and the losing rate is 0%.\n- If GoodGuy holds a Queen (20% probability), he will likely check (50% probability) or fold (50% probability). If the public card is a Queen, I will lose. If the public card is a King or Jack, I will win. Overall, the winning rate is 20%*50%*66.67% = 7%, the drawing rate is 0%, and the losing rate is 20%*50%*33.33% = 3.33%.\n- If GoodGuy holds a Jack (10% probability), he will likely check (60% probability) or fold (40% probability). If the public card is a Jack, I will lose. If the public card is a King or Queen, I will win. Overall, the winning rate is 10%*60%*66.67% = 4%, the drawing rate is 0%, and the losing rate is 10%*40%*33.33% = 1.33%.\n\nPlan 3: Fold\n- If I fold, I will lose the round regardless of GoodGuy's card or the public card. The losing rate is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 6 chips. If I lose, the losing payoff would be 2 chips.\n- Plan 2: If I win, the winning payoff would be 10 chips. If I lose, the losing payoff would be 4 chips.\n- Plan 3: If I fold, I will lose 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 28%*6 - 3.33%*2 = 1.56 chips\n- Plan 2: Expected Chips Gain = 28%*10 - 3.33%*4 = 2.67 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I will choose this plan."}}
{"message": "", "56_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (50% probability), he will likely check (50% probability) or raise (50% probability). If he checks, I will win (100% probability). If he raises, I will still win (100% probability). Overall, the winning rate for his Queen is 50%.\n- If GoodGuy holds a Jack (50% probability), he will likely check (60% probability), raise (20% probability), or fold (20% probability). If he checks or raises, I will win (100% probability). If he folds, I will still win (100% probability). Overall, the winning rate for his Jack is 50%.\n\nPlan 2: Check\n- If GoodGuy holds a Queen (50% probability), he will likely check (50% probability) or raise (50% probability). If he checks, I will win (100% probability). If he raises, I will still win (100% probability). Overall, the winning rate for his Queen is 50%.\n- If GoodGuy holds a Jack (50% probability), he will likely check (60% probability), raise (20% probability), or fold (20% probability). If he checks or raises, I will win (100% probability). If he folds, I will still win (100% probability). Overall, the winning rate for his Jack is 50%.\n\nPlan 3: Fold\n- This plan is not reasonable because I have a strong hand (pair of Kings) and I am guaranteed to win unless GoodGuy also holds a King, which is impossible because I hold one King and the public card is also a King.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, chips in the pot: 14. If win, the winning payoff would be 7. If lose, the lose payoff would be 7.\n- Plan 2: After the action, chips in the pot: 12. If win, the winning payoff would be 6. If lose, the lose payoff would be 6.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = winning rate * Winning Payoff - lose rate * Lose Payoff = 1 * 7 - 0 * 7 = 7\n- Plan 2: Expected Chips Gain = winning rate * Winning Payoff - lose rate * Lose Payoff = 1 * 6 - 0 * 6 = 6\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain (7), so I will choose Plan 1: Raise."}}
{"message": "", "57_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a Queen (50% probability), he will likely raise (60% probability) or call (40% probability). If he raises, I will win as my King beats his Queen. If he calls, the outcome will depend on the public card. If the public card is a King or Queen, I will win. If the public card is a Jack, it will be a draw. Therefore, the winning rate for this plan is 50% * (60% + 40% * 2/3) = 43.3%, the draw rate is 50% * 40% * 1/3 = 6.7%, and the lose rate is 0%.\n- If GoodGuy holds a Jack (50% probability), he will likely raise (60% probability) or call (40% probability). If he raises, I will win as my King beats his Jack. If he calls, the outcome will depend on the public card. If the public card is a King or Queen, I will win. If the public card is a Jack, I will lose. Therefore, the winning rate for this plan is 50% * (60% + 40% * 2/3) = 43.3%, the draw rate is 0%, and the lose rate is 50% * 40% * 1/3 = 6.7%.\n- Overall, the winning rate for Plan 1 is 43.3% + 43.3% = 86.6%, the draw rate is 6.7%, and the lose rate is 6.7%.\n\nPlan 2: Raise\n- If GoodGuy holds a Queen (50% probability), he will likely call (40% probability) or fold (60% probability). If he calls, I will win as my King beats his Queen. If he folds, I will also win. Therefore, the winning rate for this plan is 50% * 100% = 50%, the draw rate is 0%, and the lose rate is 0%.\n- If GoodGuy holds a Jack (50% probability), he will likely call (40% probability) or fold (60% probability). If he calls, the outcome will depend on the public card. If the public card is a King or Queen, I will win. If the public card is a Jack, I will lose. Therefore, the winning rate for this plan is 50% * (60% + 40% * 2/3) = 43.3%, the draw rate is 0%, and the lose rate is 50% * 40% * 1/3 = 6.7%.\n- Overall, the winning rate for Plan 2 is 50% + 43.3% = 93.3%, the draw rate is 0%, and the lose rate is 6.7%.\n\nPlan 3: Fold\n- If I fold, I will automatically lose, regardless of GoodGuy's card. Therefore, the winning rate for this plan is 0%, the draw rate is 0%, and the lose rate is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the pot, which is (2+4+4)/2 = 5 chips. If I lose, the lose payoff would be half of the pot, which is (2+4)/2 = 3 chips.\n- Plan 2: If I win, the winning payoff would be half of the pot, which is (2+4+4+8)/2 = 9 chips. If I lose, the lose payoff would be half of the pot, which is (2+4+4)/2 = 5 chips.\n- Plan 3: If I fold, I will lose 2 chips.\n\nThe expected chips gain for each plan:\n- Plan 1: The expected chips gain is 86.6% * 5 - 6.7% * 3 = 4.33 chips.\n- Plan 2: The expected chips gain is 93.3% * 9 - 6.7% * 5 = 8.33 chips.\n- Plan 3: The expected chips gain is -2 chips.\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I will choose this plan."}}
{"message": "", "57_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen, he will likely raise (80%) or call (20%). If he raises, I will lose as he has a pair of Queens. If he calls, I will win as I have a higher single card. The winning rate is 20%, the losing rate is 80%, and the draw rate is 0%.\n- If GoodGuy holds a King, he will likely call (60%) or check (40%). If he calls or checks, it will be a draw as we both have a single King. The winning rate is 0%, the losing rate is 0%, and the draw rate is 100%.\n\nPlan 2: Fold\n- If I fold, I will lose the round regardless of GoodGuy's card. The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a Queen, he will likely raise (80%) or call (20%). If he raises, I will lose as he has a pair of Queens. If he calls, I will win as I have a higher single card. The winning rate is 20%, the losing rate is 80%, and the draw rate is 0%.\n- If GoodGuy holds a King, he will likely call (60%) or check (40%). If he calls or checks, it will be a draw as we both have a single King. The winning rate is 0%, the losing rate is 0%, and the draw rate is 100%.\n\nWinning/Lose Payoffs for Each Plan:\n- Plan 1: If I win, the pot will be 16 chips and my winning payoff will be 8 chips. If I lose, the pot will be 16 chips and my losing payoff will be 8 chips.\n- Plan 2: If I fold, I will lose 6 chips.\n- Plan 3: If I win, the pot will be 12 chips and my winning payoff will be 6 chips. If I lose, the pot will be 12 chips and my losing payoff will be 6 chips.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected gain = 20% * 8 chips - 80% * 8 chips = -4.8 chips\n- Plan 2: Expected gain = 0% * 0 chips - 100% * 6 chips = -6 chips\n- Plan 3: Expected gain = 20% * 6 chips - 80% * 6 chips = -3.6 chips\n\nPlan Selection:\n- Plan 1: -4.8 chips\n- Plan 2: -6 chips\n- Plan 3: -3.6 chips\n\nBased on the expected chips gain, Plan 3 (Check) is the best strategy as it has the highest expected chips gain (-3.6 chips)."}}
