{"message": "", "1_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (30% probability), he will likely raise (70% probability). If the public card is a King, I will lose (probability 1/3). If the public card is a Queen or Jack, I will win (probability 2/3). Overall, the winning rate is 0.3*0.7*2/3=14%, the losing rate is 0.3*0.7*1/3=7%.\n- If GoodGuy holds a Queen (40% probability), he will likely call (60% probability). If the public card is a Queen, it will be a draw (probability 1/3). If the public card is a King or Jack, I will win (probability 2/3). Overall, the winning rate is 0.4*0.6*2/3=16%, the draw rate is 0.4*0.6*1/3=8%.\n- If GoodGuy holds a Jack (30% probability), he will likely call (70% probability). If the public card is a Jack, I will lose (probability 1/3). If the public card is a Queen or King, I will win (probability 2/3). Overall, the winning rate is 0.3*0.7*2/3=14%, the losing rate is 0.3*0.7*1/3=7%.\n- The overall winning rate for plan 1 is 14%+16%+14%=44%, the overall losing rate is 7%+7%=14%, and the draw rate is 8%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (30% probability), he will likely call (30% probability). If the public card is a King, I will lose (probability 1/3). If the public card is a Queen or Jack, I will win (probability 2/3). Overall, the winning rate is 0.3*0.3*2/3=6%, the losing rate is 0.3*0.3*1/3=3%.\n- If GoodGuy holds a Queen (40% probability), he will likely raise (40% probability). If the public card is a Queen, it will be a draw (probability 1/3). If the public card is a King or Jack, I will win (probability 2/3). Overall, the winning rate is 0.4*0.4*2/3=11%, the draw rate is 0.4*0.4*1/3=5%.\n- If GoodGuy holds a Jack (30% probability), he will likely call (30% probability). If the public card is a Jack, I will lose (probability 1/3). If the public card is a Queen or King, I will win (probability 2/3). Overall, the winning rate is 0.3*0.3*2/3=6%, the losing rate is 0.3*0.3*1/3=3%.\n- The overall winning rate for plan 2 is 6%+11%+6%=23%, the overall losing rate is 3%+3%=6%, and the draw rate is 5%.\n\nPlan 3: Fold\n- If I fold, I will lose all the chips I have put into the pot. The overall 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 half of the pot (6 chips). If I lose, the losing payoff would be half of the pot (6 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 half of the pot (8 chips).\n- Plan 3: If I fold, 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: 44% * 6 chips - 14% * 6 chips = 1.8 chips\n- Plan 2: 23% * 8 chips - 6% * 8 chips = 1.36 chips\n- Plan 3: -2 chips\n\nPlan Selection:\n- Plan 1 has the highest estimated expected chips gain, so I should choose to call."}}
{"message": "", "1_3": {"plan": "Plan 1: Call\nIf I call, I will match my opponent's bet of 8 chips, bringing the total chips in the pot to 20. \n\n- If GoodGuy holds a King (probability 30%), he will likely raise (probability 100%). If he raises, the total chips in the pot will be 28. If I win, the winning payoff would be 14 chips. If I lose, the losing payoff would be 14 chips. The winning rate is 0 (since my Queen does not match the public King), the losing rate is 1, and the draw rate is 0. \n- If GoodGuy holds a Queen (probability 60%), he will likely call (probability 50%) or fold (probability 50%). If he calls, the total chips in the pot will be 20. If I win, the winning payoff would be 10 chips. If I lose, the losing payoff would be 10 chips. The winning rate is 0.5 (since we both hold Queens), the losing rate is 0, and the draw rate is 0.5. \n- If GoodGuy holds a Jack (probability 70%), he will likely call (probability 50%) or fold (probability 50%). If he calls, the total chips in the pot will be 20. If I win, the winning payoff would be 10 chips. If I lose, the losing payoff would be 10 chips. The winning rate is 1 (since my Queen is higher than his Jack), the losing rate is 0, and the draw rate is 0. \n\nPlan 1 overall Winning/Lose/Draw rates: \n- Winning rate: 0.3*0 + 0.6*0.5 + 0.7*1 = 0.9\n- Losing rate: 0.3*1 + 0.6*0 + 0.7*0 = 0.3\n- Draw rate: 0.3*0 + 0.6*0.5 + 0.7*0 = 0.3\n\nPlan 2: Raise\nIf I raise, I will increase the bet by 4 chips, bringing my total contribution to 12 chips and the total chips in the pot to 24. \n\n- If GoodGuy holds a King (probability 30%), he will likely raise (probability 100%). If he raises, the total chips in the pot will be 32. If I win, the winning payoff would be 16 chips. If I lose, the losing payoff would be 16 chips. The winning rate is 0, the losing rate is 1, and the draw rate is 0. \n- If GoodGuy holds a Queen (probability 60%), he will likely call (probability 50%) or fold (probability 50%). If he calls, the total chips in the pot will be 28. If I win, the winning payoff would be 14 chips. If I lose, the losing payoff would be 14 chips. The winning rate is 0.5, the losing rate is 0, and the draw rate is 0.5. \n- If GoodGuy holds a Jack (probability 70%), he will likely call (probability 50%) or fold (probability 50%). If he calls, the total chips in the pot will be 28. If I win, the winning payoff would be 14 chips. If I lose, the losing payoff would be 14 chips. The winning rate is 1, the losing rate is 0, and the draw rate is 0. \n\nPlan 2 overall Winning/Lose/Draw rates: \n- Winning rate: 0.3*0 + 0.6*0.5 + 0.7*1 = 0.9\n- Losing rate: 0.3*1 + 0.6*0 + 0.7*0 = 0.3\n- Draw rate: 0.3*0 + 0.6*0.5 + 0.7*0 = 0.3\n\nPlan 3: Fold\nIf I fold, I will forfeit the round and lose my contribution of 4 chips. The winning rate, losing rate, and draw rate are all 0. \n\nEstimated Expected Chips Gain for Each Plan:\n- Plan 1: 0.9*10 - 0.3*10 = 6 chips\n- Plan 2: 0.9*14 - 0.3*14 = 8.4 chips\n- Plan 3: 0 - 4 = -4 chips\n\nPlan Selection:\nBased on the estimated expected chips gains, Plan 2 (Raise) is the best strategy with the highest expected gain of 8.4 chips. Plan 1 (Call) is the second best strategy with an expected gain of 6 chips. Plan 3 (Fold) is the worst strategy with an expected loss of 4 chips. Therefore, I should execute Plan 2 and raise the bet."}}
{"message": "", "2_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (80% probability), he will likely call if I raise (80% probability). If the public card is a King, I will win (probability = 0.8 * 0.8 = 0.64). If the public card is not a King, it will be a draw (probability = 0.8 * 0.2 = 0.16).\n- If GoodGuy holds a Queen (15% probability), he will likely call if I raise (60% probability). Regardless of the public card, I will win (probability = 0.15 * 0.6 = 0.09).\n- If GoodGuy holds a Jack (5% probability), he will likely fold if I raise (70% probability). Regardless of the public card, I will win (probability = 0.05 * 0.7 = 0.035).\n- Overall, the winning rate for Plan 1 is 0.64 + 0.09 + 0.035 = 0.765, the losing rate is 0, and the draw rate is 0.16.\n\nPlan 2: Raise\n- If GoodGuy holds a King (80% probability), he will likely call if I raise (80% probability). If the public card is a King, I will win (probability = 0.8 * 0.8 = 0.64). If the public card is not a King, it will be a draw (probability = 0.8 * 0.2 = 0.16).\n- If GoodGuy holds a Queen (15% probability), he will likely fold if I raise significantly (40% probability). Regardless of the public card, I will win (probability = 0.15 * 0.4 = 0.06).\n- If GoodGuy holds a Jack (5% probability), he will likely fold if I raise (70% probability). Regardless of the public card, I will win (probability = 0.05 * 0.7 = 0.035).\n- Overall, the winning rate for Plan 2 is 0.64 + 0.06 + 0.035 = 0.735, the losing rate is 0, and the draw rate is 0.16.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of GoodGuy's card or the public card. The losing rate is 1, 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 half of the pot (6 chips). If I lose, the lose payoff would be half of the pot (6 chips).\n- Plan 2: If I win, the winning payoff would be half of the pot (8 chips). If I lose, the lose payoff would be half of the pot (8 chips).\n- Plan 3: If I lose, the lose payoff would be half of the pot (6 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.765 * 6 - 0 * 6 = 4.59 chips\n- Plan 2: Expected Chips Gain = 0.735 * 8 - 0 * 8 = 5.88 chips\n- Plan 3: Expected Chips Gain = 0 * 6 - 1 * 6 = -6 chips\n\nPlan Selection:\n- Plan 1: 4.59 chips\n- Plan 2: 5.88 chips\n- Plan 3: -6 chips\n\nBased on the estimated expected chips gains, Plan 2 (Raise) is the best strategy to use in this situation."}}
{"message": "", "2_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (40% probability), he will likely call (10% probability). If he calls, I will win because my King is higher than the public Jack. So, the winning rate for this plan is 40% * 10% = 4%.\n- If GoodGuy holds a Queen (60% probability), he will likely fold (30% probability). If he folds, I will win because he forfeits the game. So, the winning rate for this plan is 60% * 30% = 18%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. So, the losing rate for this plan is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (40% probability), he will likely call (10% probability). If he calls, I will win because my King is higher than the public Jack. So, the winning rate for this plan is 40% * 10% = 4%.\n- If GoodGuy holds a Queen (60% probability), he will likely call (70% probability). If he calls, I will win because my King is higher than his Queen. So, the winning rate for this plan is 60% * 70% = 42%.\n\nThe number of winning and 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\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 4% * 7 - 96% * 7 = -6.44\n- Plan 2: Expected Chips Gain = 0% * 3 - 100% * 3 = -3\n- Plan 3: Expected Chips Gain = 46% * 3 - 54% * 3 = -0.24\n\nPlan Selection:\n- Plan 3 (Check) has the highest expected chips gain (-0.24), followed by Plan 2 (Fold) (-3), and Plan 1 (Raise) (-6.44). Therefore, I should choose Plan 3 (Check)."}}
{"message": "", "2_5": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (probability 85%), he might raise (probability 90%) or call (probability 10%). If he raises, I will lose (probability 100%) because his King matches the public card. If he calls, I will win (probability 100%) because my King is higher than the public Jack. Overall, the winning rate for his King is 8.5% (85% * 10%), the losing rate is 76.5% (85% * 90%), and the draw rate is 0%.\n- If GoodGuy holds a Queen (probability 15%), he might fold (probability 30%) or call (probability 70%). If he folds, I will win (probability 100%) because my King is higher than the public Jack. If he calls, I will win (probability 100%) because my King is higher than his Queen. Overall, the winning rate for his Queen is 15% (15% * 100%), the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (probability 85%), he might raise (probability 90%) or call (probability 10%). If he raises, I will lose (probability 100%) because his King matches the public card. If he calls, I will win (probability 100%) because my King is higher than the public Jack. Overall, the winning rate for his King is 8.5% (85% * 10%), the losing rate is 76.5% (85% * 90%), and the draw rate is 0%.\n- If GoodGuy holds a Queen (probability 15%), he might fold (probability 30%) or call (probability 70%). If he folds, I will win (probability 100%) because my King is higher than the public Jack. If he calls, I will win (probability 100%) because my King is higher than his Queen. Overall, the winning rate for his Queen is 15% (15% * 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 what card GoodGuy holds. 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: After the call, chips in the pot would be 20. If win, the winning payoff would be 10. If lose, the lose payoff would be 10.\n- Plan 2: After the raise, chips in the pot would be 26. If win, the winning payoff would be 13. If lose, the lose payoff would be 13.\n- Plan 3: If fold, I will lose the game and the lose payoff would be 10.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 23.5% * 10 - 76.5% * 10 = -5.3 chips\n- Plan 2: Expected Chips Gain = 23.5% * 13 - 76.5% * 13 = -6.9 chips\n- Plan 3: Expected Chips Gain = 0% * 0 - 100% * 10 = -10 chips\n\nPlan Selection:\n- Plan 1: -5.3 chips\n- Plan 2: -6.9 chips\n- Plan 3: -10 chips\n\nBased on the estimated expected chips gains, the best plan to execute would be Plan 1 (Call), as it has the highest estimated expected chips gain."}}
{"message": "", "3_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (20% probability), he will likely raise in the second round regardless of the public card. If the public card is a King, I will lose (20% * 20% = 4% lose rate). If the public card is a Queen or Jack, I have a chance to win (20% * 80% = 16% win rate). \n- If GoodGuy holds a Queen (20% probability), he will likely call in the second round. If the public card is a Queen, it will be a draw (20% * 20% = 4% draw rate). If the public card is a King or Jack, I will lose (20% * 80% = 16% lose rate).\n- If GoodGuy holds a Jack (20% probability), he will likely call in the second round. If the public card is a Jack, I will lose (20% * 20% = 4% lose rate). If the public card is a King or Queen, I will win (20% * 80% = 16% win rate).\n- If the public card is a King or Queen (40% probability), I will lose (40% * 100% = 40% lose rate).\n- If the public card is a Jack (20% probability), I will win (20% * 100% = 20% win rate).\n- Winning payoff: 3 chips (half of the pot after calling)\n- Losing payoff: -2 chips (half of the pot after calling)\n- Expected chips gain: 16% * 3 - 64% * 2 = -0.92 chips\n\nPlan 2: Raise\n- If GoodGuy holds a King (20% probability), he will likely call in the first round and raise in the second round. If the public card is a King, I will lose (20% * 20% = 4% lose rate). If the public card is a Queen or Jack, I have a chance to win (20% * 80% = 16% win rate).\n- If GoodGuy holds a Queen (20% probability), he will likely call in both rounds. If the public card is a Queen, it will be a draw (20% * 20% = 4% draw rate). If the public card is a King or Jack, I will lose (20% * 80% = 16% lose rate).\n- If GoodGuy holds a Jack (20% probability), he will likely call in both rounds. If the public card is a Jack, I will lose (20% * 20% = 4% lose rate). If the public card is a King or Queen, I will win (20% * 80% = 16% win rate).\n- If the public card is a King or Queen (40% probability), I will lose (40% * 100% = 40% lose rate).\n- If the public card is a Jack (20% probability), I will win (20% * 100% = 20% win rate).\n- Winning payoff: 7 chips (half of the pot after raising)\n- Losing payoff: -6 chips (half of the pot after raising)\n- Expected chips gain: 16% * 7 - 64% * 6 = -1.88 chips\n\nPlan 3: Fold\n- If I fold, I will lose 1 chip (the small blind I have already put in the pot), and there is no chance to win or draw.\n- Expected chips gain: -1 chip\n\nPlan Selection:\n- Plan 1: -0.92 chips\n- Plan 2: -1.88 chips\n- Plan 3: -1 chip\n\nBased on the expected chips gain, Plan 1 (Call) is the best strategy to use in this situation."}}
{"message": "", "3_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (50% probability), he will call (100% probability). In this case, it will be a draw as we both have a pair of Queens. \n- If GoodGuy holds a King or Jack (50% probability), he will call (100% probability). In this case, I will win as my pair of Queens is higher. \n\nPlan 2: Fold\n- If I fold, I will lose the round regardless of GoodGuy's card. \n\nPlan 3: Check\n- If GoodGuy holds a Queen (50% probability), he will check (100% probability). In this case, it will be a draw as we both have a pair of Queens. \n- If GoodGuy holds a King or Jack (50% probability), he will check (100% probability). In this case, I will win as my pair of Queens is higher. \n\nWinning/Lose/Draw Rates for Each Plan:\n- Plan 1: Winning rate = 50%, Lose rate = 0%, Draw rate = 50%\n- Plan 2: Winning rate = 0%, Lose rate = 100%, Draw rate = 0%\n- Plan 3: Winning rate = 50%, Lose rate = 0%, Draw rate = 50%\n\nNumber of Winning/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\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 50% * 4 - 0% * 2 = 2 chips\n- Plan 2: Expected Chips Gain = 0% * 0 - 100% * 2 = -2 chips\n- Plan 3: Expected Chips Gain = 50% * 2 - 0% * 2 = 1 chip\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I will choose Plan 1: Raise."}}
{"message": "", "4_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (probability 1/3), he will likely raise (70%). If he raises, I will lose as my Jack is lower than his King. The probability of losing is 0.7*1/3 = 0.23. If he calls (30%), it will be a draw as we both have the same amount of chips in the pot. The probability of a draw is 0.3*1/3 = 0.1.\n- If GoodGuy holds a Queen (probability 1/3), he will likely raise (40%). If he raises, I will lose as my Jack is lower than his Queen. The probability of losing is 0.4*1/3 = 0.13. If he calls (60%), it will be a draw as we both have the same amount of chips in the pot. The probability of a draw is 0.6*1/3 = 0.2.\n- If GoodGuy holds a Jack (probability 1/3), he will likely call (50%). If he calls, it will be a draw as we both have the same amount of chips in the pot. The probability of a draw is 0.5*1/3 = 0.17. If he checks (50%), it will be a draw as we both have the same amount of chips in the pot. The probability of a draw is 0.5*1/3 = 0.17.\n\nPlan 1 overall GoodGuy's Winning/Lose/Draw rates: Winning rate = 0; Lose rate = 0.23 + 0.13 = 0.36; Draw Rate = 0.1 + 0.2 + 0.17 + 0.17 = 0.64.\n\nPlan 2: Raise\n- If GoodGuy holds a King (probability 1/3), he will likely raise (70%). If he raises, I will lose as my Jack is lower than his King. The probability of losing is 0.7*1/3 = 0.23. If he calls (30%), it will be a draw as we both have the same amount of chips in the pot. The probability of a draw is 0.3*1/3 = 0.1.\n- If GoodGuy holds a Queen (probability 1/3), he will likely raise (40%). If he raises, I will lose as my Jack is lower than his Queen. The probability of losing is 0.4*1/3 = 0.13. If he calls (60%), it will be a draw as we both have the same amount of chips in the pot. The probability of a draw is 0.6*1/3 = 0.2.\n- If GoodGuy holds a Jack (probability 1/3), he will likely call (50%). If he calls, it will be a draw as we both have the same amount of chips in the pot. The probability of a draw is 0.5*1/3 = 0.17. If he checks (50%), it will be a draw as we both have the same amount of chips in the pot. The probability of a draw is 0.5*1/3 = 0.17.\n\nPlan 2 overall GoodGuy's Winning/Lose/Draw rates: Winning rate = 0; Lose rate = 0.23 + 0.13 = 0.36; Draw Rate = 0.1 + 0.2 + 0.17 + 0.17 = 0.64.\n\nPlan 3: Fold\n- If I fold, I will lose the game immediately. So, the losing rate is 1, and the winning and draw rates are 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 lose, the lose payoff would be 0.5.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0*1.5 - 0.36*1.5 = -0.54\n- Plan 2: Expected Chips Gain = 0*2.5 - 0.36*2.5 = -0.9\n- Plan 3: Expected Chips Gain = 0*0 - 1*0.5 = -0.5\n\nPlan Selection: \n- Plan 1: -0.54\n- Plan 2: -0.9\n- Plan 3: -0.5\n\nBased on the estimated expected chips gains, Plan 3 (Fold) is the best strategy to minimize the loss."}}
{"message": "", "5_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King, he will likely raise (80% probability) or call (20% probability). If he raises, I will have a 50% chance of winning (if the public card is a King) or a 50% chance of losing (if the public card is not a King). If he calls, I will have a 100% chance of winning because my card is higher. \n- If GoodGuy holds a Queen, he will likely call (70% probability) or fold (30% probability). If he calls, I will have a 100% chance of winning because my card is higher. If he folds, I will also win. \n- If GoodGuy holds a Jack, he will likely fold (80% probability) or call (20% probability). In either case, I will win because my card is higher. \n\nPlan 2: Raise\n- If GoodGuy holds a King, he will likely raise (80% probability) or call (20% probability). If he raises, I will have a 50% chance of winning (if the public card is a King) or a 50% chance of losing (if the public card is not a King). If he calls, I will have a 100% chance of winning because my card is higher. \n- If GoodGuy holds a Queen, he will likely call (70% probability) or fold (30% probability). If he calls, I will have a 100% chance of winning because my card is higher. If he folds, I will also win. \n- If GoodGuy holds a Jack, he will likely fold (80% probability) or call (20% probability). In either case, I will win because my card is higher. \n\nPlan 3: Fold\n- If I fold, I will lose the round and lose any chips I have already put in the pot. \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 (currently 3 chips, so 1.5 chips). If I lose, the lose payoff would be half of the pot (currently 3 chips, so 1.5 chips).\n- Plan 2: If I win, the winning payoff would be half of the pot (currently 7 chips, so 3.5 chips). If I lose, the lose payoff would be half of the pot (currently 7 chips, so 3.5 chips).\n- Plan 3: If I fold, I will lose 1 chip. \n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.8 * 1.5 - 0.2 * 1.5 = 1.2 chips\n- Plan 2: Expected Chips Gain = 0.8 * 3.5 - 0.2 * 3.5 = 2.8 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": "", "5_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (90% probability), he will likely raise (90% probability). This would result in a draw, as we both have a pair of Kings. The overall draw rate for this plan is 81% (90% * 90%).\n- If GoodGuy holds a Queen (20% probability), he will likely fold (50% probability). This would result in a win for me, as my pair of Kings beats his Queen. The overall win rate for this plan is 10% (20% * 50%).\n- If GoodGuy holds a Jack (30% probability), he will likely fold (60% probability). This would result in a win for me, as my pair of Kings beats his Jack. The overall win rate for this plan is 18% (30% * 60%).\n\nPlan 2: Fold\n- If I fold, I automatically lose the game, regardless of what card GoodGuy holds. The overall lose rate for this plan is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (90% probability), he will likely raise (90% probability). This would result in a draw, as we both have a pair of Kings. The overall draw rate for this plan is 81% (90% * 90%).\n- If GoodGuy holds a Queen (20% probability), he will likely call (50% probability). This would result in a win for me, as my pair of Kings beats his Queen. The overall win rate for this plan is 10% (20% * 50%).\n- If GoodGuy holds a Jack (30% probability), he will likely call (40% probability). This would result in a win for me, as my pair of Kings beats his Jack. The overall win rate for this plan is 12% (30% * 40%).\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 automatically 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 Chips Gain = 0.28 * 4 - 0 * 4 = 1.12 chips\n- Plan 2: Expected Chips Gain = 0 * 4 - 1 * 4 = -4 chips\n- Plan 3: Expected Chips Gain = 0.22 * 4 - 0 * 4 = 0.88 chips\n\nPlan Selection:\n- Plan 1: 1.12 chips\n- Plan 2: -4 chips\n- Plan 3: 0.88 chips\n\nBased on the estimated expected chips gain, Plan 1 (Raise) is the best strategy to use in this situation."}}
{"message": "", "5_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (90% probability), he will likely raise (90% probability). This results in a draw as we both have a pair of Kings. \n- If GoodGuy holds a Queen (10% probability), he will likely fold (50% probability) or call (50% probability). This results in a win for me as my pair of Kings is higher than his Queen.\n\nPlan 2: Fold\n- If GoodGuy holds a King (90% probability), he will likely raise (90% probability). This results in a loss for me as I forfeit the game.\n- If GoodGuy holds a Queen (10% probability), he will likely fold (50% probability) or call (50% probability). This results in a loss for me as I forfeit the game.\n\nWinning/Lose/Draw Rate for Each Plan:\n- Plan 1: Winning rate is 5% (10% * 50%), draw rate is 90% (90% * 100%), and lose rate is 5% (10% * 50%).\n- Plan 2: Winning rate is 0%, draw rate is 0%, and lose rate is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 10 chips (half of the pot). If lose, the lose payoff would be 12 chips (half of the pot).\n- Plan 2: If win, the winning payoff would be 0 chips (as I forfeit the game). If lose, the lose payoff would be 12 chips (half of the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected chips gain is 5% * 10 chips - 5% * 12 chips = 0.5 chips - 0.6 chips = -0.1 chips.\n- Plan 2: Expected chips gain is 0% * 0 chips - 100% * 12 chips = -12 chips.\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain (-0.1 chips) than Plan 2 (-12 chips). Therefore, I should choose Plan 1: Call."}}