{"message": "", "58_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he will likely raise (70% probability) or call (30% probability). If the public card is a King, I will lose (probability = 70% * 70% = 49%). If the public card is a Queen, I will win (probability = 70% * 30% = 21%). If the public card is a Jack, I will win (probability = 70% * 30% = 21%).\n- If GoodGuy holds a Queen (30% probability), he will likely call (60% probability) or raise (40% probability). If the public card is a King, I will lose (probability = 30% * 60% = 18%). If the public card is a Queen, it will be a draw (probability = 30% * 40% = 12%). If the public card is a Jack, I will win (probability = 30% * 40% = 12%).\n- Overall, the winning rate for plan 1 is 21% + 21% + 12% = 54%, the losing rate is 49% + 18% = 67%, and the draw rate is 12%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (70% probability), he will likely raise (70% probability) or call (30% probability). If the public card is a King, I will lose (probability = 70% * 70% = 49%). If the public card is a Queen, I will win (probability = 70% * 30% = 21%). If the public card is a Jack, I will win (probability = 70% * 30% = 21%).\n- If GoodGuy holds a Queen (30% probability), he will likely fold (60% probability) or call (40% probability). If the public card is a King, I will win (probability = 30% * 60% = 18%). If the public card is a Queen, it will be a draw (probability = 30% * 40% = 12%). If the public card is a Jack, I will win (probability = 30% * 40% = 12%).\n- Overall, the winning rate for plan 2 is 21% + 21% + 18% + 12% = 72%, the losing rate is 49%, and the draw rate is 12%.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot, which is 2 chips. The winning rate for plan 3 is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, chips in the pot: 6. If win, the winning payoff would be 3 chips. If lose, the lose payoff would be 3 chips.\n- Plan 2: After the action, chips in the pot: 8. If win, the winning payoff would be 4 chips. If lose, the lose payoff would be 4 chips.\n- Plan 3: After the action, chips in the pot: 2. If lose, the lose payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected chips gain = winning rate * winning payoff - losing rate * losing payoff = 54% * 3 - 67% * 3 = -0.39 chips.\n- Plan 2: Expected chips gain = winning rate * winning payoff - losing rate * losing payoff = 72% * 4 - 49% * 4 = 0.92 chips.\n- Plan 3: Expected chips gain = -2 chips (since I will lose the chips I have already put in the pot).\n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 2 > Plan 1 > Plan 3.\n- Therefore, I should choose Plan 2: Raise, as it has the highest estimated expected chips gain."}}
{"message": "", "58_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (30% probability), he will likely raise (80%) or call (20%). If he raises, I will lose as his King beats my Queen. If he calls, I will also lose as his King beats my Queen. Therefore, the overall winning rate for this plan is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (30% probability), he will likely raise (70%) or call (30%). If he raises or calls, it will be a draw as we both have Queens. Therefore, the overall winning rate for this plan is 0%, the losing rate is 0%, and the draw rate is 100%.\n- If GoodGuy holds a Jack (40% probability), he will likely check (80%) or fold (20%). If he checks, I will win as my Queen beats his Jack. If he folds, I will also win as he forfeits the game. Therefore, the overall winning rate for this plan is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. Therefore, the overall winning rate for this plan is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King (30% probability), he will likely check (60%) or fold (40%). If he checks, I will lose as his King beats my Queen. If he folds, I will win as he forfeits the game. Therefore, the overall winning rate for this plan is 40%, the losing rate is 60%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (30% probability), he will likely check (70%) or fold (30%). If he checks or folds, it will be a draw as we both have Queens. Therefore, the overall winning rate for this plan is 0%, the losing rate is 0%, and the draw rate is 100%.\n- If GoodGuy holds a Jack (40% probability), he will likely check (80%) or fold (20%). If he checks, I will win as my Queen beats his Jack. If he folds, I will also win as he forfeits the game. Therefore, the overall winning rate for this plan is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 6 chips (half of the pot). If I lose, the losing payoff would be 6 chips.\n- Plan 2: If I fold, I will lose 6 chips.\n- Plan 3: If I win, the winning payoff would be 6 chips. If I lose, the losing payoff would be 6 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0% * 6 chips - 100% * 6 chips = -6 chips\n- Plan 2: Expected Chips Gain = 0% * 6 chips - 100% * 6 chips = -6 chips\n- Plan 3: Expected Chips Gain = 70% * 6 chips - 30% * 6 chips = 2.4 chips\n\nPlan Selection:\n- Plan 1: -6 chips\n- Plan 2: -6 chips\n- Plan 3: 2.4 chips\n\nTherefore, I should choose Plan 3 (Check) as it has the highest expected chips gain."}}
{"message": "", "59_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (35% chance), he will likely raise (70% chance). If the public card is a King or Queen, I will lose. If the public card is a Jack, it will be a draw. Overall, the winning rate is 0%, the losing rate is 70%, and the draw rate is 30%.\n- If GoodGuy holds a Queen (30% chance), he will likely call (60% chance). If the public card is a King, I will lose. If the public card is a Queen or Jack, I will win. Overall, the winning rate is 60%, the losing rate is 40%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (35% chance), he will likely raise (50% chance). If the public card is a King or Queen, I will win. If the public card is a Jack, it will be a draw. Overall, the winning rate is 50%, the losing rate is 0%, and the draw rate is 50%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (35% chance), he will likely raise (70% chance). If the public card is a King or Queen, I will lose. If the public card is a Jack, it will be a draw. Overall, the winning rate is 0%, the losing rate is 70%, and the draw rate is 30%.\n- If GoodGuy holds a Queen (30% chance), he will likely raise (40% chance). If the public card is a King, I will lose. If the public card is a Queen or Jack, I will win. Overall, the winning rate is 60%, the losing rate is 40%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (35% chance), he will likely fold (60% chance). If the public card is a King or Queen, I will win. If the public card is a Jack, it will be a draw. Overall, the winning rate is 60%, the losing rate is 0%, and the draw rate is 40%.\n\nPlan 3: Fold\n- If I fold, I will lose the chips in the pot. The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips. If I lose, the losing payoff would be 1 chip.\n- Plan 2: If I win, the winning payoff would be 7 chips. If I lose, the losing payoff would be 3 chips.\n- Plan 3: If I fold, the losing payoff would be 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.6 * 3 - 0.4 * 1 = 1.4 chips\n- Plan 2: Expected Chips Gain = 0.6 * 7 - 0.4 * 3 = 3.2 chips\n- Plan 3: Expected Chips Gain = 0 - 1 = -1 chip\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I will choose this plan."}}
{"message": "", "59_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (30% probability), he will likely raise (80% probability). If he raises, I will lose as King is higher than my Queen. So, the losing rate for this scenario is 0.3*0.8 = 0.24. \n- If GoodGuy holds a Queen (60% probability), he will likely check (60% probability). If he checks, it will be a draw as we both have a pair of Queens. So, the draw rate for this scenario is 0.6*0.6 = 0.36. \n- If GoodGuy holds a Jack (10% probability), he will likely fold (60% probability). If he folds, I will win. So, the winning rate for this scenario is 0.1*0.6 = 0.06. \n\nPlan 2: Fold\n- If I fold, I will lose regardless of GoodGuy's card. So, the losing rate for this scenario is 1. \n\nPlan 3: Check\n- If GoodGuy holds a King (30% probability), he will likely raise (80% probability). If he raises, I will lose as King is higher than my Queen. So, the losing rate for this scenario is 0.3*0.8 = 0.24. \n- If GoodGuy holds a Queen (60% probability), he will likely check (60% probability). If he checks, it will be a draw as we both have a pair of Queens. So, the draw rate for this scenario is 0.6*0.6 = 0.36. \n- If GoodGuy holds a Jack (10% probability), he will likely check (40% probability). If he checks, I will win as my Queen is higher than his Jack. So, the winning rate for this scenario is 0.1*0.4 = 0.04. \n\nWinning/Lose Payoffs for Each Plan:\n- Plan 1: If I win, the pot will be 12 chips (8 from me, 4 from GoodGuy), so the winning payoff would be 6 chips. If I lose, the pot will be 12 chips, so the losing payoff would be 6 chips. \n- Plan 2: If I fold, I will lose 4 chips. \n- Plan 3: If I win, the pot will be 8 chips (4 from me, 4 from GoodGuy), so the winning payoff would be 4 chips. If I lose, the pot will be 8 chips, so the losing payoff would be 4 chips. \n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected gain = winning rate * winning payoff - losing rate * losing payoff = 0.06*6 - 0.24*6 = -1.08 chips\n- Plan 2: Expected gain = -4 chips (as I will lose regardless)\n- Plan 3: Expected gain = winning rate * winning payoff - losing rate * losing payoff = 0.04*4 - 0.24*4 = -0.8 chips\n\nPlan Selection:\nBased on the expected chips gain, Plan 3 (Check) is the best strategy as it has the highest expected chips gain (-0.8 chips). Plan 1 (Raise) is the second best strategy (-1.08 chips), and Plan 2 (Fold) is the worst strategy (-4 chips). Therefore, I should choose to check in this round."}}
{"message": "", "60_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Jack (30% probability), he will likely fold (70% probability) or check (30% probability) in the second round if the public card is higher. If the public card is a Jack, I will win. If the public card is a Queen or King, it will be a draw or I will lose. Overall, the winning rate is 30%*70% = 21%, the losing rate is 30%*30% = 9%, and the draw rate is 70%.\n- If GoodGuy holds a Queen (50% probability), he will likely fold (60% probability) or check (40% probability) in the second round if the public card is higher. If the public card is a Queen, I will lose. If the public card is a Jack or King, it will be a draw or I will win. Overall, the winning rate is 50%*40% = 20%, the losing rate is 50%*60% = 30%, and the draw rate is 50%.\n- If GoodGuy holds a King (20% probability), he will check in the second round. If the public card is a King, I will lose. If the public card is a Jack or Queen, it will be a draw or I will win. Overall, the winning rate is 20%*50% = 10%, the losing rate is 20%*50% = 10%, and the draw rate is 20%.\n\nPlan 2: Fold\n- If I fold, I will lose the chips in the pot. The losing rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a Jack (30% probability), he will likely fold (70% probability) or check (30% probability) in the second round if the public card is higher. If the public card is a Jack, I will win. If the public card is a Queen or King, it will be a draw or I will lose. Overall, the winning rate is 30%*70% = 21%, the losing rate is 30%*30% = 9%, and the draw rate is 70%.\n- If GoodGuy holds a Queen (50% probability), he will likely fold (60% probability) or check (40% probability) in the second round if the public card is higher. If the public card is a Queen, I will lose. If the public card is a Jack or King, it will be a draw or I will win. Overall, the winning rate is 50%*40% = 20%, the losing rate is 50%*60% = 30%, and the draw rate is 50%.\n- If GoodGuy holds a King (20% probability), he will check in the second round. If the public card is a King, I will lose. If the public card is a Jack or Queen, it will be a draw or I will win. Overall, the winning rate is 20%*50% = 10%, the losing rate is 20%*50% = 10%, and the draw rate is 20%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, Chips in the pot: 6. If win, the winning payoff would be 3. If lose, the lose payoff would be 3.\n- Plan 2: After the action, Chips in the pot: 2. If lose, the lose payoff would be 1.\n- Plan 3: After the action, Chips in the pot: 4. If win, the winning payoff would be 2. If lose, the lose payoff would be 2.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 21%*3 - 9%*3 = 0.36\n- Plan 2: 0 - 100%*1 = -1\n- Plan 3: 21%*2 - 9%*2 = 0.24\n\nPlan Selection:\n- Plan 1: 0.36\n- Plan 2: -1\n- Plan 3: 0.24\n\nBased on the estimated expected chips gains, I should select Plan 1 (Raise) as it has the highest expected chips gain."}}
{"message": "", "60_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Jack, he will likely fold (70% probability). I will win the pot, which is currently 8 chips. The winning rate is 0.7 * 0.2 (probability of him holding a Jack) = 0.14. The lose rate and draw rate are both 0.\n- If GoodGuy holds a Queen, he will likely check (40% probability) or fold (60% probability). I will win the pot if he folds, and lose if he checks. The winning rate is 0.6 * 0.5 = 0.3. The lose rate is 0.4 * 0.5 = 0.2. The draw rate is 0.\n- If GoodGuy holds a King, he will check (100% probability). I will lose the pot. The winning rate is 0. The lose rate is 1 * 0.3 = 0.3. The draw rate is 0.\n- Overall, the winning rate for Plan 1 is 0.44, the lose rate is 0.5, and the draw rate is 0.\n\nPlan 2: Fold\n- If I fold, I will lose the pot regardless of GoodGuy's card. The winning rate is 0. The lose rate is 1. The draw rate is 0.\n\nPlan 3: Check\n- If GoodGuy holds a Jack, he will likely fold (70% probability). I will win the pot. The winning rate is 0.7 * 0.2 = 0.14. The lose rate and draw rate are both 0.\n- If GoodGuy holds a Queen, he will likely check (40% probability) or fold (60% probability). I will win the pot if he folds, and lose if he checks. The winning rate is 0.6 * 0.5 = 0.3. The lose rate is 0.4 * 0.5 = 0.2. The draw rate is 0.\n- If GoodGuy holds a King, he will check (100% probability). I will lose the pot. The winning rate is 0. The lose rate is 1 * 0.3 = 0.3. The draw rate is 0.\n- Overall, the winning rate for Plan 3 is 0.44, the lose rate is 0.5, and the draw rate is 0.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 4 chips. If lose, the lose payoff would be 4 chips.\n- Plan 2: If lose, the lose payoff would be 4 chips.\n- Plan 3: If win, the winning payoff would be 4 chips. If lose, the lose payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0.44 * 4 - 0.5 * 4 = -0.24 chips\n- Plan 2: 0 - 1 * 4 = -4 chips\n- Plan 3: 0.44 * 4 - 0.5 * 4 = -0.24 chips\n\nPlan Selection:\n- Plan 1: -0.24 chips\n- Plan 2: -4 chips\n- Plan 3: -0.24 chips\n\nBased on the estimated expected chips gain, Plan 1 (Raise) and Plan 3 (Check) are the best strategies. However, considering the strategy improvement, I should be more cautious when the public card is higher than my hand. Therefore, I will choose Plan 3 (Check)."}}