{"message": "", "6_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (80% probability), he is likely to raise (80% probability) or call (20% probability). If he raises, I will lose (80% * 80% = 64%). If he calls, it will be a draw (80% * 20% = 16%).\n- If GoodGuy holds a Queen (10% probability), he is likely to call (60% probability) or fold (40% probability). If he calls, I will win (10% * 60% = 6%). If he folds, I will win (10% * 40% = 4%).\n- If GoodGuy holds a Jack (10% probability), he is likely to call (30% probability) or fold (70% probability). If he calls, I will win (10% * 30% = 3%). If he folds, I will win (10% * 70% = 7%).\n- Overall, the winning rate for Plan 1 is 6% + 4% + 3% + 7% = 20%, the losing rate is 64%, and the draw rate is 16%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (80% probability), he is likely to raise (80% probability) or call (20% probability). If he raises, I will lose (80% * 80% = 64%). If he calls, it will be a draw (80% * 20% = 16%).\n- If GoodGuy holds a Queen (10% probability), he is likely to call (60% probability) or fold (40% probability). If he calls, I will win (10% * 60% = 6%). If he folds, I will win (10% * 40% = 4%).\n- If GoodGuy holds a Jack (10% probability), he is likely to fold (70% probability) or call (30% probability). If he folds, I will win (10% * 70% = 7%). If he calls, I will win (10% * 30% = 3%).\n- Overall, the winning rate for Plan 2 is 6% + 4% + 7% + 3% = 20%, the losing rate is 64%, and the draw rate is 16%.\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 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 2: If I win, the winning payoff would be half of the pot (8 chips). If I lose, the lose payoff would be half of the pot (8 chips).\n- Plan 3: If I fold, I will lose 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 20% * 6 - 64% * 6 = -2.64 chips\n- Plan 2: 20% * 8 - 64% * 8 = -3.52 chips\n- Plan 3: -2 chips\n\nPlan Selection:\n- Plan 1: -2.64 chips\n- Plan 2: -3.52 chips\n- Plan 3: -2 chips\n\nBased on the estimated expected chips gains, Plan 3 (Fold) is the best strategy to minimize loss."}}
{"message": "", "7_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (20% chance), he will likely raise (80% chance). If the public card is a King, I will lose. If the public card is a Queen or Jack, I have a 50% chance of winning (if it's a Queen) or losing (if it's a Jack). Overall, my winning rate is 10%, losing rate is 10%, and draw rate is 0%.\n- If GoodGuy holds a Queen (20% chance), he will likely call (70% chance) or fold (30% chance). If the public card is a Queen, it's a draw. If the public card is a King or Jack, I will lose. Overall, my winning rate is 0%, losing rate is 14%, and draw rate is 6%.\n- If GoodGuy holds a Jack (60% chance), he will likely fold (60% chance) or call (40% chance). If the public card is a Jack, I will lose. If the public card is a King or Queen, I will win. Overall, my winning rate is 24%, losing rate is 24%, and draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (20% chance), he will likely raise (80% chance). If the public card is a King, I will lose. If the public card is a Queen or Jack, I have a 50% chance of winning (if it's a Queen) or losing (if it's a Jack). Overall, my winning rate is 10%, losing rate is 10%, and draw rate is 0%.\n- If GoodGuy holds a Queen (20% chance), he will likely fold (30% chance) or call (70% chance). If the public card is a Queen, it's a draw. If the public card is a King or Jack, I will lose. Overall, my winning rate is 0%, losing rate is 14%, and draw rate is 6%.\n- If GoodGuy holds a Jack (60% chance), he will likely fold (60% chance) or call (40% chance). If the public card is a Jack, I will lose. If the public card is a King or Queen, I will win. Overall, my winning rate is 24%, losing rate is 24%, and draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the 1 chip I have already put in the pot. My 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 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 = 10% * 3 - 10% * 1 = 0.2 chips\n- Plan 2: Expected Chips Gain = 10% * 7 - 10% * 3 = 0.4 chips\n- Plan 3: Expected Chips Gain = 0% * 0 - 100% * 1 = -1 chips\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain, so I should choose Plan 2: Raise."}}
{"message": "", "7_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King, he is likely to call (60%) or fold (40%). If he calls, I will lose (as King is higher than Queen) with a probability of 60%. If he folds, I will win with a probability of 40%. \n- If GoodGuy holds a Queen, he is likely to call (50%) or fold (50%). If he calls or folds, it will be a draw as we both hold Queens. \n- If GoodGuy holds a Jack, he is likely to fold (80%) or call (20%). If he folds, I will win with a probability of 80%. If he calls, I will win (as Queen is higher than Jack) with a probability of 20%. \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, I will lose (as King is higher than Queen) with a probability of 60%. If he folds, I will win with a probability of 40%. \n- If GoodGuy holds a Queen, he is likely to call (50%) or fold (50%). If he calls or folds, it will be a draw as we both hold Queens. \n- If GoodGuy holds a Jack, he is likely to fold (80%) or call (20%). If he folds, I will win with a probability of 80%. If he calls, I will win (as Queen is higher than Jack) with a probability of 20%. \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 4 chips. If I lose, the lose payoff would be half of the pot, which is 4 chips. \n- Plan 2: If I fold, I will lose 4 chips. \n- Plan 3: If I win, the winning payoff would be half of the pot, which is 4 chips. If I lose, the lose payoff would be half of the pot, which is 4 chips. \n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.6 * 4 - 0.4 * 4 = 0.8 chips\n- Plan 2: Expected Chips Gain = -4 chips\n- Plan 3: Expected Chips Gain = 0.6 * 4 - 0.4 * 4 = 0.8 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 have the highest expected chips gain, so I will choose between these two plans. Since Plan 1 (raise) is more aggressive and may intimidate GoodGuy into folding, I will choose Plan 1."}}
{"message": "", "8_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (33.33% probability), he is likely to raise (80% probability) or call (20% probability). If he raises, I will lose as we both have Kings. If he calls, it will be a draw. Overall, the winning rate is 0%, the losing rate is 26.67% (33.33% * 80%), and the draw rate is 6.67% (33.33% * 20%).\n- If GoodGuy holds a Queen (33.33% probability), he is likely to call (60% probability) or fold (40% probability). If he calls or folds, I will win as my King is higher than his Queen. Overall, the winning rate is 33.33%, the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (33.33% probability), he is likely to fold (70% probability) or call (30% probability). If he folds or calls, I will win as my King is higher than his Jack. Overall, the winning rate is 33.33%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (33.33% probability), he is likely to call (80% probability) or raise (20% probability). If he calls or raises, I will lose as we both have Kings. Overall, the winning rate is 0%, the losing rate is 33.33%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (33.33% probability), he is likely to call (60% probability) or fold (40% probability). If he calls, I will win as my King is higher than his Queen. If he folds, I will also win as he forfeits the game. Overall, the winning rate is 33.33%, the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (33.33% probability), he is likely to fold (70% probability) or call (30% probability). If he folds or calls, I will win as my King is higher than his Jack. Overall, the winning rate is 33.33%, 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. 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 (half of the pot). If I lose, the losing payoff would be 1 chip (my bet).\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 2 chips (my bet).\n- Plan 3: If I fold, the losing payoff would be 1 chip (my bet).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 66.67% * 3 - 26.67% * 1 = 1.67 chips\n- Plan 2: Expected Chips Gain = 66.67% * 5 - 33.33% * 2 = 2.33 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, followed by Plan 1 (Call), and Plan 3 (Fold). Therefore, I should choose to raise."}}
{"message": "", "8_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King: He will likely raise (90% probability) or call (10% probability). Since I also hold a King, the game will result in a draw. \n- If GoodGuy holds a Queen or Jack: He will likely fold (80% probability) or call (20% probability). Since my card is higher, I will win the game.\n\nPlan 2: Check\n- If GoodGuy holds a King: He will likely raise (90% probability) or call (10% probability). Since I also hold a King, the game will result in a draw. \n- If GoodGuy holds a Queen or Jack: He will likely fold (80% probability) or call (20% probability). Since my card is higher, I will win the game.\n\nPlan 3: Fold\n- This plan is not reasonable because I hold the highest card and it matches with the public card. \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\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.9 * 4 - 0.1 * 4 = 3.6 - 0.4 = 3.2\n- Plan 2: Expected Chips Gain = 0.9 * 2 - 0.1 * 2 = 1.8 - 0.2 = 1.6\n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 1 > Plan 2.\n- Therefore, I should select Plan 1 (Raise) as it has the highest estimated expected chips gain."}}
{"message": "", "8_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a King: \n  - He will likely raise (90% probability) or call (10% probability). \n  - If he raises, I will win as we both have a pair of Kings (winning rate = 90% * 1 = 90%). \n  - If he calls, I will win as we both have a pair of Kings (winning rate = 10% * 1 = 10%). \n  - Overall winning rate for his King is 100%. \n- If GoodGuy holds a Queen or Jack: \n  - He will likely fold (80% probability) or call (20% probability). \n  - If he folds, I will win (winning rate = 80% * 1 = 80%). \n  - If he calls, I will win as my King is higher than his Queen or Jack (winning rate = 20% * 1 = 20%). \n  - Overall winning rate for his Queen or Jack is 100%. \n\nPlan 2: Fold\n- If GoodGuy holds a King: \n  - He will likely raise (90% probability) or call (10% probability). \n  - If he raises, I will lose as I forfeit the game (losing rate = 90% * 1 = 90%). \n  - If he calls, I will lose as I forfeit the game (losing rate = 10% * 1 = 10%). \n  - Overall losing rate for his King is 100%. \n- If GoodGuy holds a Queen or Jack: \n  - He will likely fold (80% probability) or call (20% probability). \n  - If he folds, I will lose as I forfeit the game (losing rate = 80% * 1 = 80%). \n  - If he calls, I will lose as I forfeit the game (losing rate = 20% * 1 = 20%). \n  - Overall losing rate for his Queen or Jack is 100%. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: \n  - After the action, chips in the pot: 24. If win, the winning payoff would be 12. \n  - After the action, chips in the pot: 24. If lose, the lose payoff would be 12. \n- Plan 2: \n  - After the action, chips in the pot: 20. If win, the winning payoff would be 10. \n  - After the action, chips in the pot: 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 - losing rate * Lose Payoff = 100% * 12 - 0% * 12 = 12 chips. \n- Plan 2: Expected Chips Gain = winning rate * Winning Payoff - losing rate * Lose Payoff = 0% * 10 - 100% * 10 = -10 chips. \n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 1 > Plan 2. \n- Therefore, I should select Plan 1 (Call) as it has the highest estimated expected chips gain."}}
{"message": "", "9_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (33.33% probability), he will likely call if I call (100% probability). If the public card is a King, I will lose (as my Jack is lower rank). If the public card is a Queen or Jack, it's a draw (as neither of us has a pair). Overall, the winning rate is 0%, the losing rate is 33.33%, and the draw rate is 33.33%.\n- If GoodGuy holds a Queen (33.33% probability), he will likely call if I call (100% probability). If the public card is a Queen, I will lose. If the public card is a King or Jack, it's a draw. Overall, the winning rate is 0%, the losing rate is 33.33%, and the draw rate is 33.33%.\n- If GoodGuy holds a Jack (33.33% probability), he will likely fold if I call (100% probability). If the public card is a Jack, I will win. If the public card is a King or Queen, it's a draw. Overall, the winning rate is 33.33%, the losing rate is 0%, and the draw rate is 33.33%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (33.33% probability), he will likely call if I raise (100% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, it's a draw. Overall, the winning rate is 0%, the losing rate is 33.33%, and the draw rate is 33.33%.\n- If GoodGuy holds a Queen (33.33% probability), he will likely call if I raise (100% probability). If the public card is a Queen, I will lose. If the public card is a King or Jack, it's a draw. Overall, the winning rate is 0%, the losing rate is 33.33%, and the draw rate is 33.33%.\n- If GoodGuy holds a Jack (33.33% probability), he will likely fold if I raise (100% probability). If the public card is a Jack, I will win. If the public card is a King or Queen, it's a draw. Overall, the winning rate is 33.33%, the losing rate is 0%, and the draw rate is 33.33%.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card or the public 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: If I win, the winning payoff would be 3 chips (half of the pot). If I lose, the losing payoff would be 2 chips (my current bet).\n- Plan 2: If I win, the winning payoff would be 7 chips (half of the pot). If I lose, the losing payoff would be 6 chips (my current bet plus the raise).\n- Plan 3: If I fold, I will lose 2 chips (my current bet).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0% * 3 chips - 66.67% * 2 chips = -1.33 chips\n- Plan 2: 33.33% * 7 chips - 66.67% * 6 chips = -2.33 chips\n- Plan 3: 0% * 0 chips - 100% * 2 chips = -2 chips\n\nPlan Selection:\n- Plan 1 has the highest estimated expected chips gain (-1.33 chips), followed by Plan 3 (-2 chips), and Plan 2 (-2.33 chips). Therefore, I should choose Plan 1: Call."}}
{"message": "", "9_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (50% probability), he will call (100% probability). If he calls, I will lose (100% probability) because his King is higher than my Jack. The winning rate is 0%, the losing rate is 50%, and the drawing rate is 0%.\n- If GoodGuy holds a Jack (50% probability), he will fold (100% probability). If he folds, I will win (100% probability) because he forfeits the game. The winning rate is 50%, the losing rate is 0%, and the drawing rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose (100% probability) regardless of GoodGuy's cards. The winning rate is 0%, the losing rate is 100%, and the drawing rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King (50% probability), he will check (100% probability). If he checks, I will lose (100% probability) because his King is higher than my Jack. The winning rate is 0%, the losing rate is 50%, and the drawing rate is 0%.\n- If GoodGuy holds a Jack (50% probability), he will check (100% probability). If he checks, it will be a draw (100% probability) because we both have a Jack. The winning rate is 0%, the losing rate is 0%, and the drawing rate is 50%.\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 4 chips (half of the pot).\n- Plan 2: If I lose, the losing 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 losing payoff would be 2 chips (half of the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 50% * 6 chips - 50% * 4 chips = 1 chip\n- Plan 2: Expected Chips Gain = 0% * 0 chips - 100% * 2 chips = -2 chips\n- Plan 3: Expected Chips Gain = 0% * 2 chips - 50% * 2 chips = -1 chip\n\nPlan Selection:\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": "", "10_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (which he does), he will raise (100% probability). If the public card is a King, GoodGuy will win (100% probability). If the public card is not a King, GoodGuy will still have a high chance of winning because the King is the highest rank. \n- If GoodGuy holds a Queen, he will call if the opponent raises (100% probability). If the public card is a Queen, GoodGuy will win (100% probability). If the public card is not a Queen, GoodGuy will lose (100% probability).\n- If GoodGuy holds a Jack, he will fold if the opponent raises (100% probability). If the public card is a Jack, GoodGuy will lose (100% probability). If the public card is not a Jack, GoodGuy will lose (100% probability).\n- Overall, the winning rate for plan 1 is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If GoodGuy folds, he will lose the game regardless of what card he holds or what the public card is. \n- Overall, the winning rate for plan 2 is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King (which he does), he will check (100% probability). If the public card is a King, GoodGuy will win (100% probability). If the public card is not a King, GoodGuy will still have a high chance of winning because the King is the highest rank. \n- If GoodGuy holds a Queen, he will check (100% probability). If the public card is a Queen, GoodGuy will win (100% probability). If the public card is not a Queen, GoodGuy will lose (100% probability).\n- If GoodGuy holds a Jack, he will check (100% probability). If the public card is a Jack, GoodGuy will win (100% probability). If the public card is not a Jack, GoodGuy will lose (100% probability).\n- Overall, the winning rate for plan 3 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 win, the winning payoff would be half of the pot (currently 2 chips). If lose, the lose payoff would be half of the pot (currently 2 chips).\n- Plan 2: If win, the winning payoff would be half of the pot (currently 2 chips). If lose, the lose payoff would be half of the pot (currently 2 chips).\n- Plan 3: If win, the winning payoff would be half of the pot (currently 2 chips). If lose, the lose payoff would be half of the pot (currently 2 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = winning rate * Winning Payoff - losing rate * Lose Payoff = 100% * 2 chips - 0% * 2 chips = 2 chips\n- Plan 2: Expected Chips Gain = winning rate * Winning Payoff - losing rate * Lose Payoff = 0% * 2 chips - 100% * 2 chips = -2 chips\n- Plan 3: Expected Chips Gain = winning rate * Winning Payoff - losing rate * Lose Payoff = 100% * 2 chips - 0% * 2 chips = 2 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 both have the highest expected chips gain (2 chips), while Plan 2 has the lowest expected chips gain (-2 chips). Therefore, the best strategy would be to either raise (Plan 1) or check (Plan 3)."}}
{"message": "", "11_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (33.3% probability), he will likely raise in the first round. If I call, he will likely call in the second round. If the public card is a King, I will lose (probability 33.3%). If the public card is a Queen, I will win (probability 33.3%). If the public card is a Jack, I will win (probability 33.3%).\n- If GoodGuy holds a Queen (33.3% probability), he will likely call in the first round. If I call, he will likely fold in the second round. If the public card is a Queen, I will win (probability 33.3%). If the public card is a King or a Jack, I will win (probability 66.6%).\n- If GoodGuy holds a Jack (33.3% probability), he will likely fold in the first round. If I call, he will likely fold in the second round. If the public card is a Jack, I will lose (probability 33.3%). If the public card is a King or a Queen, I will win (probability 66.6%).\n\nPlan 2: Raise\n- If GoodGuy holds a King (33.3% probability), he will likely call in the first round. If I raise, he will likely call in the second round. If the public card is a King, I will lose (probability 33.3%). If the public card is a Queen, I will win (probability 33.3%). If the public card is a Jack, I will win (probability 33.3%).\n- If GoodGuy holds a Queen (33.3% probability), he will likely call in the first round. If I raise, he will likely fold in the second round. If the public card is a Queen, I will win (probability 33.3%). If the public card is a King or a Jack, I will win (probability 66.6%).\n- If GoodGuy holds a Jack (33.3% probability), he will likely fold in the first round. If I raise, he will likely fold in the second round. If the public card is a Jack, I will lose (probability 33.3%). If the public card is a King or a Queen, I will win (probability 66.6%).\n\nPlan 3: Fold\n- If I fold, I will lose the round 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 losing payoff would be 2 chips (half of the pot).\n- Plan 2: If I win, the winning payoff would be 4 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 = 0.67 * 3 - 0.33 * 2 = 1.01 chips\n- Plan 2: Expected Chips Gain = 0.67 * 4 - 0.33 * 3 = 1.35 chips\n- Plan 3: Expected Chips Gain = -2 chips (as I will lose my initial bet)\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I will choose this plan."}}
{"message": "", "11_2": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (50% probability), he will likely call if I call (100% 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. So, the winning rate is 0%, the losing rate is 50%, and the draw rate is 50%.\n- If GoodGuy holds a Jack (50% probability), he will likely fold if I call (100% probability). If the public card is a Jack, I will win. If the public card is a Queen or King, I will also win. So, the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If GoodGuy holds a King (50% probability), he will likely call if I fold (100% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I will also lose. So, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (50% probability), he will likely fold if I fold (100% probability). If the public card is a Jack, I will lose. If the public card is a Queen or King, I will also lose. 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: 10. If win, the winning payoff would be 5. After the action, chips in the pot: 10. If lose, the lose payoff would be 5.\n- Plan 2: After the action, chips in the pot: 6. If win, the winning payoff would be 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 = 0.5 * 5 - 0.5 * 5 = 0\n- Plan 2: Expected Chips Gain = 0 * 3 - 1 * 3 = -3\n\nPlan Selection:\n- Plan 1 has an expected chips gain of 0, and Plan 2 has an expected chips gain of -3. Therefore, Plan 1 (Call) is the better strategy."}}