{"message": "", "60_5": {"plan": "Plan 1: Call\n- If GoodGuy holds a Jack (30% probability), he will likely fold (70% probability) or check (30% probability). If he folds, I win the pot (70% * 30% = 21% winning rate). If he checks, I lose (30% * 30% = 9% losing rate).\n- If GoodGuy holds a Queen (50% probability), he will likely fold (60% probability) or check (40% probability). If he folds, I win the pot (60% * 50% = 30% winning rate). If he checks, it's a draw (40% * 50% = 20% draw rate).\n- If GoodGuy holds a King (20% probability), he will check (100% probability), and I lose (20% losing rate).\nPlan 1 overall Winning/Lose/Draw rates: Winning rate = 21% + 30% = 51%, Losing rate = 9% + 20% = 29%, Draw rate = 20%.\n\nPlan 2: Raise\n- If GoodGuy holds a Jack (30% probability), he will likely fold (70% probability) or check (30% probability). If he folds, I win the pot (70% * 30% = 21% winning rate). If he checks, I lose (30% * 30% = 9% losing rate).\n- If GoodGuy holds a Queen (50% probability), he will likely fold (60% probability) or check (40% probability). If he folds, I win the pot (60% * 50% = 30% winning rate). If he checks, it's a draw (40% * 50% = 20% draw rate).\n- If GoodGuy holds a King (20% probability), he will check (100% probability), and I lose (20% losing rate).\nPlan 2 overall Winning/Lose/Draw rates: Winning rate = 21% + 30% = 51%, Losing rate = 9% + 20% = 29%, Draw rate = 20%.\n\nPlan 3: Fold\n- If I fold, I lose the pot (100% losing rate).\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the call, chips in the pot: 16. If win, the winning payoff would be 8. If lose, the lose payoff would be 8.\n- Plan 2: After the raise, chips in the pot: 20. If win, the winning payoff would be 10. If lose, the lose payoff would be 10.\n- Plan 3: After the fold, chips in the pot: 12. If lose, the lose payoff would be 6.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 51% * 8 - 29% * 8 = 1.76\n- Plan 2: Expected Chips Gain = 51% * 10 - 29% * 10 = 2.2\n- Plan 3: Expected Chips Gain = -100% * 6 = -6\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain (2.2), followed by Plan 1 (Call) with 1.76, and Plan 3 (Fold) with -6. Therefore, I should choose Plan 2: Raise."}}
{"message": "", "61_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he will likely raise (80% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, it will be a draw. The overall winning rate is 0%, losing rate is 56% (70% * 80%), and drawing rate is 14% (70% * 20%).\n- If GoodGuy holds a Queen (30% probability), he will likely call (70% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, it will be a draw. The overall winning rate is 0%, losing rate is 21% (30% * 70%), and drawing rate is 9% (30% * 30%).\n- Plan 1 overall winning rate is 0%, losing rate is 77%, and drawing rate is 23%. \n- After the action, chips in the pot: 6. If win, the winning payoff would be 3. If lose, the lose payoff would be 3. \n- Expected chips gain for Plan 1: 0 * 3 - 0.77 * 3 = -2.31\n\nPlan 2: Raise\n- If GoodGuy holds a King (70% probability), he will likely raise (80% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, it will be a draw. The overall winning rate is 0%, losing rate is 56% (70% * 80%), and drawing rate is 14% (70% * 20%).\n- If GoodGuy holds a Queen (30% probability), he will likely call (70% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, it will be a draw. The overall winning rate is 0%, losing rate is 21% (30% * 70%), and drawing rate is 9% (30% * 30%).\n- Plan 2 overall winning rate is 0%, losing rate is 77%, and drawing rate is 23%. \n- After the action, chips in the pot: 10. If win, the winning payoff would be 5. If lose, the lose payoff would be 5. \n- Expected chips gain for Plan 2: 0 * 5 - 0.77 * 5 = -3.85\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot, but I will not lose any additional chips. The overall winning rate is 0%, losing rate is 100%, and drawing rate is 0%. \n- After the action, chips in the pot: 2. If win, the winning payoff would be 1. If lose, the lose payoff would be 1. \n- Expected chips gain for Plan 3: 0 * 1 - 1 * 1 = -1\n\nPlan Selection: \n- Plan 1: -2.31\n- Plan 2: -3.85\n- Plan 3: -1\n\nBased on the estimated expected chips gains, Plan 3 (Fold) is the best strategy to minimize the loss in this round."}}
{"message": "", "62_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (probability 0.7), he is likely to raise (probability 0.7). If the public card is a Queen, I will lose. If the public card is a Jack, I will win. If the public card is a King, it will be a draw. Overall, the winning rate is 0.3, the losing rate is 0.4, and the draw rate is 0.3.\n- If GoodGuy holds a Queen (probability 0.6), he is likely to call (probability 0.6). If the public card is a Queen, it will be a draw. If the public card is a King or a Jack, I will win. Overall, the winning rate is 0.4, the losing rate is 0, and the draw rate is 0.6.\n- If GoodGuy holds a Jack (probability 0.5), he is likely to call (probability 0.5). If the public card is a Queen or a King, I will win. If the public card is a Jack, I will lose. Overall, the winning rate is 0.5, the losing rate is 0.5, and the draw rate is 0.\n- Winning Payoff: 3 chips (half of the pot after calling)\n- Losing Payoff: 2 chips (half of the pot before calling)\n- Expected Chips Gain: (0.4 * 3 - 0.3 * 2) + (0.4 * 3 - 0 * 2) + (0.5 * 3 - 0.5 * 2) = 0.8 + 1.2 + 0.5 = 2.5 chips\n\nPlan 2: Raise\n- If GoodGuy holds a King (probability 0.7), he is likely to call (probability 0.3). If the public card is a Queen, I will lose. If the public card is a Jack, I will win. If the public card is a King, it will be a draw. Overall, the winning rate is 0.3, the losing rate is 0.4, and the draw rate is 0.3.\n- If GoodGuy holds a Queen (probability 0.6), he is likely to fold (probability 0.4). If the public card is a Queen, it will be a draw. If the public card is a King or a Jack, I will win. Overall, the winning rate is 0.6, the losing rate is 0, and the draw rate is 0.4.\n- If GoodGuy holds a Jack (probability 0.5), he is likely to fold (probability 0.5). If the public card is a Queen or a King, I will win. If the public card is a Jack, I will lose. Overall, the winning rate is 0.5, the losing rate is 0.5, and the draw rate is 0.\n- Winning Payoff: 5 chips (half of the pot after raising)\n- Losing Payoff: 3 chips (half of the pot before raising)\n- Expected Chips Gain: (0.3 * 5 - 0.4 * 3) + (0.6 * 5 - 0 * 3) + (0.5 * 5 - 0.5 * 3) = 0.5 + 3 + 1 = 4.5 chips\n\nPlan 3: Fold\n- If I fold, I will lose 1 chip (the chip I have already put in the pot).\n- Expected Chips Gain: -1 chip\n\nPlan Selection:\n- Plan 1 Expected Chips Gain: 2.5 chips\n- Plan 2 Expected Chips Gain: 4.5 chips\n- Plan 3 Expected Chips Gain: -1 chip\n\nBased on the expected chips gain, the best strategy is Plan 2: Raise."}}
{"message": "", "62_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (60% probability), he is likely to raise (40%) or call (60%). If he raises, we will have a draw. If he calls, I will win. So, the winning rate is 60%*60%=36%, the draw rate is 60%*40%=24%, and the lose rate is 0%.\n- If GoodGuy holds a Jack (40% probability), he is likely to fold (50%) or call (50%). If he folds, I will win. If he calls, I will also win. So, the winning rate is 40%*100%=40%, the draw rate is 0%, and the lose rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. So, the winning rate is 0%, the draw rate is 0%, and the lose rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a Queen (60% probability), he is likely to raise (40%) or check (60%). If he raises, we will have a draw. If he checks, I will win. So, the winning rate is 60%*60%=36%, the draw rate is 60%*40%=24%, and the lose rate is 0%.\n- If GoodGuy holds a Jack (40% probability), he is likely to fold (50%) or check (50%). If he folds, I will win. If he checks, I will also win. So, the winning rate is 40%*100%=40%, the draw rate is 0%, and the lose rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the raise, chips in the pot would be 16. If win, the winning payoff would be 8. If lose, the lose payoff would be 8.\n- Plan 2: After the fold, chips in the pot would be 8. If lose, the lose payoff would be 4.\n- Plan 3: After the check, chips in the pot would be 8. If win, the winning payoff would be 4. If lose, the lose payoff would be 4.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 76%*8 - 0%*8 = 6.08\n- Plan 2: Expected Chips Gain = 0%*0 - 100%*4 = -4\n- Plan 3: Expected Chips Gain = 76%*4 - 0%*4 = 3.04\n\nPlan Selection:\n- Plan 1: Raise (Expected Chips Gain = 6.08)\n- Plan 3: Check (Expected Chips Gain = 3.04)\n- Plan 2: Fold (Expected Chips Gain = -4)\n\nTherefore, the best plan to execute would be Plan 1: Raise."}}
{"message": "", "63_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he will likely raise (40% probability) or check (60% probability) in the next round. If he raises, I will have a 50% chance of winning (if the public card is a King) or losing (if the public card is a Queen or Jack). If he checks, I will have a 100% chance of winning (as my King is higher than his Queen or Jack). \n- If GoodGuy holds a Queen (30% probability), he will likely check (70% probability) or fold (30% probability) in the next round. If he checks, I will have a 100% chance of winning (as my King is higher than his Queen). If he folds, I will also win. \n\nPlan 2: Raise\n- If GoodGuy holds a King (70% probability), he will likely raise (40% probability) or check (60% probability) in the next round. If he raises, I will have a 50% chance of winning (if the public card is a King) or losing (if the public card is a Queen or Jack). If he checks, I will have a 100% chance of winning (as my King is higher than his Queen or Jack). \n- If GoodGuy holds a Queen (30% probability), he will likely check (70% probability) or fold (30% probability) in the next round. If he checks, I will have a 100% chance of winning (as my King is higher than his Queen). If he folds, I will also win. \n\nPlan 3: Fold\n- If I fold, I will automatically lose the game. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips (half of the pot). If I lose, the losing payoff would be 2 chips (half of the pot). \n- Plan 2: If I win, the winning payoff would be 6 chips (half of the pot). If I lose, the losing payoff would be 3 chips (half of the pot). \n- Plan 3: If I fold, I will lose 2 chips (my initial bet). \n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.7 * (0.4 * 4 - 0.6 * 2) + 0.3 * (0.7 * 4 - 0.3 * 2) = 0.8 chips\n- Plan 2: Expected Chips Gain = 0.7 * (0.4 * 6 - 0.6 * 3) + 0.3 * (0.7 * 6 - 0.3 * 3) = 1.2 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain, so I should choose to raise."}}
{"message": "", "63_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (40% probability), he will likely call (30%). If he calls, it will be a draw. If he folds (70%), I will win. \n- If GoodGuy holds a Queen (60% probability), he will likely raise (70%). If he raises, I will lose. If he folds (30%), I will win. \n\nPlan 1 overall Winning/Lose/Draw rates: \n- Winning rate: 0.4*0.7 + 0.6*0.3 = 0.42\n- Lose rate: 0.6*0.7 = 0.42\n- Draw rate: 0.4*0.3 = 0.12\n\nPlan 2: Fold\n- If I fold, I will lose regardless of GoodGuy's card. \n\nPlan 2 overall Winning/Lose/Draw rates: \n- Winning rate: 0\n- Lose rate: 1\n- Draw rate: 0\n\nPlan 3: Check\n- If GoodGuy holds a King (40% probability), he will likely raise (80%). If he raises, it will be a draw. If he checks (20%), it will be a draw. \n- If GoodGuy holds a Queen (60% probability), he will likely check (30%). If he checks, I will lose. If he raises (70%), I will lose. \n\nPlan 3 overall Winning/Lose/Draw rates: \n- Winning rate: 0\n- Lose rate: 0.6*0.3 + 0.6*0.7 = 0.6\n- Draw rate: 0.4*0.8 + 0.4*0.2 = 0.4\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, Chips in the pot: 14. If win, the winning payoff would be 7. If lose, the lose payoff would be 7.\n- Plan 2: After the action, Chips in the pot: 6. If lose, the lose payoff would be 3.\n- Plan 3: After the action, Chips in the pot: 6. If lose, the lose payoff would be 3.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0.42*7 - 0.42*7 = 0\n- Plan 2: 0 - 1*3 = -3\n- Plan 3: 0 - 0.6*3 = -1.8\n\nPlan Selection:\n- Plan 1: 0\n- Plan 2: -3\n- Plan 3: -1.8\n\nBased on the estimated expected chips gains, Plan 1 (Raise) is the best strategy."}}
{"message": "", "64_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (40% probability), he is likely to raise (70%) or call (30%). If he raises, I will lose unless the public card is a Jack. If he calls, the outcome will depend on the public card. The estimated winning rate is 12% (0.4*0.3), the losing rate is 28% (0.4*0.7), and the draw rate is 0%.\n- If GoodGuy holds a Queen (40% probability), he is likely to raise (40%) or call (60%). If he raises, I will lose unless the public card is a Jack. If he calls, the outcome will depend on the public card. The estimated winning rate is 24% (0.4*0.6), the losing rate is 16% (0.4*0.4), and the draw rate is 0%.\n- If GoodGuy holds a Jack (20% probability), he is likely to call (70%) or raise (30%). If he raises, it will be a draw. If he calls, the outcome will depend on the public card. The estimated winning rate is 14% (0.2*0.7), the losing rate is 0%, and the draw rate is 6% (0.2*0.3).\n- The overall winning rate for Plan 1 is 50%, the losing rate is 44%, and the draw rate is 6%. If I win, the pot will be 4 chips, so the winning payoff would be 2 chips. If I lose, the pot will be 4 chips, so the losing payoff would be 2 chips. The expected chips gain for Plan 1 is 0.12 chips (0.5*2 - 0.44*2).\n\nPlan 2: Raise\n- If GoodGuy holds a King (40% probability), he is likely to raise (70%) or call (30%). If he raises, I will lose unless the public card is a Jack. If he calls, the outcome will depend on the public card. The estimated winning rate is 12% (0.4*0.3), the losing rate is 28% (0.4*0.7), and the draw rate is 0%.\n- If GoodGuy holds a Queen (40% probability), he is likely to raise (40%) or call (60%). If he raises, I will lose unless the public card is a Jack. If he calls, the outcome will depend on the public card. The estimated winning rate is 24% (0.4*0.6), the losing rate is 16% (0.4*0.4), and the draw rate is 0%.\n- If GoodGuy holds a Jack (20% probability), he is likely to fold (50%) or call (50%). If he folds, I will win. If he calls, it will be a draw. The estimated winning rate is 10% (0.2*0.5), the losing rate is 0%, and the draw rate is 10% (0.2*0.5).\n- The overall winning rate for Plan 2 is 46%, the losing rate is 44%, and the draw rate is 10%. If I win, the pot will be 6 chips, so the winning payoff would be 3 chips. If I lose, the pot will be 6 chips, so the losing payoff would be 3 chips. The expected chips gain for Plan 2 is 0.06 chips (0.46*3 - 0.44*3).\n\nPlan 3: Fold\n- If I fold, I will lose the 1 chip I have already put in the pot. The expected chips gain for Plan 3 is -1 chip.\n\nPlan Selection:\n- Plan 1: Expected chips gain is 0.12 chips.\n- Plan 2: Expected chips gain is 0.06 chips.\n- Plan 3: Expected chips gain is -1 chip.\n- Therefore, I should choose Plan 1 (Call), which has the highest expected chips gain."}}