{"message": "", "11_4": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (probability 1/3), he will call (probability 100%). I will lose as his King pairs with the public card. The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (probability 1/3), he will fold (probability 100%). I will win as he forfeits the game. The winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (probability 1/3), he will fold (probability 100%). I will win as he forfeits the game. The winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: 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\nPlan 3: Check\n- If GoodGuy holds a King (probability 1/3), he will raise (probability 100%). I will lose as his King pairs with the public card. The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (probability 1/3), he will check (probability 100%). I will lose as his Queen is higher than my Jack. The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (probability 1/3), he will check (probability 100%). The game will draw as we both hold a Jack. The winning rate is 0%, the losing rate is 0%, and the draw rate is 100%.\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: (2/3 * 7) - (1/3 * 7) = 1.33\n- Plan 2: 0 - (1 * 3) = -3\n- Plan 3: 0 - (2/3 * 3) = -2\n\nPlan Selection:\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": "", "12_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (20% probability), he is likely to raise (80%) or call (20%). If he raises, I will lose (as Jack < King). If he calls, the outcome depends on the public card. If the public card is a Jack, I will win. If the public card is a King or Queen, I will lose. \n- If GoodGuy holds a Queen (60% probability), he is likely to call (60%) or raise (40%). If he raises, the outcome depends on the public card. If the public card is a Jack, I will win. If the public card is a Queen or King, I will lose. If he calls, the outcome also depends on the public card.\n- If GoodGuy holds a Jack (20% probability), he is likely to fold (60%) or call (40%). If he folds, I will win. If he calls, the outcome depends on the public card.\n\nPlan 2: Fold\n- If I fold, I will lose the 2 chips in the pot, regardless of GoodGuy's card.\n\nPlan 3: Check\n- If GoodGuy holds a King (20% probability), he is likely to raise (80%) or check (20%). If he raises, I can fold and lose 2 chips. If he checks, the outcome depends on the public card.\n- If GoodGuy holds a Queen (60% probability), he is likely to check (60%) or raise (40%). If he raises, I can fold and lose 2 chips. If he checks, the outcome also depends on the public card.\n- If GoodGuy holds a Jack (20% probability), he is likely to fold (60%) or check (40%). If he folds, I will win. If he checks, the outcome depends on the public card.\n\nWinning/Lose Payoff for Each Plan:\n- Plan 1: If I win, the winning payoff would be half of the pot (currently 4 chips, so 2 chips). If I lose, the losing payoff would be the chips I put in the pot (currently 2 chips).\n- Plan 2: If I fold, I will lose the 2 chips in the pot.\n- Plan 3: If I win, the winning payoff would be half of the pot (currently 4 chips, so 2 chips). If I lose, the losing payoff would be the chips I put in the pot (currently 2 chips).\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected gain = winning rate * winning payoff - losing rate * losing payoff. \n- Plan 2: Expected gain = -2 chips (as I will lose the 2 chips in the pot).\n- Plan 3: Expected gain = winning rate * winning payoff - losing rate * losing payoff. \n\nPlan Selection:\n- I would calculate the expected chips gain for each plan, and select the plan with the highest expected gain. This requires estimating the winning and losing rates for each plan, which depends on GoodGuy's behavior pattern and the public card."}}
{"message": "", "14_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (33.33% probability), he will likely raise (100% probability). If the public card is a King, I will lose. If the public card is not a King, I will win if it's a Jack, and draw if it's a Queen. The overall winning rate is 16.67%, losing rate is 33.33%, and drawing rate is 16.67%.\n- If GoodGuy holds a Queen (33.33% probability), he will likely raise (80% probability) or check (20% probability). If the public card is a Queen, I will lose. If the public card is not a Queen, I will win if it's a Jack, and draw if it's a King. The overall winning rate is 16.67%, losing rate is 26.67%, and drawing rate is 6.67%.\n- If GoodGuy holds a Jack (16.67% probability), he will likely check (100% probability). If the public card is a Jack, it's a draw. If the public card is not a Jack, I will win. The overall winning rate is 16.67%, losing rate is 0%, and drawing rate is 16.67%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (33.33% probability), he will likely call (70% probability) or raise (30% probability). If the public card is a King, I will lose. If the public card is not a King, I will win if it's a Jack, and draw if it's a Queen. The overall winning rate is 16.67%, losing rate is 23.33%, and drawing rate is 10%.\n- If GoodGuy holds a Queen (33.33% probability), he will likely call (60% probability) or raise (40% probability). If the public card is a Queen, I will lose. If the public card is not a Queen, I will win if it's a Jack, and draw if it's a King. The overall winning rate is 16.67%, losing rate is 20%, and drawing rate is 6.67%.\n- If GoodGuy holds a Jack (16.67% probability), he will likely call (50% probability) or fold (50% probability). If the public card is a Jack, it's a draw. If the public card is not a Jack, I will win. The overall winning rate is 16.67%, losing rate is 0%, and drawing rate is 8.33%.\n\nPlan 3: Fold\n- If I fold, I will lose 1 chip. 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 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 7 chips. If lose, the lose payoff would be 5 chips.\n- Plan 3: If lose, the lose payoff would be 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 16.67% * 3 - 33.33% * 1 = 0.167 chips\n- Plan 2: 16.67% * 7 - 23.33% * 5 = -0.332 chips\n- Plan 3: 0% * 0 - 100% * 1 = -1 chip\n\nPlan Selection:\n- Plan 1: Call\n- Plan 2: Raise\n- Plan 3: Fold\n\nBased on the estimated expected chips gain, the best plan is to call."}}
{"message": "", "14_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (40% probability), he is likely to call (60%) or raise (40%). If he calls, we will draw as neither of us matches the public card, but the King ranks higher than the Jack. If he raises, I will lose as the King ranks higher than the Jack. Overall, the winning rate is 0%, the losing rate is 40%, and the draw rate is 60%.\n- If GoodGuy holds a Jack (60% probability), he is likely to fold (100%). If he folds, I will win as I will be the only player left in the game. Overall, the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If GoodGuy holds a King (40% probability), I will lose as I have folded. Overall, the losing rate is 100%.\n- If GoodGuy holds a Jack (60% probability), I will lose as I have folded. Overall, the losing rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (40% probability), he is likely to raise (40%) or check (60%). If he raises, I will lose as the King ranks higher than the Jack. If he checks, we will draw as neither of us matches the public card, but the King ranks higher than the Jack. Overall, the winning rate is 0%, the losing rate is 40%, and the draw rate is 60%.\n- If GoodGuy holds a Jack (60% probability), he is likely to check (100%). If he checks, we will draw as neither of us matches the public card and we both hold a Jack. Overall, the winning rate is 0%, the losing rate is 0%, and the draw rate is 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: 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 = 0.6 * 2 - 0.4 * 2 = 0.4\n- Plan 2: Expected Chips Gain = 0 - 1 = -1\n- Plan 3: Expected Chips Gain = 0 - 0.4 * 1 = -0.4\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 select Plan 1: Raise, as it has the highest estimated expected chips gain."}}
{"message": "", "14_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (probability 1/3): \n  - GoodGuy will raise (probability 40%). I will lose as my Jack is lower than his King. \n  - GoodGuy will call (probability 60%). I will lose as my Jack is lower than his King. \n  - Overall, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (probability 1/3): \n  - GoodGuy will raise (probability 50%). I will lose as my Jack is lower than the public Queen. \n  - GoodGuy will call (probability 50%). I will lose as my Jack is lower than the public Queen. \n  - Overall, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (probability 1/3): \n  - GoodGuy will fold (probability 100%). I will win as GoodGuy forfeits the round. \n  - Overall, the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 1 overall Winning/Lose/Draw rates: \n- Winning rate: 33.3% (100% * 1/3)\n- Losing rate: 66.7% (100% * 2/3)\n- Draw rate: 0%\n\nPlan 2: Fold\n- If I fold, I will lose the round regardless of what card GoodGuy holds. \n- Overall, 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: \n  - After the action, chips in the pot: 16. If win, the winning payoff would be 8. \n  - After the action, chips in the pot: 16. If lose, the lose payoff would be 8.\n- Plan 2: \n  - After the action, chips in the pot: 10. If lose, the lose payoff would be 5.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Winning rate * Winning Payoff - Losing rate * Lose Payoff = 33.3% * 8 - 66.7% * 8 = -2.67 chips\n- Plan 2: Winning rate * Winning Payoff - Losing rate * Lose Payoff = 0% * 0 - 100% * 5 = -5 chips\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain (-2.67 chips) than Plan 2 (-5 chips). Therefore, I should choose Plan 1: Call."}}
{"message": "", "15_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (probability 1/3), he will likely raise (80%) or call (20%). 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. Overall, my winning rate is 20%, losing rate is 80%, and draw rate is 0%.\n- If GoodGuy holds a Queen (probability 1/3), 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. Overall, my winning rate is 30%, losing rate is 0%, and draw rate is 70%.\n- If GoodGuy holds a Jack (probability 1/3), he will likely fold (60%) or call (40%). If he folds, I will win. If he calls, I will win unless the public card is a Jack. Overall, my winning rate is 100%, losing rate is 0%, and draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (probability 1/3), he will likely raise (80%) or call (20%). 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. Overall, my winning rate is 20%, losing rate is 80%, and draw rate is 0%.\n- If GoodGuy holds a Queen (probability 1/3), 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. Overall, my winning rate is 30%, losing rate is 0%, and draw rate is 70%.\n- If GoodGuy holds a Jack (probability 1/3), he will likely fold (60%) or call (40%). If he folds, I will win. If he calls, I will win unless the public card is a Jack. Overall, my winning rate is 100%, losing rate is 0%, and draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of GoodGuy's cards. My 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 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 2 chips.\n- Plan 3: If I fold, I will lose 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: (20% * 3 + 30% * 3 + 100% * 3) - (80% * 1 + 0% * 1 + 0% * 1) = 1.9 chips\n- Plan 2: (20% * 5 + 30% * 5 + 100% * 5) - (80% * 2 + 0% * 2 + 0% * 2) = 3.1 chips\n- Plan 3: 0 - 100% * 1 = -1 chip\n\nPlan Selection:\n- Plan 2 (Raise) has the highest estimated expected chips gain, followed by Plan 1 (Call), and Plan 3 (Fold). Therefore, I should choose Plan 2 (Raise)."}}
{"message": "", "15_2": {"plan": "Plan 1: Call\n- If GoodGuy holds a King: \n  - In the 2nd round, if the public card is a King, GoodGuy is likely to raise (90%) or call (10%). If the public card is not a King, GoodGuy is likely to call (60%) or fold (40%). \n  - Winning rate: 0% (since King is higher than Queen)\n  - Lose rate: 100% \n  - Draw rate: 0%\n- If GoodGuy holds a Queen: \n  - In the 2nd round, if the public card is a Queen, GoodGuy is likely to raise (80%) or call (20%). If the public card is not a Queen, GoodGuy is likely to call (50%) or fold (50%).\n  - Winning rate: 50% (since both have Queen)\n  - Lose rate: 50% \n  - Draw rate: 0%\n- If GoodGuy holds a Jack: \n  - In the 2nd round, if the public card is a Jack, GoodGuy is likely to raise (70%) or call (30%). If the public card is not a Jack, GoodGuy is likely to fold (80%) or call (20%).\n  - Winning rate: 100% (since Queen is higher than Jack)\n  - Lose rate: 0% \n  - Draw rate: 0%\n\nPlan 2: Fold\n- If GoodGuy holds a King, Queen or Jack: \n  - Winning rate: 0% (since I fold)\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: 10. If win, the winning payoff would be 5. If lose, the lose payoff would be 5.\n- Plan 2: After the action, Chips in the pot: 6. If win, the winning payoff would be 0 (since I fold). If lose, the lose payoff would be 3.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Winning rate * Winning Payoff - Lose rate * Lose Payoff = 0.5 * 5 - 0.5 * 5 = 0\n- Plan 2: Winning rate * Winning Payoff - Lose rate * Lose Payoff = 0 * 0 - 1 * 3 = -3\n\nPlan Selection: \n- Plan 1 is ranked first with an expected chips gain of 0.\n- Plan 2 is ranked second with an expected chips gain of -3.\n- Therefore, I should select Plan 1 (Call) as it has the highest estimated expected chips gain."}}
{"message": "", "15_4": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King: \n  - He is likely to call (60%) or fold (40%). If he calls, I will win as I have a pair of Queens. If he folds, I will also win as he forfeits the round. Therefore, the winning rate is 100%.\n- If GoodGuy holds a Queen: \n  - He is likely to raise (80%) or call (20%). In either case, it will be a draw as we both have a pair of Queens. Therefore, the draw rate is 100%.\n- If GoodGuy holds a Jack: \n  - He is likely to fold (80%) or call (20%). If he folds, I will win. If he calls, I will also win as I have a higher hand. Therefore, the winning rate is 100%.\n\nPlan 2: Fold\n- If I fold, I will lose the round regardless of GoodGuy's hand. Therefore, the losing rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King: \n  - He is likely to call (60%) or fold (40%). If he calls, I will win as I have a pair of Queens. If he folds, I will also win as he forfeits the round. Therefore, the winning rate is 100%.\n- If GoodGuy holds a Queen: \n  - He is likely to raise (80%) or call (20%). In either case, it will be a draw as we both have a pair of Queens. Therefore, the draw rate is 100%.\n- If GoodGuy holds a Jack: \n  - He is likely to fold (80%) or call (20%). If he folds, I will win. If he calls, I will also win as I have a higher hand. Therefore, the winning rate is 100%.\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 = 1.0 * 7 - 0 * 7 = 7\n- Plan 2: Expected chips gain = winning rate * winning payoff - losing rate * losing payoff = 0 * 3 - 1.0 * 3 = -3\n- Plan 3: Expected chips gain = winning rate * winning payoff - losing rate * losing payoff = 1.0 * 3 - 0 * 3 = 3\n\nPlan Selection:\n- Plan 1: Raise (Expected chips gain = 7)\n- Plan 3: Check (Expected chips gain = 3)\n- Plan 2: Fold (Expected chips gain = -3)\n\nTherefore, the best strategy would be to raise (Plan 1), as it has the highest expected chips gain."}}
{"message": "", "17_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King:\n  - In the 1st round, GoodGuy might believe that I would call (60%) or raise (40%).\n  - In the 2nd round, if the public card is a King, GoodGuy might believe that I would raise (80%) or call (20%).\n- If GoodGuy holds a Queen:\n  - In the 1st round, GoodGuy might believe that I would call (60%) or raise (40%).\n  - In the 2nd round, if the public card is a Queen, GoodGuy might believe that I would raise (80%) or call (20%).\n- If GoodGuy holds a Jack:\n  - In the 1st round, GoodGuy might believe that I would call (50%) or fold (50%).\n  - In the 2nd round, if the public card is a Jack, GoodGuy might believe that I would raise (70%) or call (30%).\n\nPlan 2: Raise\n- If GoodGuy holds a King:\n  - In the 1st round, GoodGuy might believe that I would raise (80%) or call (20%).\n  - In the 2nd round, if the public card is a King, GoodGuy might believe that I would raise (90%) or call (10%).\n- If GoodGuy holds a Queen:\n  - In the 1st round, GoodGuy might believe that I would call (60%) or raise (40%).\n  - In the 2nd round, if the public card is a Queen, GoodGuy might believe that I would raise (80%) or call (20%).\n- If GoodGuy holds a Jack:\n  - In the 1st round, GoodGuy might believe that I would call (50%) or fold (50%).\n  - In the 2nd round, if the public card is a Jack, GoodGuy might believe that I would raise (70%) or call (30%).\n\nPlan 3: Fold\n- If GoodGuy holds a King:\n  - In the 1st round, GoodGuy might believe that I would raise (80%) or call (20%).\n  - In the 2nd round, if the public card is a King, GoodGuy might believe that I would raise (90%) or call (10%).\n- If GoodGuy holds a Queen:\n  - In the 1st round, GoodGuy might believe that I would call (60%) or raise (40%).\n  - In the 2nd round, if the public card is a Queen, GoodGuy might believe that I would raise (80%) or call (20%).\n- If GoodGuy holds a Jack:\n  - In the 1st round, GoodGuy might believe that I would call (50%) or fold (50%).\n  - In the 2nd round, if the public card is a Jack, GoodGuy might believe that I would raise (70%) or call (30%).\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. After the action, Chips in the pot: 3. 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. After the action, Chips in the pot: 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. 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: Expected Chips Gain = 0.6 * 1.5 - 0.4 * 1.5 = 0.3\n- Plan 2: Expected Chips Gain = 0.8 * 2.5 - 0.2 * 2.5 = 1.5\n- Plan 3: Expected Chips Gain = 0.5 * 0.5 - 0.5 * 0.5 = 0\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain, so I would select Plan 2."}}
{"message": "", "17_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (67% probability), he will likely call (60%) or raise (40%). If he calls, I will win as my Queen is higher than the public Jack. If he raises, it's likely he's bluffing as the public card is not a King. Therefore, my winning rate is 100%.\n- If GoodGuy holds a Queen (33% probability), he will likely call (70%) or raise (30%). If he calls, it will be a draw as we both hold Queens. If he raises, it's likely he's bluffing as the public card is not a Queen. Therefore, my winning rate is 70% and draw rate is 30%.\n\nPlan 2: Fold\n- If I fold, I will lose the round regardless of GoodGuy's card. Therefore, my losing rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (67% probability), he will likely call (60%) or raise (40%). If he calls, I will win as my Queen is higher than the public Jack. If he raises, it's likely he's bluffing as the public card is not a King. Therefore, my winning rate is 100%.\n- If GoodGuy holds a Queen (33% probability), he will likely call (70%) or raise (30%). If he calls, it will be a draw as we both hold Queens. If he raises, it's likely he's bluffing as the public card is not a Queen. Therefore, my winning rate is 70% and draw rate is 30%.\n\nWinning/Lose Payoffs:\n- Plan 1: If I win, the pot will be 8 chips (4 from me, 4 from GoodGuy). My winning payoff would be 4 chips. 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 (4 from me, 4 from GoodGuy). My winning payoff would be 4 chips. If I lose, I will lose 4 chips.\n\nExpected Chips Gain:\n- Plan 1: (100% * 4) - (0% * 4) = 4 chips\n- Plan 2: 0 - (100% * 4) = -4 chips\n- Plan 3: (100% * 4) - (0% * 4) = 4 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 both have the highest expected chips gain of 4 chips. However, considering the strategy improvement, I should choose Plan 1 (Raise) as it is more aggressive and can potentially confuse GoodGuy."}}
{"message": "", "19_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (40% chance), he will likely raise (80% chance). 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 0.4*0.8*1/3 = 0.1067, the losing rate is 0.4*0.8*2/3 = 0.2133.\n- If GoodGuy holds a Queen (40% chance), he will likely raise (40% chance) or check (60% chance). 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 0.4*(0.4*2/3+0.6*2/3) = 0.2667, the losing rate is 0.4*(0.4*1/3+0.6*1/3) = 0.1333.\n- If GoodGuy holds a Jack (20% chance), he will likely check (70% chance) or raise (30% 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. The overall losing rate is 0.2*(0.7*2/3+0.3*2/3) = 0.2, the draw rate is 0.2*(0.7*1/3+0.3*1/3) = 0.1.\n- The overall winning rate for Plan 1 is 0.1067+0.2667 = 0.3733, the overall losing rate is 0.2133+0.1333+0.2 = 0.5467, the overall draw rate is 0.1.\n- If I win, the pot will be 4 chips, so the winning payoff is 2 chips. If I lose, the pot will be 4 chips, so the losing payoff is 2 chips.\n- The expected chips gain for Plan 1 is 0.3733*2 - 0.5467*2 = -0.3467 chips.\n\nPlan 2: Raise\n- If GoodGuy holds a King (40% chance), he will likely raise (80% chance). 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 0.4*0.8*1/3 = 0.1067, the losing rate is 0.4*0.8*2/3 = 0.2133.\n- If GoodGuy holds a Queen (40% chance), he will likely call (60% chance) or fold (40% chance). 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 0.4*(0.6*2/3+0.4*2/3) = 0.2667, the losing rate is 0.4*(0.6*1/3+0.4*1/3) = 0.1333.\n- If GoodGuy holds a Jack (20% chance), he will likely fold (60% chance) or call (40% 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. The overall losing rate is 0.2*(0.4*2/3) = 0.1333, the draw rate is 0.2*(0.4*1/3) = 0.0667.\n- The overall winning rate for Plan 2 is 0.1067+0.2667 = 0.3733, the overall losing rate is 0.2133+0.1333+0.1333 = 0.48, the overall draw rate is 0.0667.\n- If I win, the pot will be 6 chips, so the winning payoff is 3 chips. If I lose, the pot will be 6 chips, so the losing payoff is 3 chips.\n- The expected chips gain for Plan 2 is 0.3733*3 - 0.48*3 = -0.32 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 for Plan 3 is -2 chips.\n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 2 > Plan 1 > Plan 3.\n- Considering both the strategy improvement and the estimated expected chips gains, I should choose Plan 2: Raise."}}
{"message": "", "19_2": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (20% probability), he is likely to raise (80%) or call (20%). If he raises, I will lose as King is higher than Jack. If he calls, the result will depend on the public card. If the public card is a Jack, I will win. If the public card is a King or Queen, I will lose. \n- If GoodGuy holds a Queen (60% probability), he is likely to call (60%) or raise (40%). If he raises or calls, the result will depend on the public card. If the public card is a Jack, I will win. If the public card is a Queen, I will lose. If the public card is a King, I will lose.\n- If GoodGuy holds a Jack (40% probability), he is likely to fold (60%) or call (40%). If he folds, I will win. If he calls, the result will depend on the public card. If the public card is a Jack, it will be a draw. If the public card is a King or Queen, I will lose.\n\nPlan 2: Fold\n- If I fold, I will lose the round regardless of GoodGuy's card or the public card.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the call, chips in the pot will be 10. If win, the winning payoff would be 5. If lose, the lose payoff would be 5.\n- Plan 2: After the fold, chips in the pot will be 6. If lose, the lose payoff would be 3.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.2 * 5 (winning with Jack public card) - 0.8 * 5 (losing with King or Queen public card) = -2\n- Plan 2: Expected Chips Gain = -3 (losing by folding)\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain (-2) than Plan 2 (-3). Therefore, I should choose Plan 1: Call."}}
{"message": "", "19_4": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (48% probability), he is likely to call (60%) or fold (40%). If he calls, I will lose (as King is higher than Jack), if he folds, I will win. So, the winning rate is 40%, and the losing rate is 60%.\n- If GoodGuy holds a Jack (16% probability), he is likely to call (40%) or fold (60%). If he calls, it will be a draw (as we both have Jacks), if he folds, I will win. So, the winning rate is 60%, and the draw rate is 40%.\n\nPlan 2: Fold\n- If I fold, I will lose the pot regardless of what card GoodGuy holds. So, the losing rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (48% probability), he is likely to raise (30%) or check (70%). If he raises, I will lose (as King is higher than Jack), if he checks, it will be a draw (as we both have Jacks). So, the losing rate is 30%, and the draw rate is 70%.\n- If GoodGuy holds a Jack (16% probability), he is likely to raise (30%) or check (70%). If he raises, it will be a draw (as we both have Jacks), if he checks, it will be a draw. So, the draw rate is 100%.\n\nWinning/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 lose, the losing payoff would be 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\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.4 * 6 - 0.6 * 6 = -1.2 chips\n- Plan 2: Expected Chips Gain = 0 - 1 * 6 = -6 chips\n- Plan 3: Expected Chips Gain = 0 - 0.3 * 6 = -1.8 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain (-1.2 chips), followed by Plan 3 (-1.8 chips), and Plan 2 (-6 chips). Therefore, I should choose Plan 1: Raise."}}