{"message": "", "64_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (probability 33%), he will likely raise (80%) or call (20%). If he raises, I will lose (probability 100%). If he calls, I will lose (probability 100%). Overall, the winning rate is 0%, the losing rate is 33%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (probability 33%), he will likely call (60%) or raise (40%). If he calls, I will lose (probability 100%). If he raises, I will lose (probability 100%). Overall, the winning rate is 0%, the losing rate is 33%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (probability 33%), he will likely fold (60%) or call (40%). If he folds, I will win (probability 100%). If he calls, it will be a draw (probability 100%). Overall, the winning rate is 20%, the losing rate is 0%, and the draw rate is 13%.\n\nPlan 2: Fold\n- If I fold, I will lose the current pot. The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King (probability 33%), he will likely raise (80%) or check (20%). If he raises, I will lose (probability 100%). If he checks, I will lose (probability 100%). Overall, the winning rate is 0%, the losing rate is 33%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (probability 33%), he will likely check (70%) or call (30%). If he checks, I will lose (probability 100%). If he calls, I will lose (probability 100%). Overall, the winning rate is 0%, the losing rate is 33%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (probability 33%), he will likely check (70%) or call (30%). If he checks, it will be a draw (probability 100%). If he calls, it will be a draw (probability 100%). Overall, the winning rate is 0%, the losing rate is 0%, and the draw rate is 33%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, Chips in the pot: 4. If win, the winning payoff would be 2. If lose, the lose payoff would be 2.\n- Plan 2: After the action, Chips in the pot: 2. If win, the winning payoff would be 1. If lose, the lose payoff would be 1.\n- Plan 3: After the action, Chips in the pot: 2. If win, the winning payoff would be 1. If lose, the lose payoff would be 1.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 20% * 2 - 66% * 2 = -0.92\n- Plan 2: Expected Chips Gain = 0% * 1 - 100% * 1 = -1\n- Plan 3: Expected Chips Gain = 0% * 1 - 66% * 1 = -0.66\n\nPlan Selection:\n- Plan 1: Rank 2\n- Plan 2: Rank 3\n- Plan 3: Rank 1\n\nTherefore, I should choose Plan 3: Check, as it has the highest estimated expected chips gain."}}
{"message": "", "65_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (30% probability), he will likely raise (70%) or call (30%). If he raises, I will lose unless the public card is a Jack. If he calls, I will win if the public card is a Jack, and lose otherwise. Overall, my winning rate is 15%, losing rate is 85%, and drawing rate is 0%.\n- If GoodGuy holds a Queen (20% probability), he will likely call (60%) or raise (40%). If he calls, I will win if the public card is a Jack, and lose otherwise. If he raises, I will lose unless the public card is a Jack. Overall, my winning rate is 12%, losing rate is 88%, and drawing rate is 0%.\n- If GoodGuy holds a Jack (50% probability), he will likely call (50%) or raise (50%). In either case, the game will be a draw unless the public card is a King or Queen. Overall, my winning rate is 0%, losing rate is 0%, and drawing rate is 100%.\n\nPlan 2: Fold\n- If I fold, I will lose the 2 chips in the pot regardless of GoodGuy's card or action. My winning rate is 0%, losing rate is 100%, and drawing rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King (30% probability), he will likely raise (70%) or check (30%). If he raises, I will lose unless the public card is a Jack. If he checks, the game will be a draw unless the public card is a King or Queen. Overall, my winning rate is 21%, losing rate is 49%, and drawing rate is 30%.\n- If GoodGuy holds a Queen (20% probability), he will likely raise (40%) or check (60%). If he raises, I will lose unless the public card is a Jack. If he checks, the game will be a draw unless the public card is a King or Jack. Overall, my winning rate is 24%, losing rate is 36%, and drawing rate is 40%.\n- If GoodGuy holds a Jack (50% probability), he will likely raise (50%) or check (50%). In either case, the game will be a draw unless the public card is a King or Queen. Overall, my winning rate is 0%, losing rate is 0%, and drawing rate is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips. If I lose, the losing payoff would be 2 chips.\n- Plan 2: If I fold, I will lose 2 chips.\n- Plan 3: If I win, the winning payoff would be 2 chips. If I lose, the losing payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 15% * 4 - 85% * 2 = -1.1 chips\n- Plan 2: Expected Chips Gain = 0% * 0 - 100% * 2 = -2 chips\n- Plan 3: Expected Chips Gain = 45% * 2 - 85% * 2 = -0.8 chips\n\nPlan Selection:\n- Plan 1: -1.1 chips\n- Plan 2: -2 chips\n- Plan 3: -0.8 chips\n\nBased on the estimated expected chips gain, Plan 3 (Check) is the best strategy to use in this situation."}}
{"message": "", "65_3": {"plan": "Plan 1: Call\n- If GoodGuy holds a Queen (60% probability), he will likely raise (80% probability). If this happens, I will lose as his pair of Queens beats my single Jack. The overall losing rate for this scenario is 60% * 80% = 48%.\n- If GoodGuy holds a King (30% probability), he will likely check (60% probability). If this happens, I will lose as his King beats my Jack. The overall losing rate for this scenario is 30% * 60% = 18%.\n- If GoodGuy holds a Jack (10% probability), he will likely raise (70% probability). If this happens, it will be a draw as we both have a single Jack. The overall draw rate for this scenario is 10% * 70% = 7%.\n\nPlan 2: Raise\n- If GoodGuy holds a Queen (60% probability), he will likely raise (80% probability). If this happens, I will lose as his pair of Queens beats my single Jack. The overall losing rate for this scenario is 60% * 80% = 48%.\n- If GoodGuy holds a King (30% probability), he will likely check (60% probability). If this happens, I will lose as his King beats my Jack. The overall losing rate for this scenario is 30% * 60% = 18%.\n- If GoodGuy holds a Jack (10% probability), he will likely raise (70% probability). If this happens, it will be a draw as we both have a single Jack. The overall draw rate for this scenario is 10% * 70% = 7%.\n\nPlan 3: Fold\n- If I fold, I will lose the 2 chips I have already put into the pot. However, I will not lose any more chips in this round.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, chips in the pot: 8. If win, the winning payoff would be 4. If lose, the lose payoff would be 4.\n- Plan 2: After the action, chips in the pot: 14. If win, the winning payoff would be 7. If lose, the lose payoff would be 7.\n- Plan 3: After the action, chips in the pot: 2. If win, the winning payoff would be 1. If lose, the lose payoff would be 1.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0 * Winning Rate - 4 * Losing Rate = -4 * 66% = -2.64 chips\n- Plan 2: Expected Chips Gain = 0 * Winning Rate - 7 * Losing Rate = -7 * 66% = -4.62 chips\n- Plan 3: Expected Chips Gain = 0 * Winning Rate - 1 * Losing Rate = -1 * 100% = -1 chip\n\nPlan Selection:\n- Plan 1: -2.64 chips\n- Plan 2: -4.62 chips\n- Plan 3: -1 chip\n\nBased on the expected chips gain, Plan 3 (Fold) is the best strategy in this situation."}}