{"message": "", "20_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (100% probability), he will likely raise (80%) or call (20%). If he raises, I will lose (80% * 100% = 80% lose rate). If he calls, it will be a draw (20% * 100% = 20% draw rate). \n- If GoodGuy holds a Queen (0% probability), it's impossible since I'm holding the other Queen. \n- If GoodGuy holds a Jack (0% probability), it's impossible since he has already raised in the first round. \n\nPlan 2: Raise\n- If GoodGuy holds a King (100% probability), he will likely raise (80%) or call (20%). If he raises, I will lose (80% * 100% = 80% lose rate). If he calls, it will be a draw (20% * 100% = 20% draw rate). \n- If GoodGuy holds a Queen (0% probability), it's impossible since I'm holding the other Queen. \n- If GoodGuy holds a Jack (0% probability), it's impossible since he has already raised in the first round. \n\nPlan 3: Fold\n- If GoodGuy holds a King (100% probability), I will lose (100% lose rate). \n- If GoodGuy holds a Queen (0% probability), it's impossible since I'm holding the other Queen. \n- If GoodGuy holds a Jack (0% probability), it's impossible since he has already raised in the first 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: 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% * 4 - 80% * 4 = -3.2 chips\n- Plan 2: Expected Chips Gain = 0% * 6 - 80% * 6 = -4.8 chips\n- Plan 3: Expected Chips Gain = -3 chips\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is: Plan 3 > Plan 1 > Plan 2. Therefore, I should select Plan 3: Fold."}}
{"message": "", "21_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (60% probability), he is likely to call (30% probability) or raise (70% probability). If he calls, I will win if the public card is a Queen (33.33% probability). If he raises, I will lose unless the public card is a Queen (33.33% probability). \n- If GoodGuy holds a Jack (40% probability), he is likely to fold (50% probability) or call (50% probability). If he folds, I will win. If he calls, I will win unless the public card is a Jack (33.33% probability). \n\nPlan 2: Fold\n- If I fold, I will lose the 2 chips in the pot. \n\nPlan 3: Check\n- If GoodGuy holds a King (60% probability), he is likely to call (30% probability) or raise (70% probability). If he calls, I will win if the public card is a Queen (33.33% probability). If he raises, I will lose unless the public card is a Queen (33.33% probability). \n- If GoodGuy holds a Jack (40% probability), he is likely to fold (50% probability) or call (50% probability). If he folds, I will win. If he calls, I will win unless the public card is a Jack (33.33% probability). \n\nWinning/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 fold, I will lose 2 chips. \n- Plan 3: If I win, the winning payoff would be 2 chips (half of the pot). If I lose, the losing payoff would be 2 chips (half of the pot). \n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected gain = 0.6 * 4 - 0.4 * 2 = 1.6 chips\n- Plan 2: Expected gain = -2 chips\n- Plan 3: Expected gain = 0.6 * 2 - 0.4 * 2 = 0.4 chips\n\nPlan Selection:\n- Based on the expected chips gain, the ranking of the plans is: Plan 1 > Plan 3 > Plan 2. Therefore, I should choose Plan 1: Raise."}}
{"message": "", "22_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a Jack:\n  - In the 1st round, he is likely to fold (70%) or call (30%). If he folds, I win the pot (1 chip). If he calls, the game proceeds to the 2nd round.\n  - In the 2nd round, if the public card is a Jack, he is likely to raise (80%) or call (20%). If he raises, I lose the pot (5 chips). If he calls, the game ends in a draw.\n  - If the public card is not a Jack, he is likely to fold (80%) or call (20%). If he folds, I win the pot (1 chip). If he calls, I win the pot (1 chip).\n- If GoodGuy holds a Queen or King:\n  - In the 1st round, he is likely to raise (60-70%) or call (30-40%). If he raises, I lose the pot (5 chips). If he calls, the game proceeds to the 2nd round.\n  - In the 2nd round, if the public card matches his card, he is likely to raise (90%) or call (10%). If he raises, I lose the pot (13 chips). If he calls, I lose the pot (5 chips).\n  - If the public card does not match his card, he is likely to call (60%) or fold (40%). If he calls, I win the pot (1 chip). If he folds, I win the pot (1 chip).\n\nPlan 2: Raise\n- If GoodGuy holds a Jack:\n  - In the 1st round, he is likely to fold (70%) or call (30%). If he folds, I win the pot (3 chips). If he calls, the game proceeds to the 2nd round.\n  - In the 2nd round, if the public card is a Jack, he is likely to raise (80%) or call (20%). If he raises, I lose the pot (9 chips). If he calls, the game ends in a draw.\n  - If the public card is not a Jack, he is likely to fold (80%) or call (20%). If he folds, I win the pot (3 chips). If he calls, I win the pot (3 chips).\n- If GoodGuy holds a Queen or King:\n  - In the 1st round, he is likely to raise (60-70%) or call (30-40%). If he raises, I lose the pot (9 chips). If he calls, the game proceeds to the 2nd round.\n  - In the 2nd round, if the public card matches his card, he is likely to raise (90%) or call (10%). If he raises, I lose the pot (21 chips). If he calls, I lose the pot (9 chips).\n  - If the public card does not match his card, he is likely to call (60%) or fold (40%). If he calls, I win the pot (3 chips). If he folds, I win the pot (3 chips).\n\nPlan 3: Fold\n- If I fold, I lose the pot (1 chip).\n\nExpected Chips Gain for Each Plan:\n- Plan 1: (0.7 * 1 + 0.3 * 0.2 * 1 + 0.3 * 0.8 * -5 + 0.3 * 0.2 * 1 + 0.3 * 0.8 * -5) / 2 = -1.1 chips\n- Plan 2: (0.7 * 3 + 0.3 * 0.2 * 3 + 0.3 * 0.8 * -9 + 0.3 * 0.2 * 3 + 0.3 * 0.8 * -9) / 2 = -1.5 chips\n- Plan 3: -1 chip\n\nPlan Selection:\n- Plan 1: -1.1 chips\n- Plan 2: -1.5 chips\n- Plan 3: -1 chip\n\nBased on the expected chips gain, I should choose Plan 3 (Fold) as it has the highest expected chips gain."}}
{"message": "", "23_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (30% chance), he might raise (70% chance) or call (30% chance). If he raises, I would likely lose unless the public card is a Queen. If he calls, I would likely win unless the public card is a King. Overall, the winning rate is 30% * 30% = 9%, the losing rate is 30% * 70% = 21%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (60% chance), he might call (60% chance) or raise (30% chance). If he calls or raises, it would be a draw unless the public card is a King or Jack. Overall, the winning rate is 0%, the losing rate is 0%, and the draw rate is 60%.\n- If GoodGuy holds a Jack (10% chance), he might call (50% chance) or fold (40% chance). If he calls, I would likely win unless the public card is a King. If he folds, I would win. Overall, the winning rate is 10% * 90% = 9%, the losing rate is 10% * 10% = 1%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I would lose the 2 chips in the pot regardless of GoodGuy's card or action. 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% chance), he might raise (70% chance) or call (30% chance). If he raises, I would likely lose unless the public card is a Queen. If he calls, I would likely win unless the public card is a King. Overall, the winning rate is 30% * 30% = 9%, the losing rate is 30% * 70% = 21%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (60% chance), he might call (60% chance) or raise (30% chance). If he calls or raises, it would be a draw unless the public card is a King or Jack. Overall, the winning rate is 0%, the losing rate is 0%, and the draw rate is 60%.\n- If GoodGuy holds a Jack (10% chance), he might call (50% chance) or fold (40% chance). If he calls, I would likely win unless the public card is a King. If he folds, I would win. Overall, the winning rate is 10% * 90% = 9%, the losing rate is 10% * 10% = 1%, and the draw rate is 0%.\n\nWinning/Lose Payoffs:\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, I would lose the 2 chips 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:\n- Plan 1: Expected gain = 9% * 4 chips - 21% * 4 chips = -0.48 chips\n- Plan 2: Expected gain = 0% * 0 chips - 100% * 2 chips = -2 chips\n- Plan 3: Expected gain = 9% * 2 chips - 21% * 2 chips = -0.24 chips\n\nPlan Selection:\n- Plan 1: -0.48 chips\n- Plan 2: -2 chips\n- Plan 3: -0.24 chips\n\nBased on the expected chips gain, Plan 3 (Check) is the best strategy."}}
{"message": "", "23_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (probability 33%), he will likely raise (probability 70%). If he raises, I will lose this round as his King matches the public card. The overall losing rate for this plan is 33% * 70% = 23.1%.\n- If GoodGuy holds a Queen (probability 33%), he will likely call (probability 60%). If he calls, it will be a draw as we both hold a Queen. The overall draw rate for this plan is 33% * 60% = 19.8%.\n- If GoodGuy holds a Jack (probability 33%), he will likely fold (probability 40%). If he folds, I will win this round as my Queen is higher than his Jack. The overall winning rate for this plan is 33% * 40% = 13.2%.\n\nPlan 2: Fold\n- If I fold, I will lose this round regardless of GoodGuy's card. The overall losing rate for this plan is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (probability 33%), he will likely raise (probability 70%). If he raises, I will lose this round as his King matches the public card. The overall losing rate for this plan is 33% * 70% = 23.1%.\n- If GoodGuy holds a Queen (probability 33%), he will likely call (probability 60%). If he calls, it will be a draw as we both hold a Queen. The overall draw rate for this plan is 33% * 60% = 19.8%.\n- If GoodGuy holds a Jack (probability 33%), he will likely fold (probability 40%). If he folds, I will win this round as my Queen is higher than his Jack. The overall winning rate for this plan is 33% * 40% = 13.2%.\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 fold, I will lose 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 losing payoff would be 2 chips (half of the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 13.2% * 4 - 23.1% * 2 = 0.28 chips\n- Plan 2: Expected Chips Gain = -100% * 2 = -2 chips\n- Plan 3: Expected Chips Gain = 13.2% * 2 - 23.1% * 2 = -0.2 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I will choose Plan 1: Raise."}}
{"message": "", "24_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (20% probability), he will likely raise (80% probability). If he raises, I will win as we both have a King. The winning rate for his King is 0.2*0.8=0.16. The lose rate is 0 and the draw rate is 0.2*0.2=0.04.\n- If GoodGuy holds a Queen (40% probability), he will likely raise (70% probability) or call (30% probability). If he raises or calls, I will win as my King is higher than his Queen. The winning rate for his Queen is 0.4*1=0.4. The lose rate is 0 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 he folds, I will win. If he calls, I will win as my King is higher than his Jack. The winning rate for his Jack is 0.4*1=0.4. The lose rate is 0 and the draw rate is 0.\n- Overall, the winning rate for plan 1 is 0.16+0.4+0.4=0.96. The lose rate is 0 and the draw rate is 0.04.\n\nPlan 2: Raise\n- If GoodGuy holds a King (20% probability), he will likely raise (80% probability). If he raises, I will win as we both have a King. The winning rate for his King is 0.2*0.8=0.16. The lose rate is 0 and the draw rate is 0.2*0.2=0.04.\n- If GoodGuy holds a Queen (40% probability), he will likely raise (70% probability) or call (30% probability). If he raises or calls, I will win as my King is higher than his Queen. The winning rate for his Queen is 0.4*1=0.4. The lose rate is 0 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 he folds, I will win. If he calls, I will win as my King is higher than his Jack. The winning rate for his Jack is 0.4*1=0.4. The lose rate is 0 and the draw rate is 0.\n- Overall, the winning rate for plan 2 is 0.16+0.4+0.4=0.96. The lose rate is 0 and the draw rate is 0.04.\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 lose rate is 1 and the draw rate is 0.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the call, chips in the pot: 2. If win, the winning payoff would be 1. If lose, the lose payoff would be 1.\n- Plan 2: 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 3: After the fold, chips in the pot: 2. If lose, the lose payoff would be 1.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0.96*1 - 0*1 = 0.96\n- Plan 2: 0.96*3 - 0*3 = 2.88\n- Plan 3: 0*0 - 1*1 = -1\n\nPlan Selection:\n- Plan 2 (Raise) has the highest estimated expected chips gain of 2.88, followed by Plan 1 (Call) with 0.96, and Plan 3 (Fold) with -1. Therefore, I should choose Plan 2: Raise."}}
{"message": "", "24_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King: \n  - He will raise with a 50% probability or check with a 50% probability. \n  - If he raises, I will win as my card is higher. \n  - If he checks, I will also win as my card is higher. \n  - Overall winning rate for his King is 100%.\n- If GoodGuy holds a Queen: \n  - He will raise with a 80% probability or call with a 20% probability. \n  - If he raises or calls, I will lose as his card matches the public card. \n  - Overall losing rate for his Queen is 100%.\n\nPlan 2: Fold\n- If GoodGuy holds a King: \n  - He will raise with a 50% probability or check with a 50% probability. \n  - If he raises or checks, I will lose as I have folded. \n  - Overall losing rate for his King is 100%.\n- If GoodGuy holds a Queen: \n  - He will raise with a 80% probability or call with a 20% probability. \n  - If he raises or calls, I will lose as I have folded. \n  - Overall losing rate for his Queen is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King: \n  - He will raise with a 50% probability or check with a 50% probability. \n  - If he raises, I will win as my card is higher. \n  - If he checks, I will also win as my card is higher. \n  - Overall winning rate for his King is 100%.\n- If GoodGuy holds a Queen: \n  - He will raise with a 80% probability or call with a 20% probability. \n  - If he raises or calls, I will lose as his card matches the public card. \n  - Overall losing rate for his Queen is 100%.\n\nWinning/Lose Payoffs for Each Plan:\n- Plan 1: After the action, 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 action, chips in the pot would be 4. If lose, the lose payoff would be 2.\n- Plan 3: After the action, chips in the pot would be 4. If win, the winning payoff would be 2. If lose, the lose payoff would be 2.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 100% * 8 - 100% * 8 = 0\n- Plan 2: Expected Chips Gain = 0 - 100% * 2 = -2\n- Plan 3: Expected Chips Gain = 100% * 2 - 100% * 2 = 0\n\nPlan Selection:\n- Plan 1 and Plan 3 have the same expected chips gain, but Plan 1 is more aggressive which aligns with the strategy improvement. Therefore, I will choose Plan 1: Raise."}}
{"message": "", "24_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (50% probability), he will check (50% probability). If he checks, it will be a draw and the pot will be split evenly. \n- If GoodGuy holds a Queen (30% probability), he will raise (40% probability) or check (60% probability). If he raises, I will lose. If he checks, I will win.\n- If GoodGuy holds a Jack (20% probability), he will raise (20% probability) or check (80% probability). If he raises, I will win. If he checks, I will win.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds.\n\nWinning/Lose/Draw Rates for Each Plan:\n- Plan 1: Winning rate = 50% (King) * 50% (check) + 30% (Queen) * 60% (check) + 20% (Jack) * 100% = 55%. Lose rate = 30% (Queen) * 40% (raise) = 12%. Draw rate = 50% (King) * 50% (check) = 25%.\n- Plan 2: Winning rate = 0%. Lose rate = 100%. Draw rate = 0%.\n\nNumber of Winning/Lose Payoffs for Each Plan:\n- Plan 1: If win, the winning payoff would be half of the pot (12 chips) = 6 chips. If lose, the lose payoff would be half of the pot (8 chips) = 4 chips.\n- Plan 2: If lose, the lose payoff would be half of the pot (8 chips) = 4 chips.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected chips gain = 55% * 6 chips - 12% * 4 chips = 2.7 chips.\n- Plan 2: Expected chips gain = 0% * 0 chips - 100% * 4 chips = -4 chips.\n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 1 > Plan 2.\n- Therefore, the plan with the highest estimated expected chips gain is Plan 1: Call."}}
{"message": "", "25_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (33.3% chance), he will likely call (30% chance). If the public card is a King, it will be a draw. If the public card is a Queen or Jack, I will win unless the public card matches GoodGuy's card. The overall winning rate is 0.333*0.7 = 0.2331, the draw rate is 0.333*0.3 = 0.0999, and the losing rate is 0.\n- If GoodGuy holds a Queen (33.3% chance), he will likely call (40% chance). If the public card is a King, I will win. If the public card is a Queen, it will be a draw. If the public card is a Jack, I will win. The overall winning rate is 0.333*0.6 = 0.1998, the draw rate is 0.333*0.4 = 0.1332, and the losing rate is 0.\n- If GoodGuy holds a Jack (33.3% chance), he will likely fold (50% chance). If he calls (30% chance) and the public card is a King or Queen, I will win. If the public card is a Jack, it will be a draw. The overall winning rate is 0.333*0.5 = 0.1665, the draw rate is 0.333*0.2 = 0.0666, and the losing rate is 0.\n\nPlan 2: Fold\n- If I fold, I will lose the round regardless of GoodGuy's card. The overall 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 (33.3% chance), he will likely call (30% chance). If the public card is a King, it will be a draw. If the public card is a Queen or Jack, I will win unless the public card matches GoodGuy's card. The overall winning rate is 0.333*0.7 = 0.2331, the draw rate is 0.333*0.3 = 0.0999, and the losing rate is 0.\n- If GoodGuy holds a Queen (33.3% chance), he will likely call (40% chance). If the public card is a King, I will win. If the public card is a Queen, it will be a draw. If the public card is a Jack, I will win. The overall winning rate is 0.333*0.6 = 0.1998, the draw rate is 0.333*0.4 = 0.1332, and the losing rate is 0.\n- If GoodGuy holds a Jack (33.3% chance), he will likely fold (50% chance). If he calls (30% chance) and the public card is a King or Queen, I will win. If the public card is a Jack, it will be a draw. The overall winning rate is 0.333*0.5 = 0.1665, the draw rate is 0.333*0.2 = 0.0666, 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 half of the pot (currently 4 chips), so 2 chips. If I lose, the losing payoff would be half of the pot, so 2 chips.\n- Plan 2: If I fold, I will lose the round and the losing payoff would be half of the pot, so 2 chips.\n- Plan 3: If I check and win, the winning payoff would be half of the pot (currently 4 chips), so 2 chips. If I lose, the losing payoff would be half of the pot, so 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.5994*2 - 0*2 = 1.1988 chips\n- Plan 2: Expected Chips Gain = 0*2 - 1*2 = -2 chips\n- Plan 3: Expected Chips Gain = 0.5994*2 - 0*2 = 1.1988 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 have the highest expected chips gain (1.1988 chips), so I should choose either of these plans. However, considering the strategy improvement, Plan 1 (raise) might be a better choice as it could potentially intimidate GoodGuy into folding, which would increase my chances of winning the round."}}
{"message": "", "26_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (40% chance), he will likely raise (80% chance). If the public card is a King, I will win (100% chance). If the public card is not a King, I will draw (50% chance) or lose (50% chance). Overall, the winning rate is 32%, the losing rate is 20%, and the drawing rate is 20%.\n- If GoodGuy holds a Queen (30% chance), he will likely raise (60% chance) or call (30% chance). If the public card is a King or a Queen, I will win (100% chance). If the public card is a Jack, I will lose (100% chance). Overall, the winning rate is 27%, the losing rate is 9%, and the drawing rate is 0%.\n- If GoodGuy holds a Jack (30% chance), he will likely call (70% chance) or fold (10% chance). If the public card is a King or a Queen, I will win (100% chance). If the public card is a Jack, I will draw (50% chance) or lose (50% chance). Overall, the winning rate is 21%, the losing rate is 15%, and the drawing rate is 15%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (40% chance), he will likely raise (80% chance). If the public card is a King, I will win (100% chance). If the public card is not a King, I will draw (50% chance) or lose (50% chance). Overall, the winning rate is 32%, the losing rate is 20%, and the drawing rate is 20%.\n- If GoodGuy holds a Queen (30% chance), he will likely call (30% chance) or fold (10% chance). If the public card is a King or a Queen, I will win (100% chance). If the public card is a Jack, I will lose (100% chance). Overall, the winning rate is 27%, the losing rate is 9%, and the drawing rate is 0%.\n- If GoodGuy holds a Jack (30% chance), he will likely fold (10% chance). If the public card is a King or a Queen, I will win (100% chance). If the public card is a Jack, I will draw (50% chance) or lose (50% chance). Overall, the winning rate is 30%, the losing rate is 0%, and the drawing rate is 15%.\n\nPlan 3: Fold\n- If I fold, I will lose 100% of the time. The losing rate is 100%, and the winning and drawing 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. 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 2 chips.\n- Plan 3: If I fold, I will lose 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is 0.32 * 3 - 0.20 * 1 = 0.76 chips.\n- Plan 2: The expected chips gain is 0.30 * 7 - 0.09 * 2 = 1.98 chips.\n- Plan 3: The expected chips gain is -1 chip.\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I will choose this plan."}}
{"message": "", "26_2": {"plan": "Plan 1: Call\n- If GoodGuy holds a Queen (75% probability), he will likely raise (60% probability). If the public card is a King or Jack, I will win (probability = 0.75 * 0.6 = 0.45). If the public card is a Queen, I will lose (probability = 0.75 * 0.4 = 0.3).\n- If GoodGuy holds a Jack (25% probability), he will likely call (70% probability). If the public card is a King or Queen, I will win (probability = 0.25 * 0.7 = 0.175). If the public card is a Jack, I will lose (probability = 0.25 * 0.3 = 0.075).\n- Overall, the winning rate for Plan 1 is 0.45 + 0.175 = 0.625, the losing rate is 0.3 + 0.075 = 0.375, and the draw rate is 0 (since there are no possible draws in this situation).\n\nPlan 2: Fold\n- If I fold, I will automatically lose the game, regardless of GoodGuy's cards. Therefore, the winning rate for Plan 2 is 0, the losing rate is 1, and the draw rate is 0.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the call, there will be 8 chips in the pot. 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, there will be no change in the number of chips in the pot. Therefore, there is no winning payoff, and the losing payoff would be 2 chips (the amount I have already put in the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is the winning rate * winning payoff - losing rate * losing payoff = 0.625 * 4 - 0.375 * 4 = 1 chip.\n- Plan 2: The expected chips gain is the winning rate * winning payoff - losing rate * losing payoff = 0 * 0 - 1 * 2 = -2 chips.\n\nPlan Selection:\n- The estimated expected chips gains for Plan 1 and Plan 2 are 1 chip and -2 chips, respectively. Therefore, Plan 1 (Call) is the better strategy in this situation."}}
{"message": "", "26_4": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (80% probability), he will likely raise (20% probability) or call (70% probability). If he raises, I will lose (probability = 0.8 * 0.2 = 0.16). If he calls, I will win if a King is revealed in the next round (probability = 0.8 * 0.7 * 0.33 = 0.186), otherwise I will lose (probability = 0.8 * 0.7 * 0.67 = 0.376).\n- If GoodGuy holds a Queen (60% probability), he will likely call (70% probability) or fold (10% probability). If he calls, I will win if a King is revealed in the next round (probability = 0.6 * 0.7 * 0.33 = 0.139), otherwise I will lose (probability = 0.6 * 0.7 * 0.67 = 0.281). If he folds, I will win (probability = 0.6 * 0.1 = 0.06).\n- If GoodGuy holds a Jack (20% probability), he will likely call (70% probability) or fold (10% probability). If he calls, I will win if a King is revealed in the next round (probability = 0.2 * 0.7 * 0.33 = 0.046), otherwise I will lose (probability = 0.2 * 0.7 * 0.67 = 0.094). If he folds, I will win (probability = 0.2 * 0.1 = 0.02).\n- Overall, the winning rate for plan 1 is 0.186 + 0.139 + 0.046 + 0.06 + 0.02 = 0.451. The losing rate for plan 1 is 0.16 + 0.376 + 0.281 + 0.094 = 0.911. The draw rate for plan 1 is 0.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of GoodGuy's card. The losing rate for plan 2 is 1. The winning rate and draw rate for plan 2 are 0.\n\nPlan 3: Check\n- The probabilities and rates for plan 3 are the same as for plan 1, because checking does not change the game state.\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) plus my raise (4 chips), which is 5 chips. If I lose, the lose payoff would be my raise (4 chips).\n- Plan 2: If I fold, I will lose my current bet (6 chips).\n- Plan 3: If I check and win, the winning payoff would be half of the pot (6 chips), which is 3 chips. If I lose, the lose payoff would be my current bet (6 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected chips gain = winning rate * winning payoff - losing rate * lose payoff = 0.451 * 5 - 0.911 * 4 = -1.605 chips.\n- Plan 2: Expected chips gain = -6 chips.\n- Plan 3: Expected chips gain = 0.451 * 3 - 0.911 * 6 = -4.173 chips.\n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 1 > Plan 3 > Plan 2.\n- Therefore, I should choose Plan 1 (Raise) as it has the highest estimated expected chips gain."}}
{"message": "", "27_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (50% probability), he might raise (80% probability) or call (20% probability). If he raises, I will lose (80% probability). If he calls, it will be a draw (20% probability). \n- If GoodGuy holds a Queen (50% probability), he might raise (70% probability) or call (30% probability). If he raises, I will lose (70% probability). If he calls, it will be a draw (30% probability). \n- Overall, the winning rate for plan 1 is 0%, the losing rate is 75%, and the draw rate is 25%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (50% probability), he might raise (80% probability) or call (20% probability). If he raises, I will lose (80% probability). If he calls, it will be a draw (20% probability). \n- If GoodGuy holds a Queen (50% probability), he might raise (70% probability) or call (30% probability). If he raises, I will lose (70% probability). If he calls, it will be a draw (30% probability). \n- Overall, the winning rate for plan 2 is 0%, the losing rate is 75%, and the draw rate is 25%.\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: 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: 2. If lose, the lose payoff would be 1.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0% * 1.5 - 75% * 1.5 = -1.125\n- Plan 2: 0% * 2.5 - 75% * 2.5 = -1.875\n- Plan 3: -1\n\nPlan Selection:\n- Plan 1: -1.125\n- Plan 2: -1.875\n- Plan 3: -1\n\nBased on the estimated expected chips gains, Plan 1 (Call) is the best strategy to follow."}}
{"message": "", "27_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 Queen matches the public card, while my Jack does not). If he calls, it will be a draw (as neither of our cards match the public card). Overall, the 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 King (20% probability), he will likely raise (70% probability) or call (30% probability). If he raises or calls, I will lose (as his King is higher than my Jack). Overall, the winning rate for this plan is 0%, the losing rate is 20% (20% * 100%), and the draw rate is 0%.\n- If GoodGuy holds a Jack (20% probability), he will likely fold (70% probability) or call (30% probability). If he folds, I will win. If he calls, it will be a draw (as both of our cards are Jacks). Overall, the winning rate for this plan is 14% (20% * 70%), the losing rate is 0%, and the draw rate is 6% (20% * 30%).\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. The winning rate for this plan is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- This plan has the same outcomes as Plan 1, as GoodGuy's actions will not be influenced by my checking.\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 3 chips.\n- Plan 2: If I lose, the losing payoff would be 2 chips (half of the 4 chips in the pot).\n- Plan 3: The payoffs are the same as Plan 1.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is 14% * 3 chips - 68% * 3 chips = -1.62 chips.\n- Plan 2: The expected chips loss is 100% * 2 chips = -2 chips.\n- Plan 3: The expected chips gain is the same as Plan 1.\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain (-1.62 chips), followed by Plan 3 (-1.62 chips), and Plan 2 (-2 chips). Therefore, I should choose Plan 1: Raise."}}
{"message": "", "27_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a Jack (70% probability), he will likely fold (70% probability). If he folds, I will win the pot, which is currently 16 chips. The winning rate for this scenario is 0.7 * 0.7 = 0.49.\n- If GoodGuy holds a Queen (20% probability), he will likely raise (60% probability) or call (40% probability). If he raises, I will lose the pot, which is currently 16 chips. The losing rate for this scenario is 0.2 * 0.6 = 0.12. If he calls, it will be a draw, and the draw rate for this scenario is 0.2 * 0.4 = 0.08.\n- If GoodGuy holds a King (10% probability), he will likely raise (70% probability) or call (30% probability). If he raises, I will lose the pot, which is currently 16 chips. The losing rate for this scenario is 0.1 * 0.7 = 0.07. If he calls, it will be a draw, and the draw rate for this scenario is 0.1 * 0.3 = 0.03.\n\nPlan 2: Fold\n- If I fold, I will lose the pot, which is currently 16 chips. The losing rate for this scenario is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 8 chips (half of the pot). If I lose, the losing payoff would be 8 chips.\n- Plan 2: If I fold, the losing payoff would be 8 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 0.49 * 8 - 0.19 * 8 = 2.4 chips\n- Plan 2: Expected Chips Gain = -1 * 8 = -8 chips\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain than Plan 2. Therefore, I should choose Plan 1: Call."}}
{"message": "", "28_0": {"plan": "Plan 1: Call\nIf I call, I will put 1 more chip into the pot, matching GoodGuy's bet. \n\nThe winning/lose/draw rates when GoodGuy holds a Jack: \nBased on GoodGuy's behaviour pattern, in the first round, because GoodGuy holds a Jack (60% probability) and the combination with the current public card (not yet revealed), he will likely call (70% probability) or raise (30% probability). If the public card is a Jack, I will win (70% * 60% = 42%). If the public card is a Queen or King, I will lose (30% * 60% = 18%). The draw rate is 0% as there are no other Jacks in the deck. \n\nThe winning/lose/draw rates when GoodGuy holds a Queen: \nIf GoodGuy holds a Queen (20% probability), he will likely raise (70% probability) or call (30% probability). If the public card is a Queen, I will lose (70% * 20% = 14%). If the public card is a Jack or King, I will win (30% * 20% = 6%). The draw rate is 0% as my card is not a Queen. \n\nThe winning/lose/draw rates when GoodGuy holds a King: \nIf GoodGuy holds a King (20% probability), he will likely raise (70% probability) or call (30% probability). If the public card is a King, I will lose (70% * 20% = 14%). If the public card is a Jack or Queen, I will win (30% * 20% = 6%). The draw rate is 0% as my card is not a King. \n\nPlan1 overall GoodGuy's Winning/Lose/Draw rates: \nThe Winning rate for plan 1 is 42% + 6% + 6% = 54%; \nLose rate for plan 1 is 18% + 14% + 14% = 46%; \nDraw Rate for plan 1 is 0%. \n\nPlan 2: Raise\nIf I raise, I will put 4 more chips into the pot, increasing the bet. \n\nThe winning/lose/draw rates when GoodGuy holds a Jack: \nIf GoodGuy holds a Jack (60% probability), he will likely fold (70% probability) or call (30% probability). If the public card is a Jack, I will win (30% * 60% = 18%). If the public card is a Queen or King, I will win (70% * 60% = 42%). The draw rate is 0% as there are no other Jacks in the deck. \n\nThe winning/lose/draw rates when GoodGuy holds a Queen: \nIf GoodGuy holds a Queen (20% probability), he will likely call (70% probability) or fold (30% probability). If the public card is a Queen, I will lose (70% * 20% = 14%). If the public card is a Jack or King, I will win (30% * 20% = 6%). The draw rate is 0% as my card is not a Queen. \n\nThe winning/lose/draw rates when GoodGuy holds a King: \nIf GoodGuy holds a King (20% probability), he will likely call (70% probability) or fold (30% probability). If the public card is a King, I will lose (70% * 20% = 14%). If the public card is a Jack or Queen, I will win (30% * 20% = 6%). The draw rate is 0% as my card is not a King. \n\nPlan2 overall GoodGuy's Winning/Lose/Draw rates: \nThe Winning rate for plan 2 is 18% + 6% + 6% = 30%; \nLose rate for plan 2 is 42% + 14% + 14% = 70%; \nDraw Rate for plan 2 is 0%. \n\nPlan 3: Fold\nIf I fold, I will lose the 2 chips I have already put into the pot. \n\nPlan3 overall GoodGuy's Winning/Lose/Draw rates: \nThe Winning rate for plan 3 is 0%; \nLose rate for plan 3 is 100%; \nDraw Rate for plan 3 is 0%. \n\nThe number of winning and lose payoffs for each plan: \nPlan1: After the action, Chips in the pot: 4. If win, the winning payoff would be 2. If lose, the lose payoff would be 2. \nPlan2: After the action, Chips in the pot: 7. If win, the winning payoff would be 3.5. If lose, the lose payoff would be 3.5. \nPlan3: After the action, Chips in the pot: 3. If win, the winning payoff would be 0. If lose, the lose payoff would be 2. \n\nEstimate Expected Chips Gain for Each Plan: \nPlan1: 54% * 2 - 46% * 2 = 0.16 chips\nPlan2: 30% * 3.5 - 70% * 3.5 = -1.4 chips\nPlan3: 0% * 0 - 100% * 2 = -2 chips\n\nPlan Selection: \nThe rank of estimated expected chips gains for every plan is Plan1 > Plan2 > Plan3. Therefore, I should choose Plan1: Call."}}
{"message": "", "28_2": {"plan": "Plan 1: Raise\nIf I raise, I will put 4 more chips into the pot, making the total pot 8 chips. \n\nThe winning/lose/draw rates when GoodGuy holds a King: \nBased on GoodGuy's behaviour pattern, in the second round, because GoodGuy holds a King (probability 1/3) and the combination with the current public card (Queen), and if he sees my action of raising, GoodGuy will likely call (probability 0.8) (I actually hold a Jack and the public card is a Queen, he holds a King and the public card is a Queen, considering Single Game Win/Draw/Lose Rule, I will lose), or fold (probability 0.2) (I will win). \nOverall, the winning rate for his King is 0.2*1/3=0.067, the lose rate for his King is 0.8*1/3=0.267, the draw rate for his King is 0. \n\nThe winning/lose/draw rates when GoodGuy holds a Jack: \nBased on GoodGuy's behaviour pattern, in the second round, because GoodGuy holds a Jack (probability 2/3) and the combination with the current public card (Queen), and if he sees my action of raising, GoodGuy will likely fold (probability 0.9) (I will win), or call (probability 0.1) (I will draw). \nOverall, the winning rate for his Jack is 0.9*2/3=0.6, the lose rate for his Jack is 0, the draw rate for his Jack is 0.1*2/3=0.067. \n\nPlan1 overall GoodGuy's Winning/Lose/Draw rates: \nBased on the above analysis, the Winning rate for plan 1 is 0.067+0.6=0.667; Lose rate for plan 1 is 0.267+0=0.267; Draw Rate for plan 1 is 0+0.067=0.067. \n\nPlan 2: Fold\nIf I fold, I will forfeit the game. The winning rate for this plan is 0, the lose rate is 1, and the draw rate is 0. \n\nPlan 3: Check\nIf I check, I will not add any additional chips to the pot. The winning/lose/draw rates for this plan would be similar to Plan 1, but with a lower winning rate and a higher draw rate, as GoodGuy is less likely to fold if I check. \n\nThe number of winning and lose payoffs for each plan: \nPlan1: After the action, Chips in the pot: 8. If win, the winning payoff would be 4. If lose, the lose payoff would be 4. \nPlan2: After the action, Chips in the pot: 4. If win, the winning payoff would be 0. If lose, the lose payoff would be 2. \nPlan3: 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: \nPlan 1: 0.667*4 - 0.267*4 = 1.6 chips\nPlan 2: 0*0 - 1*2 = -2 chips\nPlan 3: 0.6*2 - 0.267*2 = 0.666 chips\n\nPlan Selection: \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, which is to raise."}}
{"message": "", "30_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (50% probability), he is likely to raise the bet (80% probability) or call (20% probability). If he raises, I will win (probability = 0.5 * 0.8 = 0.4), if he calls, it will be a draw (probability = 0.5 * 0.2 = 0.1).\n- If GoodGuy holds a Queen (50% probability), he is likely to raise the bet (70% probability) or call (30% probability). If he raises, I will win (probability = 0.5 * 0.7 = 0.35), if he calls, I will win (probability = 0.5 * 0.3 = 0.15).\n- Overall, the winning rate for plan 1 is 0.4 + 0.35 + 0.15 = 0.9, the lose rate is 0, and the draw rate is 0.1.\n\nPlan 2: Raise\n- If GoodGuy holds a King (50% probability), he is likely to raise the bet (80% probability) or call (20% probability). If he raises, it will be a draw (probability = 0.5 * 0.8 = 0.4), if he calls, it will be a draw (probability = 0.5 * 0.2 = 0.1).\n- If GoodGuy holds a Queen (50% probability), he is likely to raise the bet (70% probability) or call (30% probability). If he raises, I will win (probability = 0.5 * 0.7 = 0.35), if he calls, I will win (probability = 0.5 * 0.3 = 0.15).\n- Overall, the winning rate for plan 2 is 0.35 + 0.15 = 0.5, the lose rate is 0, and the draw rate is 0.4 + 0.1 = 0.5.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card. Therefore, the winning rate for plan 3 is 0, the lose rate is 1, 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 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: 0.9 * 4 - 0 * 4 = 3.6\n- Plan 2: 0.5 * 6 - 0 * 6 = 3\n- Plan 3: 0 * 3 - 1 * 3 = -3\n\nPlan Selection:\n- Plan 1: 3.6\n- Plan 2: 3\n- Plan 3: -3\n\nTherefore, I should choose Plan 1 (Call) as it has the highest estimated expected chips gain."}}
{"message": "", "30_3": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (20% probability), he is likely to raise (90% probability) or call (10% probability). If he raises, I will lose (90% probability). If he calls, I will draw (10% probability).\n- If GoodGuy holds a Queen (30% probability), he is likely to raise (80% probability) or call (20% probability). If he raises, I will win (80% probability). If he calls, I will win (20% probability).\n- If GoodGuy holds a Jack (50% probability), he is likely to fold (70% probability) or call (30% probability). If he folds, I will win (70% probability). If he calls, I will win (30% probability).\n- Overall, the winning rate for Plan 1 is 0.2*0.8 + 0.3*1 + 0.5*1 = 1.16, the losing rate is 0.2*0.9 = 0.18, and the draw rate is 0.2*0.1 = 0.02.\n\nPlan 2: Raise\n- If GoodGuy holds a King (20% probability), he is likely to raise (90% probability) or call (10% probability). If he raises, I will lose (90% probability). If he calls, I will draw (10% probability).\n- If GoodGuy holds a Queen (30% probability), he is likely to raise (80% probability) or call (20% probability). If he raises, I will win (80% probability). If he calls, I will win (20% probability).\n- If GoodGuy holds a Jack (50% probability), he is likely to fold (70% probability) or call (30% probability). If he folds, I will win (70% probability). If he calls, I will win (30% probability).\n- Overall, the winning rate for Plan 2 is 0.2*0.8 + 0.3*1 + 0.5*1 = 1.16, the losing rate is 0.2*0.9 = 0.18, and the draw rate is 0.2*0.1 = 0.02.\n\nPlan 3: Fold\n- If I fold, I will lose all the chips I have put into the pot. The losing rate for Plan 3 is 1.\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: 16. If win, the winning payoff would be 8. If lose, the lose payoff would be 8.\n- Plan 3: After the action, chips in the pot: 8. If lose, the lose payoff would be 8.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 1.16 * 6 - 0.18 * 6 = 5.88 - 1.08 = 4.8\n- Plan 2: 1.16 * 8 - 0.18 * 8 = 9.28 - 1.44 = 7.84\n- Plan 3: -1 * 8 = -8\n\nPlan Selection:\n- Plan 2 has the highest estimated expected chips gain, so I will choose Plan 2."}}
{"message": "", "31_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a Jack, he is likely to fold (70%) or call (30%). If he folds, I will win the pot, which is currently 3 chips. If he calls, the game will proceed to the second round. In the second round, if the public card is a Jack, I will win (100%) because my hand matches the public card. If the public card is a Queen or King, I will lose (100%) because my hand is lower. Therefore, the winning rate for this plan is 70% + 30% * 1/3 = 80%, the losing rate is 30% * 2/3 = 20%, and the draw rate is 0%.\n- If GoodGuy holds a Queen or King, he is likely to raise (65%) or call (35%). If he raises, I will lose the pot, which is currently 3 chips. If he calls, the game will proceed to the second round. In the second round, if the public card is a Jack, I will win (100%) because my hand matches the public card. If the public card is a Queen or King, I will lose (100%) because my hand is lower. Therefore, the winning rate for this plan is 35% * 1/3 = 11.67%, the losing rate is 65% + 35% * 2/3 = 88.33%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a Jack, he is likely to fold (70%) or call (30%). If he folds, I will win the pot, which is currently 3 chips. If he calls, the game will proceed to the second round. In the second round, if the public card is a Jack, I will win (100%) because my hand matches the public card. If the public card is a Queen or King, I will lose (100%) because my hand is lower. Therefore, the winning rate for this plan is 70% + 30% * 1/3 = 80%, the losing rate is 30% * 2/3 = 20%, and the draw rate is 0%.\n- If GoodGuy holds a Queen or King, he is likely to raise (65%) or call (35%). If he raises, I will lose the pot, which is currently 3 chips. If he calls, the game will proceed to the second round. In the second round, if the public card is a Jack, I will win (100%) because my hand matches the public card. If the public card is a Queen or King, I will lose (100%) because my hand is lower. Therefore, the winning rate for this plan is 35% * 1/3 = 11.67%, the losing rate is 65% + 35% * 2/3 = 88.33%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the pot, which is currently 3 chips. Therefore, the 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 win, the winning payoff would be 3/2 = 1.5 chips. If lose, the lose payoff would be 3/2 = 1.5 chips.\n- Plan 2: If win, the winning payoff would be 7/2 = 3.5 chips. If lose, the lose payoff would be 7/2 = 3.5 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 = 80% * 1.5 - 20% * 1.5 = 0.9 chips\n- Plan 2: Expected Chips Gain = 11.67% * 3.5 - 88.33% * 3.5 = -2.33 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I will choose Plan 1: Call."}}
{"message": "", "31_2": {"plan": "Plan 1: Check\n- If GoodGuy holds a Jack (50% probability), he is likely to check (50% probability) or fold (50% probability). If he checks, it will be a draw (50% probability). If he folds, I will win (50% probability). \n- If GoodGuy holds a King (50% probability), he is likely to check (10% probability) or raise (90% probability). If he checks, I will lose (10% probability). If he raises, I will lose (90% probability). \n- Overall, the winning rate for plan 1 is 25% (50% * 50%), the losing rate is 45% (50% * 10% + 50% * 90%), and the draw rate is 25% (50% * 50%). \n\nPlan 2: Raise\n- If GoodGuy holds a Jack (50% probability), he is likely to fold (70% probability). If he folds, I will win (70% probability). \n- If GoodGuy holds a King (50% probability), he is likely to raise (70% probability) or call (30% probability). If he raises or calls, I will lose (100% probability). \n- Overall, the winning rate for plan 2 is 35% (50% * 70%), the losing rate is 50% (50% * 100%), and the draw rate is 0%. \n\nPlan 3: Fold\n- If I fold, I will lose regardless of what GoodGuy holds. The losing rate for plan 3 is 100%. \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: 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: 2. If lose, the lose payoff would be 1. \n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected chips gain = 25% * 2 - 45% * 2 = -0.4 chips\n- Plan 2: Expected chips gain = 35% * 3 - 50% * 3 = -0.45 chips\n- Plan 3: Expected chips gain = -100% * 1 = -1 chip\n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 1 > Plan 2 > Plan 3. Therefore, I should select Plan 1: Check."}}
{"message": "", "32_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (40% probability), he will likely raise (60% 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 40% * 60% = 24%, the losing rate is 40% * 40% = 16%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (20% probability), he will likely raise (60% probability). If the public card is a Queen, it will be a draw. If the public card is a King or Jack, I will win. Overall, the winning rate is 20% * 60% = 12%, the losing rate is 0%, and the draw rate is 20% * 40% = 8%.\n- If GoodGuy holds a Jack (40% probability), he will likely fold (70% probability). If the public card is a Queen, I will win. If the public card is a King or Jack, it will be a draw. Overall, the winning rate is 40% * 70% = 28%, the losing rate is 0%, and the draw rate is 40% * 30% = 12%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (40% probability), he will likely call (40% 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 40% * 60% = 24%, the losing rate is 40% * 40% = 16%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (20% probability), he will likely call (40% probability). If the public card is a Queen, it will be a draw. If the public card is a King or Jack, I will win. Overall, the winning rate is 20% * 60% = 12%, the losing rate is 0%, and the draw rate is 20% * 40% = 8%.\n- If GoodGuy holds a Jack (40% probability), he will likely fold (70% probability). If the public card is a Queen, I will win. If the public card is a King or Jack, it will be a draw. Overall, the winning rate is 40% * 70% = 28%, the losing rate is 0%, and the draw rate is 40% * 30% = 12%.\n\nPlan 3: Fold\n- If I fold, I will lose 1 chip regardless of GoodGuy's hand or the public 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: 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 2 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 = 24% * 3 - 16% * 1 = 0.56 chips\n- Plan 2: Expected Chips Gain = 24% * 7 - 16% * 2 = 1.12 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, so I should choose this plan."}}
{"message": "", "32_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (50% probability), he will likely raise (80% probability). If he raises, it will be a draw and the pot will be split. If he folds (20% probability), I will win. So, the winning rate is 10% (50% * 20%), the losing rate is 0%, and the draw rate is 40% (50% * 80%).\n- If GoodGuy holds a King (50% probability), he will likely raise (80% probability). If he raises, I will lose. If he folds (20% probability), I will win. So, the winning rate is 10% (50% * 20%), the losing rate is 40% (50% * 80%), and the draw 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 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 raise (80% probability). If he raises, it will be a draw and the pot will be split. If he checks (20% probability), it will also be a draw. So, the winning rate is 0%, the losing rate is 0%, and the draw rate is 50%.\n- If GoodGuy holds a King (50% probability), he will likely raise (80% probability). If he raises, I will lose. If he checks (20% probability), I will also lose. So, 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: 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 check, 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 Chips Gain = 10% * 4 - 40% * 4 = -1.2 chips\n- Plan 2: Expected Chips Gain = 0% * 4 - 100% * 4 = -4 chips\n- Plan 3: Expected Chips Gain = 0% * 4 - 50% * 4 = -2 chips\n\nPlan Selection:\n- Plan 1: -1.2 chips\n- Plan 2: -4 chips\n- Plan 3: -2 chips\n\nBased on the estimated expected chips gain, Plan 1 (Raise) is the best strategy to use in this situation."}}