{"message": "", "66_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (35% chance), he will likely raise (70% chance). If the public card is a King or a Queen, I will lose. If the public card is a Jack, it will be a draw. Overall, the winning rate is 0%, the losing rate is 70%, and the draw rate is 30%.\n- If GoodGuy holds a Queen (20% chance), he will likely call (60% chance) or raise (40% chance). If the public card is a King, I will lose. If the public card is a Queen or a Jack, it will be a draw. Overall, the winning rate is 0%, the losing rate is 40%, and the draw rate is 60%.\n- If GoodGuy holds a Jack (25% chance), he will likely raise (50% chance) or call (50% chance). If the public card is a King or a Queen, I will win. If the public card is a Jack, it will be a draw. Overall, the winning rate is 50%, the losing rate is 0%, and the draw rate is 50%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (35% chance), he will likely raise (70% chance). If the public card is a King or a Queen, I will lose. If the public card is a Jack, it will be a draw. Overall, the winning rate is 0%, the losing rate is 70%, and the draw rate is 30%.\n- If GoodGuy holds a Queen (20% chance), he will likely call (60% chance) or raise (40% chance). If the public card is a King, I will lose. If the public card is a Queen or a Jack, it will be a draw. Overall, the winning rate is 0%, the losing rate is 40%, and the draw rate is 60%.\n- If GoodGuy holds a Jack (25% chance), he will likely raise (50% chance) or call (50% chance). If the public card is a King or a Queen, I will win. If the public card is a Jack, it will be a draw. Overall, the winning rate is 50%, the losing rate is 0%, and the draw rate is 50%.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot. The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips. If I lose, the losing payoff would be 1 chip.\n- Plan 2: If I win, the winning payoff would be 7 chips. If I lose, the losing payoff would be 5 chips.\n- Plan 3: If I fold, I will lose 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0% * 3 - 70% * 1 = -0.7 chips\n- Plan 2: 0% * 7 - 70% * 5 = -3.5 chips\n- Plan 3: 0% * 0 - 100% * 1 = -1 chip\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain (-0.7 chips), followed by Plan 3 (-1 chip), and Plan 2 (-3.5 chips). Therefore, I should choose Plan 1: Call."}}
{"message": "", "66_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (30% probability), he will likely raise (80% probability). If he raises, I will lose as his pair of Kings beats my single Queen. If he checks (20% probability), I will also lose as his King beats my Queen. Therefore, the overall losing rate for this plan if GoodGuy holds a King is 100%.\n- If GoodGuy holds a Queen (40% probability), he will likely check (60% probability). If he checks, I will win as my Queen beats his Queen. If he folds (40% probability), I will also win. Therefore, the overall winning rate for this plan if GoodGuy holds a Queen is 100%.\n- If GoodGuy holds a Jack (30% probability), he will likely check (60% probability). If he checks, I will win as my Queen beats his Jack. If he folds (40% probability), I will also win. Therefore, the overall winning rate for this plan if GoodGuy holds a Jack is 100%.\n\nPlan 1 overall Winning/Lose/Draw rates: \n- Winning rate for plan 1: 70% (30% King probability * 0% win rate + 40% Queen probability * 100% win rate + 30% Jack probability * 100% win rate)\n- Lose rate for plan 1: 30% (30% King probability * 100% lose rate + 40% Queen probability * 0% lose rate + 30% Jack probability * 0% lose rate)\n- Draw rate for plan 1: 0%\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. Therefore, the overall losing rate for this plan is 100%.\n\nPlan 2 overall Winning/Lose/Draw rates: \n- Winning rate for plan 2: 0%\n- Lose rate for plan 2: 100%\n- Draw rate for plan 2: 0%\n\nPlan 3: Check\n- This plan has the same outcomes as Plan 1 because GoodGuy's actions do not change based on whether I raise or check.\n\nPlan 3 overall Winning/Lose/Draw rates: \n- Winning rate for plan 3: 70%\n- Lose rate for plan 3: 30%\n- Draw rate for plan 3: 0%\n\nWinning/Lose Payoffs for Each Plan:\n- Plan 1: If I win, the winning payoff would be 4 chips (half of the 8 chips in the pot). If I lose, the losing payoff would be 4 chips.\n- Plan 2: If I fold, there is no winning payoff and the losing payoff would be 2 chips (the chips I have already put in the pot).\n- Plan 3: If I win, the winning payoff would be 2 chips (half of the 4 chips in the pot). If I lose, the losing payoff would be 2 chips.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: 70% * 4 chips - 30% * 4 chips = 1.6 chips\n- Plan 2: 0% * 0 chips - 100% * 2 chips = -2 chips\n- Plan 3: 70% * 2 chips - 30% * 2 chips = 0.8 chips\n\nPlan Selection:\n- Plan 1: 1.6 chips\n- Plan 2: -2 chips\n- Plan 3: 0.8 chips\n\nTherefore, I should choose Plan 1 (Raise) as it has the highest expected chips gain."}}
{"message": "", "66_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he will likely raise (80% probability). If this happens, I will lose as his King pair is higher than my Queen. The overall losing rate for this scenario is 56% (0.7*0.8).\n- If GoodGuy holds a Queen (20% probability), he will likely check (60% probability). If this happens, I will win as my Queen is higher than his Jack. The overall winning rate for this scenario is 12% (0.2*0.6).\n- If GoodGuy holds a Jack (10% probability), he will likely fold (40% probability). If this happens, I will win as my Queen is higher than his Jack. The overall winning rate for this scenario is 4% (0.1*0.4).\n\nPlan 1 overall Winning/Lose/Draw rates: \n- Winning rate: 16% (12% + 4%)\n- Losing rate: 56%\n- Draw rate: 28% (100% - 16% - 56%)\n\nPlan 2: Fold\n- If I fold, I will lose the chips I have already put in the pot. However, I will not lose any additional chips. The overall losing rate for this scenario is 100%.\n\nPlan 2 overall Winning/Lose/Draw rates: \n- Winning rate: 0%\n- Losing rate: 100%\n- Draw rate: 0%\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the pot, which is currently 16 chips (half of 32 chips). If I lose, the losing payoff would be the 6 chips I have already put in the pot.\n- Plan 2: If I fold, I will lose the 6 chips I have already put in the pot. There is no winning payoff for this plan.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is the winning rate times the winning payoff minus the losing rate times the losing payoff, which is 16% * 16 chips - 56% * 6 chips = -1.04 chips.\n- Plan 2: The expected chips gain is the winning rate times the winning payoff minus the losing rate times the losing payoff, which is 0% * 0 chips - 100% * 6 chips = -6 chips.\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain (-1.04 chips) than Plan 2 (-6 chips). Therefore, I should choose Plan 1: Call."}}