{"message": "", "32_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 the round as his King beats my pair of Queens. The overall losing rate for this scenario is 0.7 * 0.8 = 0.56.\n- If GoodGuy holds a Jack (30% probability), he will likely fold (70% probability). If this happens, I will win the round as my pair of Queens beats his Jack. The overall winning rate for this scenario is 0.3 * 0.7 = 0.21.\n\nPlan 2: Fold\n- If GoodGuy holds a King (70% probability), he will likely raise (80% probability). If this happens, I will lose the round as his King beats my pair of Queens. However, since I fold, I will only lose the chips I have already put into the pot. The overall losing rate for this scenario is 0.7 * 0.8 = 0.56.\n- If GoodGuy holds a Jack (30% probability), he will likely fold (70% probability). If this happens, I will not win any chips as I have already folded. The overall draw rate for this scenario is 0.3 * 0.7 = 0.21.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the call, the chips in the pot would be 20. If I win, the winning payoff would be 10 chips. If I lose, the losing payoff would be 10 chips.\n- Plan 2: After the fold, the chips in the pot would remain at 20. If I win, there would be no winning payoff as I have already folded. If I lose, the losing payoff would be 12 chips (the amount I have already put into the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is the winning rate * winning payoff - losing rate * losing payoff = 0.21 * 10 - 0.56 * 10 = -3.5 chips.\n- Plan 2: The expected chips gain is the winning rate * winning payoff - losing rate * losing payoff = 0 * 0 - 0.56 * 12 = -6.72 chips.\n\nPlan Selection:\nBased on the estimated expected chips gains, Plan 1 (Call) is the better strategy as it has a higher expected chips gain (-3.5 chips) compared to Plan 2 (Fold) (-6.72 chips). Therefore, I should choose to call."}}
{"message": "", "34_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King or Queen (probability 66.67%), he will likely raise (probability 80%) or call (probability 20%). If he raises, I will win as I also hold a King. If he calls, I will also win unless the public card matches his hand. So, the winning rate for this plan is 66.67% * (80% + 20%) = 66.67%.\n- If GoodGuy holds a Jack (probability 33.33%), he will likely fold (probability 70%) or call (probability 30%). If he folds, I will win. If he calls, I will win unless the public card is a Jack. So, the winning rate for this plan is 33.33% * (70% + 30%) = 33.33%.\n- The overall winning rate for Plan 1 is 66.67% + 33.33% = 100%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of GoodGuy's cards. So, the losing rate for this plan is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King or Queen (probability 66.67%), he will likely raise (probability 80%) or call (probability 20%). If he raises, I will lose as I hold a King. If he calls, I will also lose unless the public card matches my hand. So, the losing rate for this plan is 66.67% * (80% + 20%) = 66.67%.\n- If GoodGuy holds a Jack (probability 33.33%), he will likely fold (probability 70%) or call (probability 30%). If he folds, I will win. If he calls, I will win unless the public card is a Jack. So, the winning rate for this plan is 33.33% * (70% + 30%) = 33.33%.\n- The overall winning rate for Plan 3 is 33.33%, and the overall losing rate is 66.67%.\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 2 chips. If I lose, the lose payoff would be half of the pot, which is currently 2 chips.\n- Plan 2: If I fold, I will lose 2 chips.\n- Plan 3: If I win, the winning payoff would be half of the pot, which is currently 2 chips. If I lose, the lose payoff would be half of the pot, which is currently 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning Rate * Winning Payoff - Losing Rate * Losing Payoff = 100% * 2 - 0% * 2 = 2 chips.\n- Plan 2: Expected Chips Gain = Winning Rate * Winning Payoff - Losing Rate * Losing Payoff = 0% * 2 - 100% * 2 = -2 chips.\n- Plan 3: Expected Chips Gain = Winning Rate * Winning Payoff - Losing Rate * Losing Payoff = 33.33% * 2 - 66.67% * 2 = -0.67 chips.\n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 1 > Plan 3 > Plan 2.\n- Therefore, I should select Plan 1 (Raise) as it has the highest estimated expected chips gain."}}
{"message": "", "35_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 Queen or Jack, I will lose (100% probability). If the public card is a King, I will draw (100% probability). Overall, the winning rate is 0%, the losing rate is 42% (70% * 60%), and the drawing rate is 42% (70% * 60%).\n- If GoodGuy holds a Queen (20% probability), he will likely call (60% probability). If the public card is a King or Jack, I will lose (100% probability). If the public card is a Queen, I will draw (100% probability). Overall, the winning rate is 0%, the losing rate is 12% (20% * 60%), and the drawing rate is 12% (20% * 60%).\n- If GoodGuy holds a Jack (10% probability), he will likely fold (40% probability). If he folds, I will win (100% probability). Overall, the winning rate is 4% (10% * 40%), the losing rate is 0%, and the drawing rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (70% probability), he will likely raise (60% probability). If the public card is a Queen or Jack, I will lose (100% probability). If the public card is a King, I will draw (100% probability). Overall, the winning rate is 0%, the losing rate is 42% (70% * 60%), and the drawing rate is 42% (70% * 60%).\n- If GoodGuy holds a Queen (20% probability), he will likely fold (40% probability). If he folds, I will win (100% probability). Overall, the winning rate is 8% (20% * 40%), the losing rate is 0%, and the drawing rate is 0%.\n- If GoodGuy holds a Jack (10% probability), he will likely fold (40% probability). If he folds, I will win (100% probability). Overall, the winning rate is 4% (10% * 40%), the losing rate is 0%, and the drawing rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose (100% probability). Overall, the winning rate is 0%, the losing rate is 100%, and the 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 2 chips (half of the 4 chips I put in the pot).\n- Plan 2: 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 3 chips (half of the 6 chips I put in the pot).\n- Plan 3: If I lose, the losing payoff would be 2 chips (half of the 4 chips I put in the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 4% * 3 chips - 54% * 2 chips = -0.92 chips\n- Plan 2: Expected Chips Gain = 12% * 4 chips - 42% * 3 chips = -0.96 chips\n- Plan 3: Expected Chips Gain = -100% * 2 chips = -2 chips\n\nPlan Selection:\n- Plan 1: -0.92 chips\n- Plan 2: -0.96 chips\n- Plan 3: -2 chips\n\nBased on the estimated expected chips gain, Plan 1 (Call) is the best strategy to use in this situation."}}
{"message": "", "35_3": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he will likely raise (100% probability). If he raises, I will lose as my Jack does not match the public King. \n- If GoodGuy holds a Queen (30% probability), he will likely call (60% probability) or fold (40% probability). If he calls, I will lose as my Jack is lower than his Queen. If he folds, I will win the pot. \n- If GoodGuy holds a Jack (0% probability), he will likely call (30% probability) or fold (70% probability). If he calls, it will be a draw as we both hold Jacks. If he folds, I will win the pot. \n\nPlan 2: Raise\n- If GoodGuy holds a King (70% probability), he will likely raise (100% probability). If he raises, I will lose as my Jack does not match the public King. \n- If GoodGuy holds a Queen (30% probability), he will likely call (60% probability) or fold (40% probability). If he calls, I will lose as my Jack is lower than his Queen. If he folds, I will win the pot. \n- If GoodGuy holds a Jack (0% probability), he will likely call (30% probability) or fold (70% probability). If he calls, it will be a draw as we both hold Jacks. If he folds, I will win the pot. \n\nPlan 3: Fold\n- If I fold, I will lose the pot regardless of what card GoodGuy holds. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 12 chips (half of the pot). If I lose, the losing payoff would be 8 chips (half of the pot). \n- Plan 2: If I win, the winning payoff would be 20 chips (half of the pot). If I lose, the losing payoff would be 12 chips (half of the pot). \n- Plan 3: If I fold, I will lose 8 chips (half of the pot). \n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.3 * 12 - 0.7 * 8 = -2.4 chips\n- Plan 2: Expected Chips Gain = 0.3 * 20 - 0.7 * 12 = -2.4 chips\n- Plan 3: Expected Chips Gain = -8 chips\n\nPlan Selection:\n- Plan 1 and Plan 2 both have the same expected chips gain, which is higher than Plan 3. Therefore, I should choose either Plan 1 or Plan 2. Considering my strategy improvement, I should be more aggressive when I have a strong hand. However, I currently hold a Jack, which is not a strong hand. Therefore, I should choose Plan 1: Call."}}
{"message": "", "36_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (53.85% probability), he is likely to raise (70% probability) or call (30% probability). If he raises, I will win (as we both have Kings, but I have more chips), if he calls, it will be a draw.\n- If GoodGuy holds a Queen (46.15% probability), he is likely to raise (60% probability) or call (40% probability). If he raises or calls, I will win (as I have a King and he has a Queen).\n- Overall, the winning rate for plan 1 is 53.85%*70% + 46.15%*100% = 87.7%, the lose rate is 0%, and the draw rate is 53.85%*30% = 16.15%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (53.85% probability), he is likely to raise (70% probability) or call (30% probability). If he raises, I will win, if he calls, it will be a draw.\n- If GoodGuy holds a Queen (46.15% probability), he is likely to raise (60% probability) or call (40% probability). If he raises or calls, I will win.\n- Overall, the winning rate for plan 2 is 53.85%*70% + 46.15%*100% = 87.7%, the lose rate is 0%, and the draw rate is 53.85%*30% = 16.15%.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card. So, the winning rate for plan 3 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 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: 87.7% * 3 - 0% * 3 = 2.63\n- Plan 2: 87.7% * 5 - 0% * 5 = 4.385\n- Plan 3: 0% * 3 - 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": "", "36_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (70% probability), he is likely to raise (80% probability) or call (20% probability). If he raises, I will win (as we both have Kings, but I acted first). If he calls, I will also win (as we both have Kings, but I acted first). Therefore, the winning rate for this plan is 100%.\n- If GoodGuy holds a Queen (30% probability), he is likely to raise (70% probability) or call (30% probability). If he raises, I will win (as my King is higher than his Queen). If he calls, I will also win (as my King is higher than his Queen). Therefore, the winning rate for this plan is 100%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. Therefore, the losing rate for this plan is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (70% probability), he is likely to raise (80% probability) or call (20% probability). If he raises, I will win (as we both have Kings, but I acted first). If he calls, I will also win (as we both have Kings, but I acted first). Therefore, the winning rate for this plan is 100%.\n- If GoodGuy holds a Queen (30% probability), he is likely to raise (70% probability) or call (30% probability). If he raises, I will win (as my King is higher than his Queen). If he calls, I will also win (as my King is higher than his Queen). Therefore, the winning rate for this plan 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 (half of the pot). If I lose, the lose payoff would be 6 chips.\n- Plan 2: If I lose, the lose payoff would be 6 chips.\n- Plan 3: If I win, the winning payoff would be 6 chips. If I lose, the lose payoff would be 6 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 1.0 * 6 - 0 * 6 = 6 chips\n- Plan 2: Expected Chips Gain = 0 * 6 - 1.0 * 6 = -6 chips\n- Plan 3: Expected Chips Gain = 1.0 * 6 - 0 * 6 = 6 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 both have the highest expected chips gain of 6 chips, while Plan 2 has the lowest expected chips gain of -6 chips. Therefore, I should either raise (Plan 1) or check (Plan 3). Considering my strategy improvement, I should be more aggressive when I have a high card, so I will choose to raise (Plan 1)."}}
{"message": "", "37_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (40% probability), he will likely raise (100% probability). If the public card is a Queen, I will lose (100% probability). If the public card is a King or Jack, I will win (50% probability) or draw (50% probability).\n- If GoodGuy holds a Queen (30% probability), he will likely call (100% probability). If the public card is a Queen, I will draw (100% probability). If the public card is a King or Jack, I will lose (50% probability) or win (50% probability).\n- If GoodGuy holds a Jack (30% probability), he will likely call (100% probability). If the public card is a Queen, I will win (100% probability). If the public card is a King or Jack, I will win (50% probability) or lose (50% probability).\n- Overall, the winning rate for Plan 1 is 40%, the losing rate is 40%, and the draw rate is 20%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (40% probability), he will likely raise (100% probability). If the public card is a Queen, I will lose (100% probability). If the public card is a King or Jack, I will win (50% probability) or draw (50% probability).\n- If GoodGuy holds a Queen (30% probability), he will likely call (100% probability). If the public card is a Queen, I will draw (100% probability). If the public card is a King or Jack, I will lose (50% probability) or win (50% probability).\n- If GoodGuy holds a Jack (30% probability), he will likely fold (100% probability), and I will win (100% probability).\n- Overall, the winning rate for Plan 2 is 50%, the losing rate is 30%, and the draw rate is 20%.\n\nPlan 3: Fold\n- If I fold, I will lose (100% probability).\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 2 chips.\n- Plan 2: If I win, the winning payoff would be 7 chips. If I lose, the losing payoff would be 6 chips.\n- Plan 3: If I lose, the losing payoff would be 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 40% * 3 - 40% * 2 = 0.2 chips\n- Plan 2: Expected Chips Gain = 50% * 7 - 30% * 6 = 1.5 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": "", "37_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (63% probability), he will likely raise (100% probability). If he raises, it will be a draw as we both have a pair of Queens. \n- If GoodGuy holds a King (37% probability), he will likely call (100% probability). If he calls, I will lose as his King is higher than my Queen.\n\nPlan 2: Fold\n- If I fold, I will automatically lose the round regardless of GoodGuy's card.\n\nPlan 3: Check\n- If GoodGuy holds a Queen (63% probability), he will likely raise (100% probability). If he raises, it will be a draw as we both have a pair of Queens. \n- If GoodGuy holds a King (37% probability), he will likely check (100% probability). If he checks, I will lose as his King is higher than my Queen.\n\nWinning/Lose/Draw Rates for Each Plan:\n- Plan 1: Winning rate = 0%, Lose rate = 37%, Draw rate = 63%\n- Plan 2: Winning rate = 0%, Lose rate = 100%, Draw rate = 0%\n- Plan 3: Winning rate = 0%, Lose rate = 37%, Draw rate = 63%\n\nNumber 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\nEstimated Expected Chips Gain for Each Plan:\n- Plan 1: Expected chips gain = 0 * 4 - 37% * 4 = -1.48 chips\n- Plan 2: Expected chips gain = 0 * 0 - 100% * 4 = -4 chips\n- Plan 3: Expected chips gain = 0 * 4 - 37% * 4 = -1.48 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 have the highest estimated expected chips gain (-1.48 chips), while Plan 2 has the lowest estimated expected chips gain (-4 chips). Therefore, I should either raise (Plan 1) or check (Plan 3) in this round. Considering the strategy improvement, I should raise more aggressively when I have a strong hand. Therefore, I will choose Plan 1: Raise."}}
{"message": "", "37_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a Queen (33% probability), he will likely call (100% probability). In this case, we will draw and the pot will be split evenly. The winning rate is 0%, the losing rate is 0%, and the draw rate is 33%.\n- If GoodGuy holds a King (67% probability), he will likely raise (100% probability). In this case, I will lose. The winning rate is 0%, the losing rate is 67%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If GoodGuy holds a Queen (33% probability), he will likely call (100% probability). In this case, I will lose because I folded. The winning rate is 0%, the losing rate is 33%, and the draw rate is 0%.\n- If GoodGuy holds a King (67% probability), he will likely raise (100% probability). In this case, I will lose because I folded. The winning rate is 0%, the losing rate is 67%, and the draw rate is 0%.\n\nPlan 1 overall GoodGuy's Winning/Lose/Draw rates: \n- Winning rate: 0%\n- Losing rate: 67%\n- Draw rate: 33%\n\nPlan 2 overall GoodGuy's 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: After the action, chips in the pot: 24. If win, the winning payoff would be 12. After the action, chips in the pot: 24. If lose, the lose payoff would be 12.\n- Plan 2: After the action, chips in the pot: 20. If win, the winning payoff would be 10. After the action, chips in the pot: 20. If lose, the lose payoff would be 10.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0% * 12 - 67% * 12 = -8.04 chips\n- Plan 2: 0% * 10 - 100% * 10 = -10 chips\n\nPlan Selection:\n- Plan 1 is ranked first with an estimated expected chips gain of -8.04 chips.\n- Plan 2 is ranked second with an estimated expected chips gain of -10 chips.\n\nTherefore, I should choose Plan 1: Call."}}
{"message": "", "38_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King, he is likely to raise (70%) or call (30%). The winning rate is 50% (if the public card is a King), the losing rate is 50% (if the public card is a Queen or Jack), and the draw rate is 0%.\n- If GoodGuy holds a Queen, he is likely to raise (50%) or call (50%). The winning rate is 33.33% (if the public card is a King or Queen), the losing rate is 66.67% (if the public card is a Jack), and the draw rate is 0%.\n- If GoodGuy holds a Jack, he is likely to call (60%) or fold (40%). The winning rate is 33.33% (if the public card is a King), the losing rate is 33.33% (if the public card is a Jack), and the draw rate is 33.33% (if the public card is a Queen).\n- The overall winning rate for Plan 1 is 38.89%, the losing rate is 50%, and the draw rate is 11.11%.\n\nPlan 2: Raise\n- If GoodGuy holds a King, he is likely to raise (70%) or call (30%). The winning rate is 50% (if the public card is a King), the losing rate is 50% (if the public card is a Queen or Jack), and the draw rate is 0%.\n- If GoodGuy holds a Queen, he is likely to raise (50%) or call (50%). The winning rate is 33.33% (if the public card is a King or Queen), the losing rate is 66.67% (if the public card is a Jack), and the draw rate is 0%.\n- If GoodGuy holds a Jack, he is likely to call (60%) or fold (40%). The winning rate is 33.33% (if the public card is a King), the losing rate is 33.33% (if the public card is a Jack), and the draw rate is 33.33% (if the public card is a Queen).\n- The overall winning rate for Plan 2 is 38.89%, the losing rate is 50%, and the draw rate is 11.11%.\n\nPlan 3: Fold\n- If GoodGuy holds a King, Queen, or Jack, 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 win, the winning payoff would be 0 chips. If lose, the lose payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 38.89% * 3 - 50% * 2 = 0.167 chips\n- Plan 2: Expected Chips Gain = 38.89% * 5 - 50% * 4 = 0.944 chips\n- Plan 3: Expected Chips Gain = 0% * 0 - 100% * 2 = -2 chips\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain, so it should be selected."}}
{"message": "", "38_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King, he is likely to call (60%) or fold (40%). If he calls, I will win if the public card is a King (1/3 chance), lose if it's a Queen or Jack (2/3 chance). If he folds, I win the pot. \n- If GoodGuy holds a Queen, he is likely to raise (80%) or call (20%). If he raises, I will lose unless the public card is a King (1/3 chance). If he calls, I will win if the public card is a King (1/3 chance), lose if it's a Jack (1/3 chance), and draw if it's a Queen (1/3 chance).\n- If GoodGuy holds a Jack, he is likely to call (60%) or fold (40%). If he calls, I will win if the public card is a King (1/3 chance), lose if it's a Queen (1/3 chance), and draw if it's a Jack (1/3 chance). If he folds, I win the pot.\n\nPlan 2: Fold\n- If I fold, I lose the pot regardless of GoodGuy's card.\n\nPlan 3: Check\n- If GoodGuy holds a King, he is likely to raise (70%) or call (30%). If he raises, I will lose unless the public card is a King (1/3 chance). If he calls, I will win if the public card is a King (1/3 chance), lose if it's a Queen or Jack (2/3 chance).\n- If GoodGuy holds a Queen, he is likely to raise (80%) or call (20%). If he raises, I will lose unless the public card is a King (1/3 chance). If he calls, I will win if the public card is a King (1/3 chance), lose if it's a Jack (1/3 chance), and draw if it's a Queen (1/3 chance).\n- If GoodGuy holds a Jack, he is likely to raise (20%) or call (80%). If he raises, I will lose unless the public card is a King (1/3 chance). If he calls, I will win if the public card is a King (1/3 chance), lose if it's a Queen (1/3 chance), and draw if it's a Jack (1/3 chance).\n\nWinning/Lose Payoffs:\n- Plan 1: If I win, I gain 12 chips (half of the pot). If I lose, I lose 6 chips (half of the pot).\n- Plan 2: If I fold, I lose 6 chips (half of the pot).\n- Plan 3: If I win, I gain 12 chips (half of the pot). If I lose, I lose 6 chips (half of the pot).\n\nExpected Chips Gain:\n- Plan 1: (Winning rate * 12) - (Lose rate * 6)\n- Plan 2: -6 (since I always lose)\n- Plan 3: (Winning rate * 12) - (Lose rate * 6)\n\nPlan Selection:\n- Plan 1 and Plan 3 have the same expected chips gain, but Plan 1 is more aggressive and may intimidate GoodGuy into folding more often. Therefore, I choose Plan 1: Raise."}}
{"message": "", "39_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he is likely to raise (80%) or call (20%). If he raises, I will lose (as King is higher than Jack). If he calls, the game will proceed to the next round and the outcome will depend on the public card. \n- If GoodGuy holds a Queen (20% probability), he is likely to check (70%) or raise (30%). If he checks, the game will proceed to the next round and the outcome will depend on the public card. If he raises, I will lose (as Queen is higher than Jack). \n- If GoodGuy holds a Jack (10% probability), he is likely to check (80%) or raise (20%). If he checks or raises, the game will proceed to the next round and the outcome will depend on the public card. \n\nPlan 2: Raise\n- If GoodGuy holds a King (70% probability), he is likely to call (80%) or fold (20%). If he calls, I will lose (as King is higher than Jack). If he folds, I will win. \n- If GoodGuy holds a Queen (20% probability), he is likely to call (60%) or fold (40%). If he calls, I will lose (as Queen is higher than Jack). If he folds, I will win. \n- If GoodGuy holds a Jack (10% probability), he is likely to call (50%) or fold (50%). If he calls, the game will proceed to the next round and the outcome will depend on the public card. If he folds, I will win. \n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot. \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 2 chips (half of the pot). \n- Plan 2: If I win, the winning payoff would be 4 chips (half of the pot). If I lose, the lose payoff would be 3 chips (half of the pot). \n- Plan 3: If I fold, the lose payoff would be 2 chips (the chips I have already put in the pot). \n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.1 * 3 - 0.9 * 2 = -1.5 chips\n- Plan 2: Expected Chips Gain = 0.3 * 4 - 0.7 * 3 = -0.9 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- Plan 1: -1.5 chips\n- Plan 2: -0.9 chips\n- Plan 3: -2 chips\n\nBased on the estimated expected chips gains, Plan 2 (Raise) is the best strategy to follow."}}
{"message": "", "39_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (80% chance), he is likely to raise (80%) or call (20%). If he raises, I will lose (100%). If he calls, I will lose (100%). Overall, the winning rate is 0%, the losing rate is 80%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (60% chance), 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 60%, the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (50% chance), he is likely to call (50%) or fold (50%). If he calls, it's a draw (100%). If he folds, I will win (100%). Overall, the winning rate is 25%, the losing rate is 0%, and the draw rate is 25%.\n\nPlan 2: Fold\n- If I fold, I will lose the chips I have put into the 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 (80% chance), he is likely to raise (80%) or call (20%). If he raises, I will lose (100%). If he calls, I will lose (100%). Overall, the winning rate is 0%, the losing rate is 80%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (60% chance), 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 60%, the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (50% chance), he is likely to call (50%) or fold (50%). If he calls, it's a draw (100%). If he folds, I will win (100%). Overall, the winning rate is 25%, the losing rate is 0%, and the draw rate is 25%.\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 = 0.85 * 4 - 0.8 * 4 = 0.2\n- Plan 2: Expected Chips Gain = 0 * 4 - 1 * 2 = -2\n- Plan 3: Expected Chips Gain = 0.85 * 2 - 0.8 * 2 = 0.1\n\nPlan Selection:\n- Plan 1: Raise\n- Plan 3: Check\n- Plan 2: Fold\n\nThe best plan is to raise."}}
{"message": "", "39_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a Jack (70% probability), he will likely call (50%) or fold (50%). If he calls, we will both have a single Jack and the game will be a draw. If he folds, I will win. So the winning rate is 35%, the losing rate is 0%, and the draw rate is 35%.\n- If GoodGuy holds a Queen (30% probability), he will likely call (60%) or fold (40%). If he calls, he will have a higher card and I will lose. If he folds, I will win. So the winning rate is 12%, the losing rate is 18%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If GoodGuy holds a Jack (70% probability), I will lose regardless of his action. So the winning rate is 0%, the losing rate is 70%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (30% probability), I will lose regardless of his action. So the winning rate is 0%, the losing rate is 30%, 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, which is 10 chips. If I lose, the losing payoff would be half of the pot, which is 10 chips.\n- Plan 2: If I fold, I will lose the 12 chips I have already put into the pot.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is 0.47 * 10 - 0.18 * 10 = 2.9 chips.\n- Plan 2: The expected chips gain is -12 chips.\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain, so I should choose to call."}}
{"message": "", "40_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (100% probability), he will likely raise (80% probability). If he raises, I will win as I also hold a King. The winning rate for his King is 0.8 (0.8*1). If he calls (20% probability), it will be a draw. The draw rate for his King is 0.2 (0.2*1). \n- Overall, the winning rate for plan 1 is 0.8, the lose rate is 0, and the draw rate is 0.2. \n\nPlan 2: Raise\n- If GoodGuy holds a King (100% probability), he will likely raise (80% probability). If he raises, I will win as I also hold a King. The winning rate for his King is 0.8 (0.8*1). If he calls (20% probability), it will be a draw. The draw rate for his King is 0.2 (0.2*1). \n- Overall, the winning rate for plan 2 is 0.8, the lose rate is 0, and the draw rate is 0.2. \n\nPlan 3: Fold\n- If GoodGuy holds a King (100% probability), he will likely raise (80% probability). If he raises, I will lose as I fold. The lose rate for his King is 0.8 (0.8*1). If he calls (20% probability), it will be a draw as I fold. The draw rate for his King is 0.2 (0.2*1). \n- Overall, the winning rate for plan 3 is 0, the lose rate is 0.8, and the draw rate is 0.2. \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: 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: 0.8 * 1.5 - 0 * 1.5 = 1.2\n- Plan 2: 0.8 * 2.5 - 0 * 2.5 = 2\n- Plan 3: 0 * 1 - 0.8 * 1 = -0.8\n\nPlan Selection:\n- Plan 2 > Plan 1 > Plan 3\n- Therefore, I should choose Plan 2: Raise."}}
{"message": "", "40_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (70% probability), he will likely raise (90% probability). If he raises, I will lose as his pair of Queens beats my single King. The overall lose rate for this card is 0.7 * 0.9 = 0.63.\n- If GoodGuy holds a King (30% probability), he will likely call (70% probability) or fold (30% probability). If he calls, it will be a draw as we both have a single King. If he folds, I will win. The overall win rate for this card is 0.3 * 0.3 = 0.09, and the draw rate is 0.3 * 0.7 = 0.21.\n\nPlan 2: Fold\n- If GoodGuy holds a Queen (70% probability), he will likely raise (90% probability). If I fold, I will lose. The overall lose rate for this card is 0.7.\n- If GoodGuy holds a King (30% probability), he will likely call (70% probability) or fold (30% probability). If I fold, I will lose. The overall lose rate for this card is 0.3.\n\nPlan 3: Check\n- If GoodGuy holds a Queen (70% probability), he will likely raise (90% probability). If he raises, I will lose as his pair of Queens beats my single King. The overall lose rate for this card is 0.7 * 0.9 = 0.63.\n- If GoodGuy holds a King (30% probability), he will likely call (70% probability) or fold (30% probability). If he calls, it will be a draw as we both have a single King. If he folds, I will win. The overall win rate for this card is 0.3 * 0.3 = 0.09, and the draw rate is 0.3 * 0.7 = 0.21.\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 4 chips. If I lose, the lose payoff would be half of the pot, which is 4 chips.\n- Plan 2: If I fold, I will lose 4 chips.\n- Plan 3: If I win, the winning payoff would be half of the pot, which is 4 chips. If I lose, the lose payoff would be half of the pot, which is 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.09 * 4 - 0.63 * 4 = -2.16 chips\n- Plan 2: Expected Chips Gain = -4 chips\n- Plan 3: Expected Chips Gain = 0.09 * 4 - 0.63 * 4 = -2.16 chips\n\nPlan Selection:\nBased on the estimated expected chips gains, Plan 1 and Plan 3 are the best strategies as they have the highest expected chips gain (-2.16 chips). However, considering the strategy improvement, I should be more aggressive when I have a high-ranking card. Therefore, I will choose Plan 1: Raise."}}
{"message": "", "40_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (50% probability), he will likely raise (80% probability). If this happens, I will lose as we both have Kings, but his raise will beat my call. The losing rate for this scenario is 0.5*0.8=0.4. If he calls (20% probability), it will be a draw as we both have Kings. The draw rate for this scenario is 0.5*0.2=0.1.\n- If GoodGuy holds a Queen (50% probability), he will likely call (70% probability) or fold (30% probability). If he calls, I will win as my King beats his Queen. The winning rate for this scenario is 0.5*0.7=0.35. If he folds, I will also win as he forfeits the round. The winning rate for this scenario is 0.5*0.3=0.15.\n\nPlan 2: Fold\n- If GoodGuy holds a King (50% probability), he will likely raise (80% probability). If this happens, I will lose as I forfeit the round. The losing rate for this scenario is 0.5*0.8=0.4. If he calls (20% probability), I will also lose as I forfeit the round. The losing rate for this scenario is 0.5*0.2=0.2.\n- If GoodGuy holds a Queen (50% probability), he will likely call (70% probability) or fold (30% probability). If he calls, I will lose as I forfeit the round. The losing rate for this scenario is 0.5*0.7=0.35. If he folds, it will be a draw as we both forfeit the round. The draw rate for this scenario is 0.5*0.3=0.15.\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 (12+8)/2=10 chips. If I lose, the lose payoff would be half of the pot, which is (12+8)/2=10 chips.\n- Plan 2: If I win, the winning payoff would be half of the pot, which is (12+8)/2=10 chips. If I lose, the lose payoff would be half of the pot, which is (12+8)/2=10 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is winning rate * winning payoff - losing rate * losing payoff = (0.35+0.15)*10 - 0.4*10 = 1 chip.\n- Plan 2: The expected chips gain is winning rate * winning payoff - losing rate * losing payoff = 0*10 - (0.4+0.2+0.35)*10 = -9 chips.\n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 1 > Plan 2.\n- Therefore, I should select Plan 1 (Call) as it has the highest estimated expected chips gain."}}
{"message": "", "41_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King, he will likely raise (70% probability). If he raises, I will win if the public card is a King (50% chance), draw if it's a Queen (25% chance), and lose if it's a Jack (25% chance). \n- If GoodGuy holds a Queen, he will likely raise (60% probability). If he raises, I will win regardless of the public card. \n- If GoodGuy holds a Jack, he will likely call (70% probability). If he calls, I will win if the public card is a King or Queen (75% chance), and lose if it's a Jack (25% chance). \n\nPlan 2: Raise\n- If GoodGuy holds a King, he will likely call (30% probability). If he calls, I will win if the public card is a King (50% chance), draw if it's a Queen (25% chance), and lose if it's a Jack (25% chance). \n- If GoodGuy holds a Queen, he will likely call (40% probability). If he calls, I will win regardless of the public card. \n- If GoodGuy holds a Jack, he will likely fold (30% probability). If he folds, I will win the round. \n\nPlan 3: Fold\n- If I fold, I will lose the round regardless of GoodGuy's card. \n\nWinning/Lose Payoff 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 2 chips (half of the pot). \n- Plan 2: If I win, the winning payoff would be 4 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 (half of the pot). \n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected gain = 0.7 * 3 - 0.3 * 2 = 1.1 chips\n- Plan 2: Expected gain = 0.7 * 4 - 0.3 * 3 = 1.7 chips\n- Plan 3: Expected gain = -2 chips\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain, so I should choose to raise."}}
{"message": "", "41_2": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he will likely raise (60% probability). If the public card matches his King, I will win (80% probability). If the public card doesn't match his King, I will lose (20% probability). \n- If GoodGuy holds a Queen (30% probability), he will likely raise (50% probability). If the public card matches his Queen, I will lose (50% probability). If the public card doesn't match his Queen, I will win (50% probability). \n- Overall, the winning rate for Plan 1 is 0.7*0.8 + 0.3*0.5 = 0.71, the losing rate is 0.7*0.2 + 0.3*0.5 = 0.29, and the draw rate is 0. \n\nPlan 2: Fold\n- If GoodGuy holds a King (70% probability), he will likely raise (60% probability). If I fold, I will lose regardless of the public card. \n- If GoodGuy holds a Queen (30% probability), he will likely raise (50% probability). If I fold, I will lose regardless of the public card. \n- Overall, the winning rate for Plan 2 is 0, the losing rate is 1, 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 would be 12. If win, the winning payoff would be 6. If lose, the lose payoff would be 6. \n- Plan 2: After the fold action, chips in the pot would be 10. If lose, the lose payoff would be 5. \n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0.71 * 6 - 0.29 * 6 = 2.52\n- Plan 2: 0 - 1 * 5 = -5\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain than Plan 2. Therefore, I should choose Plan 1, which is to call."}}
{"message": "", "41_4": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (50% probability), he will likely call (30% probability). If he calls, it will result in a draw. Therefore, the winning rate is 0%, the losing rate is 0%, and the draw rate is 15% (50% * 30%).\n- If GoodGuy holds a Jack (50% probability), he will likely fold (50% probability). If he folds, I will win. Therefore, the winning rate is 25% (50% * 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 King (50% probability), he will likely raise (60% probability). If he raises, it will result in a draw. Therefore, the winning rate is 0%, the losing rate is 0%, and the draw rate is 30% (50% * 60%).\n- If GoodGuy holds a Jack (50% probability), he will likely call (50% probability). If he calls, I will win. Therefore, the winning rate is 25% (50% * 50%), 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 = 25% * 6 chips - 0% * 6 chips = 1.5 chips\n- Plan 2: Expected Chips Gain = 0% * 6 chips - 100% * 6 chips = -6 chips\n- Plan 3: Expected Chips Gain = 25% * 6 chips - 0% * 6 chips = 1.5 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 both have the highest expected chips gain of 1.5 chips, while Plan 2 has the lowest expected chips gain of -6 chips. Therefore, I should either raise (Plan 1) or check (Plan 3). Considering my strategy improvement, I should choose to raise (Plan 1) to be more aggressive when I have a high card."}}
{"message": "", "43_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (50% probability), he is likely to raise (70% probability). If the public card is a Jack, I will win (probability = 0.5 * 0.7 = 0.35). If the public card is a Queen or King, I will lose (probability = 0.5 * 0.3 = 0.15).\n- If GoodGuy holds a Queen (50% probability), he is likely to raise (60% probability). If the public card is a Jack, I will win (probability = 0.5 * 0.6 = 0.3). If the public card is a Queen or King, I will lose (probability = 0.5 * 0.4 = 0.2).\n- Overall, the winning rate for Plan 1 is 0.35 + 0.3 = 0.65, the losing rate is 0.15 + 0.2 = 0.35, and the draw rate is 0.\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of GoodGuy's cards or the public card. Therefore, 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 (50% probability), he is likely to raise (70% probability). If the public card is a Jack, I will win (probability = 0.5 * 0.7 = 0.35). If the public card is a Queen or King, I will lose (probability = 0.5 * 0.3 = 0.15).\n- If GoodGuy holds a Queen (50% probability), he is likely to raise (60% probability). If the public card is a Jack, I will win (probability = 0.5 * 0.6 = 0.3). If the public card is a Queen or King, I will lose (probability = 0.5 * 0.4 = 0.2).\n- Overall, the winning rate for Plan 3 is 0.35 + 0.3 = 0.65, the losing rate is 0.15 + 0.2 = 0.35, 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 (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 game and the losing payoff would be half of the pot (2 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 = 0.65 * 4 - 0.35 * 4 = 1.2 chips\n- Plan 2: Expected Chips Gain = 0 * 4 - 1 * 2 = -2 chips\n- Plan 3: Expected Chips Gain = 0.65 * 4 - 0.35 * 4 = 1.2 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 have the highest expected chips gain (1.2 chips), while Plan 2 has the lowest expected chips gain (-2 chips). Therefore, I should choose either Plan 1 (Raise) or Plan 3 (Check) to maximize my expected chips gain. Considering my strategy improvement, I should choose Plan 1 (Raise) to be more aggressive and willing to bluff."}}
{"message": "", "44_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a Jack, he might believe that I will call (60%) or raise (40%). If the public card is a Queen or King, he might believe that I will raise (60%) or call (40%). The winning rate for this plan is 60%, the losing rate is 40%, and the draw rate is 0%.\n- If GoodGuy holds a Queen, he might believe that I will raise (70%) or call (30%). If the public card is a Jack or King, he might believe that I will raise (70%) or call (30%). The winning rate for this plan is 70%, the losing rate is 30%, and the draw rate is 0%.\n- If GoodGuy holds a King, he might believe that I will raise (80%) or call (20%). If the public card is a Jack or Queen, he might believe that I will raise (80%) or call (20%). The winning rate for this plan is 80%, the losing rate is 20%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a Jack, he might believe that I will call (60%) or raise (40%). If the public card is a Queen or King, he might believe that I will raise (60%) or call (40%). The winning rate for this plan is 40%, the losing rate is 60%, and the draw rate is 0%.\n- If GoodGuy holds a Queen, he might believe that I will raise (70%) or call (30%). If the public card is a Jack or King, he might believe that I will raise (70%) or call (30%). The winning rate for this plan is 30%, the losing rate is 70%, and the draw rate is 0%.\n- If GoodGuy holds a King, he might believe that I will raise (80%) or call (20%). If the public card is a Jack or Queen, he might believe that I will raise (80%) or call (20%). The winning rate for this plan is 20%, the losing rate is 80%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If GoodGuy holds a Jack, Queen, or King, the 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 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 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: Expected Chips Gain = 60% * 3 - 40% * 1 = 1.4 chips\n- Plan 2: Expected Chips Gain = 40% * 5 - 60% * 2 = 0.2 chips\n- Plan 3: Expected Chips Gain = 0% * 0 - 100% * 1 = -1 chips\n\nPlan Selection:\n- Plan 1: 1.4 chips\n- Plan 2: 0.2 chips\n- Plan 3: -1 chips\n\nBased on the estimated expected chips gains, I should select Plan 1 (Call) as it has the highest expected chips gain."}}
{"message": "", "44_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Jack (30% probability), he will likely call (40% probability). If he calls, I will win because my Queen is higher than his Jack. So, the winning rate for this scenario is 30% * 40% = 12%. \n- If GoodGuy holds a Queen (40% probability), it will be a draw because we both have Queens. So, the draw rate for this scenario is 40%.\n- If GoodGuy holds a King (30% probability), he will likely call (20% probability). If he calls, I will lose because his King is higher than my Queen. So, the losing rate for this scenario is 30% * 20% = 6%.\n\nPlan 2: Fold\n- If I fold, I will lose the 2 chips in the pot regardless of GoodGuy's card. So, the losing rate for this scenario is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a Jack (30% probability), he will likely check (60% probability). If he checks, I will win because my Queen is higher than his Jack. So, the winning rate for this scenario is 30% * 60% = 18%.\n- If GoodGuy holds a Queen (40% probability), it will be a draw because we both have Queens. So, the draw rate for this scenario is 40%.\n- If GoodGuy holds a King (30% probability), he will likely check (80% probability). If he checks, I will lose because his King is higher than my Queen. So, the losing rate for this scenario is 30% * 80% = 24%.\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 (2 chips) = 1 chip. If I lose, the lose payoff would be half of the pot (2 chips) = 1 chip.\n- Plan 2: If I fold, I will lose the 2 chips in the pot.\n- Plan 3: If I win, the winning payoff would be half of the pot (2 chips) = 1 chip. If I lose, the lose payoff would be half of the pot (2 chips) = 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = winning rate * Winning Payoff - losing rate * Lose Payoff = 12% * 1 chip - 6% * 1 chip = 0.06 chips\n- Plan 2: Expected Chips Gain = -2 chips (because I will lose the 2 chips in the pot)\n- Plan 3: Expected Chips Gain = winning rate * Winning Payoff - losing rate * Lose Payoff = 18% * 1 chip - 24% * 1 chip = -0.06 chips\n\nPlan Selection:\n- Plan 1: Expected Chips Gain = 0.06 chips\n- Plan 2: Expected Chips Gain = -2 chips\n- Plan 3: Expected Chips Gain = -0.06 chips\n\nBased on the expected chips gain, I should choose Plan 1 (Raise) as it has the highest expected chips gain."}}
{"message": "", "44_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a Jack, he has a pair and I will lose. Based on my belief, the probability of this is 70%. The pot will be 16 chips and I will lose 8 chips.\n- If GoodGuy holds a Queen, we have the same card and it will be a draw. The probability of this is 20%. The pot will be 16 chips and I will neither gain nor lose chips.\n- If GoodGuy holds a King, I will win. The probability of this is 10%. The pot will be 16 chips and I will gain 8 chips.\n\nPlan 2: Fold\n- If I fold, I will lose the 10 chips I have already put in the pot, regardless of what card GoodGuy holds.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: (10% * 8) - (70% * 8) = -4.8 chips\n- Plan 2: -10 chips\n\nPlan Selection:\nPlan 1 has a higher expected chips gain (-4.8 chips) compared to Plan 2 (-10 chips). Therefore, I should choose Plan 1: Call."}}
{"message": "", "45_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (35% probability), he will likely raise (70% probability). If the public card is a King or Queen, I will win. If the public card is a Jack, it will be a draw. The overall winning rate is 0.35*0.7*0.67 = 16.45%, the draw rate is 0.35*0.7*0.33 = 8.05%, and the lose rate is 0.\n- If GoodGuy holds a Queen (24% probability), he will likely call (60% probability). If the public card is a King, I will win. If the public card is a Queen or Jack, it will be a draw. The overall winning rate is 0.24*0.6*0.33 = 4.75%, the draw rate is 0.24*0.6*0.67 = 9.65%, and the lose rate is 0.\n- If GoodGuy holds a Jack (41% probability), he will likely call (70% probability). If the public card is a King or Queen, I will win. If the public card is a Jack, it will be a draw. The overall winning rate is 0.41*0.7*0.67 = 19.25%, the draw rate is 0.41*0.7*0.33 = 9.45%, and the lose rate is 0.\n- The overall winning rate for Plan 1 is 16.45% + 4.75% + 19.25% = 40.45%, the overall draw rate is 8.05% + 9.65% + 9.45% = 27.15%, and the overall lose rate is 0.\n- 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- The expected chips gain for Plan 1 is 40.45% * 3 - 0 = 1.21 chips.\n\nPlan 2: Raise\n- If GoodGuy holds a King (35% probability), he will likely call (30% probability). If the public card is a King or Queen, I will win. If the public card is a Jack, it will be a draw. The overall winning rate is 0.35*0.3*0.67 = 7.05%, the draw rate is 0.35*0.3*0.33 = 3.45%, and the lose rate is 0.\n- If GoodGuy holds a Queen (24% probability), he will likely fold (60% probability). If the public card is a King, I will win. If the public card is a Queen or Jack, it will be a draw. The overall winning rate is 0.24*0.6*0.33 = 4.75%, the draw rate is 0.24*0.6*0.67 = 9.65%, and the lose rate is 0.\n- If GoodGuy holds a Jack (41% probability), he will likely fold (70% probability). If the public card is a King or Queen, I will win. If the public card is a Jack, it will be a draw. The overall winning rate is 0.41*0.7*0.67 = 19.25%, the draw rate is 0.41*0.7*0.33 = 9.45%, and the lose rate is 0.\n- The overall winning rate for Plan 2 is 7.05% + 4.75% + 19.25% = 31.05%, the overall draw rate is 3.45% + 9.65% + 9.45% = 22.55%, and the overall lose rate is 0.\n- 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- The expected chips gain for Plan 2 is 31.05% * 5 - 0 = 1.55 chips.\n\nPlan 3: Fold\n- If I fold, I will lose 1 chip (my initial bet), and the game will end immediately. The expected chips gain for Plan 3 is -1 chip.\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": "", "45_2": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% chance), he is likely to call (30%) or raise (70%). If he calls, we will both have a pair of Kings if the public card is a King, resulting in a draw. If the public card is a Queen or Jack, I will win as my King is higher. If he raises, I will call and the outcome will be the same. Therefore, the winning rate is 70%, the losing rate is 0%, and the draw rate is 30%.\n- If GoodGuy holds a Queen (30% chance), he is likely to call (60%) or raise (40%). If he calls or raises, I will win unless the public card is a Queen, in which case I will lose. Therefore, the winning rate is 60%, the losing rate is 40%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose the round regardless of GoodGuy's card. Therefore, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nNumber 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 10 chips, so I would gain 5 chips. If I lose, the losing payoff would be half of the pot, so I would lose 5 chips.\n- Plan 2: If I fold, I will lose the round and forfeit the 6 chips I have already put into the pot.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is the winning rate * winning payoff - losing rate * losing payoff = 0.7 * 5 - 0.3 * 5 = 2 chips.\n- Plan 2: The expected chips gain is the winning rate * winning payoff - losing rate * losing payoff = 0 * 5 - 1 * 6 = -6 chips.\n\nPlan Selection:\n- Based on the estimated expected chips gain, Plan 1 (Call) is the better strategy as it has a higher expected chips gain. Therefore, I will choose to call."}}