{"message": "", "67_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a Jack (60% probability), he might raise (60% probability) or call (40% probability). If he raises, I will lose unless the public card is a Jack. If he calls, the game will be decided by the public card. The winning rate is 24% (60%*40%), the losing rate is 36% (60%*60%), and the draw rate is 0%.\n- If GoodGuy holds a Queen (70% probability), he might raise (30% probability) or call (70% probability). If he raises, I will lose unless the public card is a Jack. If he calls, the game will be decided by the public card. The winning rate is 49% (70%*70%), the losing rate is 21% (70%*30%), and the draw rate is 0%.\n- If GoodGuy holds a King (20% probability), he might raise (80% probability) or call (20% probability). If he raises, I will lose unless the public card is a Jack. If he calls, the game will be decided by the public card. The winning rate is 4% (20%*20%), the losing rate is 16% (20%*80%), and the draw rate is 0%.\n\nPlan 1 overall Winning/Lose/Draw rates: Winning rate is 77%, Losing rate is 73%, and Draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a Jack (60% probability), he might raise (60% probability) or call (40% probability). If he raises, I will lose unless the public card is a Jack. If he calls, the game will be decided by the public card. The winning rate is 24% (60%*40%), the losing rate is 36% (60%*60%), and the draw rate is 0%.\n- If GoodGuy holds a Queen (70% probability), he might raise (30% probability) or call (70% probability). If he raises, I will lose unless the public card is a Jack. If he calls, the game will be decided by the public card. The winning rate is 49% (70%*70%), the losing rate is 21% (70%*30%), and the draw rate is 0%.\n- If GoodGuy holds a King (20% probability), he might raise (80% probability) or call (20% probability). If he raises, I will lose unless the public card is a Jack. If he calls, the game will be decided by the public card. The winning rate is 4% (20%*20%), the losing rate is 16% (20%*80%), and the draw rate is 0%.\n\nPlan 2 overall Winning/Lose/Draw rates: Winning rate is 77%, Losing rate is 73%, and Draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the game. The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, Chips in the pot: 3. If win, the winning payoff would be 1.5. If lose, the lose payoff would be 1.5.\n- Plan 2: After the action, Chips in the pot: 5. If win, the winning payoff would be 2.5. If lose, the lose payoff would be 2.5.\n- Plan 3: After the action, Chips in the pot: 1. If win, the winning payoff would be 0.5. If lose, the lose payoff would be 0.5.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 77% * 1.5 - 73% * 1.5 = 0.06\n- Plan 2: Expected Chips Gain = 77% * 2.5 - 73% * 2.5 = 0.1\n- Plan 3: Expected Chips Gain = 0% * 0.5 - 100% * 0.5 = -0.5\n\nPlan Selection:\n- Plan 2 (Raise) has the highest estimated expected chips gain, so I will choose Plan 2."}}
{"message": "", "67_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Jack, he will likely fold with an 80% probability. This would result in a win for me, as my Jack would beat his. The winning rate for this scenario is 0.8 * 0.3 (probability he has a Jack) = 0.24.\n- If GoodGuy holds a Queen, he will likely raise with a 70% probability. This would result in a loss for me, as his Queen would beat my Jack. The losing rate for this scenario is 0.7 * 0.7 (probability he has a Queen) = 0.49.\n- If GoodGuy holds a King, he will likely raise with a 90% probability. This would result in a loss for me, as his King would beat my Jack. The losing rate for this scenario is 0.9 * 0.2 (probability he has a King) = 0.18.\n\nPlan 2: Fold\n- If I fold, I will lose the chips I have already put in the pot, but I will not lose any more chips. The losing rate for this scenario is 1, as I will definitely lose.\n\nPlan 3: Check\n- If GoodGuy holds a Jack, he will likely fold with an 80% probability. This would result in a win for me, as my Jack would beat his. The winning rate for this scenario is 0.8 * 0.3 (probability he has a Jack) = 0.24.\n- If GoodGuy holds a Queen, he will likely raise with a 70% probability. This would result in a loss for me, as his Queen would beat my Jack. The losing rate for this scenario is 0.7 * 0.7 (probability he has a Queen) = 0.49.\n- If GoodGuy holds a King, he will likely raise with a 90% probability. This would result in a loss for me, as his King would beat my Jack. The losing rate for this scenario is 0.9 * 0.2 (probability he has a King) = 0.18.\n\nWinning/Losing Payoffs:\n- Plan 1: If I win, the pot would be 8 chips, so the winning payoff would be 4 chips. If I lose, the pot would be 8 chips, so the losing payoff would be 4 chips.\n- Plan 2: If I fold, I would lose the 4 chips I have already put in the pot.\n- Plan 3: If I win, the pot would be 8 chips, so the winning payoff would be 4 chips. If I lose, the pot would be 8 chips, so the losing payoff would be 4 chips.\n\nExpected Chips Gain:\n- Plan 1: Expected gain = 0.24 * 4 - 0.67 * 4 = -1.72 chips\n- Plan 2: Expected gain = -4 chips\n- Plan 3: Expected gain = 0.24 * 4 - 0.67 * 4 = -1.72 chips\n\nPlan Selection:\n- Plan 1: Rank 2\n- Plan 2: Rank 3\n- Plan 3: Rank 1\n\nBased on the expected chips gain, I should choose Plan 3: Check. This plan has the highest expected chips gain and aligns with my strategy improvement of being more cautious when holding a Jack."}}
{"message": "", "68_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% chance), he is likely to raise (70%) or call (30%). If he raises, I will lose (100%). If he calls, I will win if the public card is a Jack (33.3%), draw if it's a Queen (33.3%), and lose if it's a King (33.3%). Overall, my winning rate is 10%, losing rate is 76.7%, and drawing rate is 10%.\n- If GoodGuy holds a Queen (30% chance), he is likely to raise (40%) or call (60%). If he raises, I will lose (100%). If he calls, I will win if the public card is a Jack (33.3%), draw if it's a Queen (33.3%), and lose if it's a King (33.3%). Overall, my winning rate is 6%, losing rate is 18%, and drawing rate is 6%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (70% chance), he is likely to fold (30%) or call (70%). If he folds, I will win (100%). If he calls, I will lose (100%). Overall, my winning rate is 21%, losing rate is 49%, and drawing rate is 0%.\n- If GoodGuy holds a Queen (30% chance), he is likely to fold (60%) or call (40%). If he folds, I will win (100%). If he calls, I will lose (100%). Overall, my winning rate is 18%, losing rate is 12%, and drawing rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose 100% of the time.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 3 chips. If lose, the lose payoff would be 2 chips.\n- Plan 2: If win, the winning payoff would be 5 chips. If lose, the lose payoff would be 4 chips.\n- Plan 3: If lose, the lose payoff would be 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 10% * 3 - 76.7% * 2 = -1.27 chips\n- Plan 2: Expected Chips Gain = 39% * 5 - 61% * 4 = -0.05 chips\n- Plan 3: Expected Chips Gain = -1 chip\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain, so I will choose to raise."}}