{"message": "", "45_4": {"plan": "Plan 1: Call\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 and I only have a King). If he calls, the game will be a draw (as neither of us have a pair). The overall winning rate for this plan is 0%, the losing rate is 30% (50% * 60%), and the draw rate is 20% (50% * 40%).\n- If GoodGuy holds a Queen (50% probability), he will likely call (70%) or raise (30%). If he calls, I will win (as I have a King and he only has a Queen). If he raises, the game will be a draw (as neither of us have a pair). The overall winning rate for this plan is 35% (50% * 70%), the losing rate is 0%, and the draw rate is 15% (50% * 30%).\n- The overall winning rate for Plan 1 is 35%, the losing rate is 30%, and the draw rate is 35%.\n\nPlan 2: Raise\n- If GoodGuy holds a Jack (50% probability), he will likely call (40%) or fold (60%). If he calls, I will lose (as he has a pair of Jacks and I only have a King). If he folds, I will win. The overall winning rate for this plan is 30% (50% * 60%), the losing rate is 20% (50% * 40%), and the draw rate is 0%.\n- If GoodGuy holds a Queen (50% probability), he will likely call (30%) or fold (70%). If he calls, I will win (as I have a King and he only has a Queen). If he folds, I will also win. The overall winning rate for this plan is 50% (50% * (30% + 70%)), the losing rate is 0%, and the draw rate is 0%.\n- The overall winning rate for Plan 2 is 80%, the losing rate is 20%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will automatically lose the game. 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 8 chips (half of the pot). If I lose, the losing payoff would be 10 chips (the chips I have put in the pot).\n- Plan 2: If I win, the winning payoff would be 12 chips (half of the pot). If I lose, the losing payoff would be 14 chips (the chips I have put in the pot).\n- Plan 3: If I lose, the losing payoff would be 10 chips (the chips I have put in the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is 35% * 8 - 30% * 10 = 0.8 chips.\n- Plan 2: The expected chips gain is 80% * 12 - 20% * 14 = 7.2 chips.\n- Plan 3: The expected chips gain is -100% * 10 = -10 chips.\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain, so I will choose this plan."}}
{"message": "", "46_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (30% chance), he is likely to call (80%) or raise (20%). If he calls, I will win if the public card is a Queen or Jack (66.67% chance), lose if it's a King (33.33% chance). If he raises, I will win if the public card is a Queen or Jack (66.67% chance), lose if it's a King (33.33% chance). Overall, the winning rate is 60%, the losing rate is 40%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (40% chance), he is likely to call (70%) or raise (30%). If he calls, I will win if the public card is a Jack (33.33% chance), lose if it's a King (33.33% chance), and draw if it's a Queen (33.33% chance). If he raises, the rates are the same. Overall, the winning rate is 13.33%, the losing rate is 13.33%, and the draw rate is 13.33%.\n- If GoodGuy holds a Jack (30% chance), he is likely to call (70%) or fold (30%). If he calls, I will win if the public card is a Queen or Jack (66.67% chance), lose if it's a King (33.33% chance). If he folds, I win. Overall, the winning rate is 70%, the losing rate is 30%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I lose 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 (30% chance), he is likely to call (80%) or raise (20%). If he calls, I will win if the public card is a Queen or Jack (66.67% chance), lose if it's a King (33.33% chance). If he raises, I will win if the public card is a Queen or Jack (66.67% chance), lose if it's a King (33.33% chance). Overall, the winning rate is 60%, the losing rate is 40%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (40% chance), he is likely to call (70%) or raise (30%). If he calls, I will win if the public card is a Jack (33.33% chance), lose if it's a King (33.33% chance), and draw if it's a Queen (33.33% chance). If he raises, the rates are the same. Overall, the winning rate is 13.33%, the losing rate is 13.33%, and the draw rate is 13.33%.\n- If GoodGuy holds a Jack (30% chance), he is likely to call (70%) or fold (30%). If he calls, I will win if the public card is a Queen or Jack (66.67% chance), lose if it's a King (33.33% chance). If he folds, I win. Overall, the winning rate is 70%, the losing rate is 30%, 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. If I lose, the losing payoff would be 4 chips.\n- Plan 2: If I fold, I 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: (60% * 4) - (40% * 4) = 0.8 chips\n- Plan 2: -2 chips\n- Plan 3: (60% * 2) - (40% * 2) = 0.4 chips\n\nPlan Selection:\n- Plan 1 is the best strategy with the highest expected chips gain of 0.8 chips.\n- Plan 3 is the second best strategy with an expected chips gain of 0.4 chips.\n- Plan 2 is the worst strategy with an expected chips loss of 2 chips."}}
{"message": "", "47_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (33.33% 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 (33.33% chance), he will likely raise (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 40%, the losing rate is 60%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (33.33% chance), he will likely call (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 40%, the losing rate is 0%, and the draw rate is 60%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (33.33% 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 (33.33% chance), he will likely raise (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 40%, the losing rate is 60%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (33.33% chance), he will likely raise (40% 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 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 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 = 0.4 * 3 - 0.6 * 1 = 0.6 chips\n- Plan 2: Expected Chips Gain = 0.6 * 7 - 0.4 * 3 = 3.6 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": "", "47_2": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (probability 2/5), he will likely raise (probability 70%) or call (probability 30%). 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 (probability 1/5), he will likely raise (probability 60%) or call (probability 40%). If he raises or calls, it will be a draw as we both hold Queens. \n- If GoodGuy holds a Jack (probability 2/5), he will likely call (probability 60%) or raise (probability 40%). If he calls or raises, I will win as Queen is higher than Jack. \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 in this round. \n\nExpected Chips Gain for Each Plan:\n- Plan 1: (2/5 * 70% * -6) + (1/5 * 60% * 0) + (2/5 * 60% * 6) = -0.6 chips\n- Plan 2: -6 chips\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain than Plan 2, so I should choose Plan 1 and call. \n\nNumber 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 6 chips, so I would gain 3 chips. If I lose, the lose payoff would be half of the pot, so I would lose 3 chips. \n- Plan 2: If I fold, I would lose the 6 chips I have already put in the pot. \n\nOverall, considering both the strategy improvement and the expected chips gain, I should choose Plan 1 and call."}}
{"message": "", "47_4": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (60% probability), he will likely call (70% probability). If he calls, we will both have Queens and the game will be a draw. The pot will be split evenly and I will neither gain nor lose chips.\n- If GoodGuy holds a Jack (40% probability), he will likely call (70% probability). If he calls, I will win because my Queen is higher than his Jack. The pot will be 14 chips (6 chips already in the pot + 4 chips from my raise + 4 chips from his call), and I will gain 7 chips.\n\nPlan 2: Fold\n- If I fold, I will lose the 6 chips I have already put into the pot, regardless of what card GoodGuy holds.\n\nPlan 3: Check\n- If GoodGuy holds a Queen (60% probability), he will likely check as well (70% probability). If he checks, we will both have Queens and the game will be a draw. The pot will be split evenly and I will neither gain nor lose chips.\n- If GoodGuy holds a Jack (40% probability), he will likely check as well (70% probability). If he checks, I will win because my Queen is higher than his Jack. The pot will be 12 chips (6 chips already in the pot + 3 chips from my check + 3 chips from his check), and I will gain 6 chips.\n\nWinning/Lose Payoff for Each Plan:\n- Plan 1: If I win, I will gain 7 chips. If I lose, I will lose 4 chips (the amount I raised).\n- Plan 2: If I fold, I will lose 6 chips (the amount I have already put into the pot).\n- Plan 3: If I win, I will gain 6 chips. If I lose, I will lose 3 chips (the amount I checked).\n\nExpected Chips Gain for Each Plan:\n- Plan 1: (0.4 * 7) - (0.6 * 4) = 0.8 chips\n- Plan 2: -6 chips\n- Plan 3: (0.4 * 6) - (0.6 * 3) = 0.6 chips\n\nPlan Selection:\nBased on the expected chips gain for each plan, Plan 1 (Raise) is the best strategy with an expected gain of 0.8 chips. Plan 3 (Check) is the second best strategy with an expected gain of 0.6 chips. Plan 2 (Fold) is the worst strategy with an expected loss of 6 chips. Therefore, I should choose to raise."}}
{"message": "", "49_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 Jack. If he calls, the game will be decided by the public card. The winning/losing/draw rates are 33.33% (win if public card is a Jack), 46.67% (lose if public card is a King or Queen), and 20% (draw if he calls and public card is not a Jack).\n- If GoodGuy holds a Queen, he will likely raise (60%) or call (40%). 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/losing/draw rates are 33.33% (win if public card is a Jack), 40% (lose if public card is a Queen or King), and 26.67% (draw if he calls and public card is not a Jack).\n- If GoodGuy holds a Jack, he will likely raise (50%) or call (50%). If he raises, I will draw unless the public card is a Jack. If he calls, the game will be decided by the public card. The winning/losing/draw rates are 33.33% (win if public card is a Jack), 0% (lose), and 66.67% (draw if he calls or raises and public card is not a Jack).\n- Overall, the winning rate for plan 1 is 33.33%, the losing rate is 28.89%, and the draw rate is 37.78%.\n\nPlan 2: Raise\n- If GoodGuy holds a King, he will likely 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 winning/losing/draw rates are 70% (win if he folds), 20% (lose if he calls and public card is not a Jack), and 10% (draw if he calls and public card is a Jack).\n- If GoodGuy holds a Queen, he will likely call (40%) or fold (60%). If he calls, I will lose unless the public card is a Jack. If he folds, I will win. The winning/losing/draw rates are 60% (win if he folds), 26.67% (lose if he calls and public card is not a Jack), and 13.33% (draw if he calls and public card is a Jack).\n- If GoodGuy holds a Jack, he will likely call (50%) or fold (50%). If he calls, the game will be a draw unless the public card is a Jack. If he folds, I will win. The winning/losing/draw rates are 50% (win if he folds), 0% (lose), and 50% (draw if he calls).\n- Overall, the winning rate for plan 2 is 60%, the losing rate is 15.56%, and the draw rate is 24.44%.\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: 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 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: 33.33% * 3 - 28.89% * 1 = 0.67 chips\n- Plan 2: 60% * 5 - 15.56% * 2 = 2.69 chips\n- Plan 3: 0% * 0 - 100% * 1 = -1 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 to raise."}}
{"message": "", "49_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King, he will likely raise (60%) or call (40%). If I win, the winning rate is 0% (as my Jack is lower than his King). If I lose, the losing rate is 100%. The draw rate is 0%.\n- If GoodGuy holds a Queen, he will likely raise (50%) or call (50%). If I win, the winning rate is 50% (as my Jack and his Queen are equal). If I lose, the losing rate is 50%. The draw rate is 0%.\n- If GoodGuy holds a Jack, he will likely raise (40%) or call (60%). If I win, the winning rate is 100% (as my Jack and his Jack are equal). If I lose, the losing rate is 0%. The draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of what card GoodGuy holds. 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 (60%) or call (40%). If I win, the winning rate is 0% (as my Jack is lower than his King). If I lose, the losing rate is 100%. The draw rate is 0%.\n- If GoodGuy holds a Queen, he will likely raise (50%) or call (50%). If I win, the winning rate is 50% (as my Jack and his Queen are equal). If I lose, the losing rate is 50%. The draw rate is 0%.\n- If GoodGuy holds a Jack, he will likely raise (40%) or call (60%). If I win, the winning rate is 100% (as my Jack and his Jack are equal). If I lose, the losing rate is 0%. 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 8 chips. If I lose, the losing payoff would be 8 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 = 0.33*(0*8 - 1*8) + 0.33*(0.5*8 - 0.5*8) + 0.33*(1*8 - 0*8) = -2.67 chips\n- Plan 2: Expected Chips Gain = -4 chips\n- Plan 3: Expected Chips Gain = 0.33*(0*4 - 1*4) + 0.33*(0.5*4 - 0.5*4) + 0.33*(1*4 - 0*4) = -1.33 chips\n\nPlan Selection:\n- Plan 1: -2.67 chips\n- Plan 2: -4 chips\n- Plan 3: -1.33 chips\n\nBased on the expected chips gain, Plan 3 (Check) is the best strategy to follow."}}
{"message": "", "50_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King, he might raise (70%) or call (30%). If he raises, I would lose unless the public card is a Queen. If he calls, it would be a draw unless the public card is a Queen. Overall, the winning rate is 30%, the losing rate is 70%, and the draw rate is 0%.\n- If GoodGuy holds a Queen, he might raise (60%) or call (40%). If he raises, it would be a draw unless the public card is a Queen. If he calls, it would be a draw unless the public card is a Queen. Overall, the winning rate is 0%, the losing rate is 0%, and the draw rate is 100%.\n- If GoodGuy holds a Jack, he might raise (50%), call (40%), or fold (10%). If he raises, I would win unless the public card is a King. If he calls, I would win unless the public card is a King. If he folds, I would win. Overall, the winning rate is 90%, the losing rate is 10%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King, he might raise (70%) or call (30%). If he raises, I would lose unless the public card is a Queen. If he calls, it would be a draw unless the public card is a Queen. Overall, the winning rate is 30%, the losing rate is 70%, and the draw rate is 0%.\n- If GoodGuy holds a Queen, he might raise (60%) or call (40%). If he raises, it would be a draw unless the public card is a Queen. If he calls, it would be a draw unless the public card is a Queen. Overall, the winning rate is 0%, the losing rate is 0%, and the draw rate is 100%.\n- If GoodGuy holds a Jack, he might raise (50%), call (40%), or fold (10%). If he raises, I would win unless the public card is a King. If he calls, I would win unless the public card is a King. If he folds, I would win. Overall, the winning rate is 90%, the losing rate is 10%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I would lose the game, losing any 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 2 chips.\n- Plan 2: If I win, the winning payoff would be 5 chips. If I lose, the losing payoff would be 4 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: The expected chips gain is 0.3 * 3 - 0.7 * 2 = -0.9 chips.\n- Plan 2: The expected chips gain is 0.3 * 5 - 0.7 * 4 = -1.5 chips.\n- Plan 3: The expected chips gain is -1 chip.\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I should choose to call."}}
{"message": "", "50_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (40% probability), he will likely raise (70% probability). If he raises, I will win because my Queen is higher than the public Jack. The winning rate for this scenario is 0.4*0.7 = 0.28.\n- If GoodGuy holds a Queen (30% probability), he will likely check (60% probability). If he checks, it will be a draw because we both hold Queens. The draw rate for this scenario is 0.3*0.6 = 0.18.\n- If GoodGuy holds a Jack (30% probability), he will likely fold (10% probability). If he folds, I will win because my Queen is higher than his Jack. The winning rate for this scenario is 0.3*0.1 = 0.03.\n\nPlan 1 overall GoodGuy's Winning/Lose/Draw rates: \n- Winning rate for plan 1: 0.28 + 0.03 = 0.31\n- Lose rate for plan 1: 0\n- Draw rate for plan 1: 0.18\n\nPlan 2: Fold\n- If GoodGuy holds a King (40% probability), he will likely raise (70% probability). If he raises, I will lose because I folded. The lose rate for this scenario is 0.4*0.7 = 0.28.\n- If GoodGuy holds a Queen (30% probability), he will likely check (60% probability). If he checks, I will lose because I folded. The lose rate for this scenario is 0.3*0.6 = 0.18.\n- If GoodGuy holds a Jack (30% probability), he will likely fold (10% probability). If he folds, it will be a draw because we both folded. The draw rate for this scenario is 0.3*0.1 = 0.03.\n\nPlan 2 overall GoodGuy's Winning/Lose/Draw rates: \n- Winning rate for plan 2: 0\n- Lose rate for plan 2: 0.28 + 0.18 = 0.46\n- Draw rate for plan 2: 0.03\n\nPlan 3: Check\n- If GoodGuy holds a King (40% probability), he will likely raise (70% probability). If he raises, I will win because my Queen is higher than the public Jack. The winning rate for this scenario is 0.4*0.7 = 0.28.\n- If GoodGuy holds a Queen (30% probability), he will likely check (60% probability). If he checks, it will be a draw because we both hold Queens. The draw rate for this scenario is 0.3*0.6 = 0.18.\n- If GoodGuy holds a Jack (30% probability), he will likely fold (10% probability). If he folds, I will win because my Queen is higher than his Jack. The winning rate for this scenario is 0.3*0.1 = 0.03.\n\nPlan 3 overall GoodGuy's Winning/Lose/Draw rates: \n- Winning rate for plan 3: 0.28 + 0.03 = 0.31\n- Lose rate for plan 3: 0\n- Draw rate for plan 3: 0.18\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\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0.31 * 4 - 0 * 2 = 1.24 chips\n- Plan 2: 0 * 0 - 0.46 * 2 = -0.92 chips\n- Plan 3: 0.31 * 2 - 0 * 2 = 0.62 chips\n\nPlan Selection:\n- Plan 1: 1.24 chips\n- Plan 2: -0.92 chips\n- Plan 3: 0.62 chips\n\nBased on the estimated expected chips gains, I should select Plan 1 (Raise) as it has the highest estimated expected chips gain."}}
{"message": "", "51_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (33.3% chance), 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 have a chance to win if the public card is a Jack. The overall winning rate is 10%, losing rate is 23.3%, and drawing rate is 0%.\n- If GoodGuy holds a Queen (33.3% chance), he is likely to raise (50%) or fold (50%). If he raises, I will lose unless the public card is a Jack. If he folds, I will win. The overall winning rate is 16.7%, losing rate is 16.7%, and drawing rate is 0%.\n- If GoodGuy holds a Jack (33.3% chance), he is likely to call (60%) or fold (40%). If he calls, it will be a draw unless the public card is a Jack. If he folds, I will win. The overall winning rate is 13.3%, losing rate is 0%, and drawing rate is 20%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (33.3% chance), 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 have a chance to win if the public card is a Jack. The overall winning rate is 10%, losing rate is 23.3%, and drawing rate is 0%.\n- If GoodGuy holds a Queen (33.3% chance), he is likely to fold (50%) or call (50%). If he folds, I will win. If he calls, I will lose unless the public card is a Jack. The overall winning rate is 16.7%, losing rate is 16.7%, and drawing rate is 0%.\n- If GoodGuy holds a Jack (33.3% chance), he is likely to fold (40%) or call (60%). If he folds, I will win. If he calls, it will be a draw unless the public card is a Jack. The overall winning rate is 13.3%, losing rate is 0%, and drawing rate is 20%.\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 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 chips. If I lose, the losing payoff would be 2 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 = 10% * 1.5 - 23.3% * 1 = -0.15 chips\n- Plan 2: Expected Chips Gain = 10% * 2 - 23.3% * 2 = -0.266 chips\n- Plan 3: Expected Chips Gain = -1 chip\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I will choose Plan 1: Call."}}
{"message": "", "51_2": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (probability 1/3), he will likely raise (70%) or call (30%). If he raises, I will lose (probability 100%). If he calls, I will draw (probability 100%). Overall, the winning rate is 0%, the losing rate is 70%, and the draw rate is 30%.\n- If GoodGuy holds a Queen (probability 1/3), he will likely raise (50%) or fold (50%). If he raises, I will lose (probability 100%). If he folds, I will win (probability 100%). Overall, the winning rate is 50%, the losing rate is 50%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (probability 1/3), he will likely call (60%) or fold (40%). If he calls, I will draw (probability 100%). If he folds, I will win (probability 100%). Overall, the winning rate is 40%, the losing rate is 0%, and the draw rate is 60%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (probability 1/3), he will likely raise (70%) or call (30%). If he raises, I will lose (probability 100%). If he calls, I will draw (probability 100%). Overall, the winning rate is 0%, the losing rate is 70%, and the draw rate is 30%.\n- If GoodGuy holds a Queen (probability 1/3), he will likely fold (50%). If he folds, I will win (probability 100%). Overall, the winning rate is 50%, the losing rate is 0%, and the draw rate is 50%.\n- If GoodGuy holds a Jack (probability 1/3), he will likely fold (40%). If he folds, I will win (probability 100%). Overall, the winning rate is 40%, the losing rate is 0%, and the draw rate is 60%.\n\nPlan 3: Fold\n- If GoodGuy holds a King (probability 1/3), he will likely raise (70%) or call (30%). 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 100%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (probability 1/3), he will likely raise (50%) or fold (50%). If he raises, I will lose (probability 100%). If he folds, I will lose (probability 100%). Overall, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (probability 1/3), he will likely call (60%) or fold (40%). If he calls, I will lose (probability 100%). If he folds, I will lose (probability 100%). Overall, 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 6 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 win, the winning payoff would be 0 chips. If lose, the lose payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: (0% * 6) - (70% * 2) = -1.4 chips\n- Plan 2: (50% * 8) - (70% * 4) = 0 chips\n- Plan 3: (0% * 0) - (100% * 2) = -2 chips\n\nPlan Selection:\n- Plan 1: 3rd place\n- Plan 2: 1st place\n- Plan 3: 2nd place\n\nTherefore, I should choose Plan 2: Raise."}}
