{"message": "", "1_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (33.3% probability), he might raise (60% probability) or call (40% probability). If he raises, I would lose (0% win, 100% lose, 0% draw). If he calls, it would be a draw (0% win, 0% lose, 100% draw).\n- If GoodGuy holds a Queen (33.3% probability), he might fold (50% probability) or call (50% probability). If he folds, I would win (100% win, 0% lose, 0% draw). If he calls, I would win (100% win, 0% lose, 0% draw).\n- If GoodGuy holds a Jack (33.3% probability), he might fold (50% probability) or call (50% probability). If he folds, I would win (100% win, 0% lose, 0% draw). If he calls, I would win (100% win, 0% lose, 0% draw).\n- Overall, the winning rate for plan 1 is 66.6%, the losing rate is 20%, and the draw rate is 13.3%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (33.3% probability), he might raise (60% probability) or call (40% probability). If he raises, I would lose (0% win, 100% lose, 0% draw). If he calls, it would be a draw (0% win, 0% lose, 100% draw).\n- If GoodGuy holds a Queen (33.3% probability), he might fold (50% probability) or call (50% probability). If he folds, I would win (100% win, 0% lose, 0% draw). If he calls, I would win (100% win, 0% lose, 0% draw).\n- If GoodGuy holds a Jack (33.3% probability), he might fold (50% probability) or call (50% probability). If he folds, I would win (100% win, 0% lose, 0% draw). If he calls, I would win (100% win, 0% lose, 0% draw).\n- Overall, the winning rate for plan 2 is 66.6%, the losing rate is 20%, and the draw rate is 13.3%.\n\nPlan 3: Fold\n- If I fold, I would lose regardless of GoodGuy's card (0% win, 100% lose, 0% draw).\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 2 chips. If I lose, the losing payoff would be 1 chip.\n- Plan 2: If I win, the winning payoff would be 6 chips. If I lose, the losing payoff would be 2 chips.\n- Plan 3: If I lose, the losing payoff would be 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 66.6% * 2 - 20% * 1 = 1.33 - 0.2 = 1.13 chips\n- Plan 2: Expected Chips Gain = 66.6% * 6 - 20% * 2 = 3.996 - 0.4 = 3.596 chips\n- Plan 3: Expected Chips Gain = 0% * 0 - 100% * 1 = -1 chip\n\nPlan Selection:\n- Plan 1: 1.13 chips\n- Plan 2: 3.596 chips\n- Plan 3: -1 chip\n\nBased on the expected chips gain, the best plan would be Plan 2 (Raise)."}}
{"message": "", "1_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (20% probability), he will likely raise (70% probability). This would result in a draw, as we both have a pair of Kings. If he calls (30% probability), it would also result in a draw.\n- If GoodGuy holds a Queen (40% probability), he might fold (50% probability), resulting in a win for me, or call (50% probability), resulting in a win for me as I have a higher hand.\n- If GoodGuy holds a Jack (40% probability), he might fold (50% probability), resulting in a win for me, or call (50% probability), resulting in a win for me as I have a higher hand.\n\nPlan 2: Fold\n- If I fold, I automatically lose the game, regardless of GoodGuy's card.\n\nPlan 3: Check\n- If GoodGuy holds a King (20% probability), he will likely raise (70% probability). This would result in a draw, as we both have a pair of Kings. If he calls (30% probability), it would also result in a draw.\n- If GoodGuy holds a Queen (40% probability), he might raise (30% probability), resulting in a win for me, or call (70% probability), resulting in a win for me as I have a higher hand.\n- If GoodGuy holds a Jack (40% probability), he might raise (30% probability), resulting in a win for me, or call (70% probability), resulting in a win for me as I have a higher hand.\n\nWinning/Lose/Draw Rates for Each Plan:\n- Plan 1: Winning rate: 80%, Lose rate: 0%, Draw rate: 20%\n- Plan 2: Winning rate: 0%, Lose rate: 100%, Draw rate: 0%\n- Plan 3: Winning rate: 80%, Lose rate: 0%, Draw rate: 20%\n\nNumber of Winning and Lose Payoffs for Each Plan:\n- Plan 1: If win, the winning payoff would be half of the pot (8 chips). If lose, the lose payoff would be half of the pot (8 chips).\n- Plan 2: If lose, the lose payoff would be half of the pot (8 chips).\n- Plan 3: If win, the winning payoff would be half of the pot (8 chips). If lose, the lose payoff would be half of the pot (8 chips).\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected chips gain = winning rate * winning payoff - lose rate * lose payoff = 80% * 8 - 0% * 8 = 6.4 chips\n- Plan 2: Expected chips gain = winning rate * winning payoff - lose rate * lose payoff = 0% * 8 - 100% * 8 = -8 chips\n- Plan 3: Expected chips gain = winning rate * winning payoff - lose rate * lose payoff = 80% * 8 - 0% * 8 = 6.4 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 both have the highest expected chips gain (6.4 chips), while Plan 2 has the lowest expected chips gain (-8 chips). Therefore, I should either raise (Plan 1) or check (Plan 3). Considering the strategy improvement, I would choose to raise (Plan 1) to potentially confuse GoodGuy and make him believe that I have a high card."}}
{"message": "", "1_4": {"plan": "Plan 1: Call\n\nThe winning/lose/draw rates when GoodGuy holds a Queen: \n- If GoodGuy holds a Queen (50% probability), he will likely call (70% probability). In this case, I will win because my pair of Kings beats his Queen. So, the winning rate for his Queen is 0.5 * 0.7 = 0.35.\n- If GoodGuy holds a Queen and decides to fold (30% probability), I will also win. So, the winning rate for his Queen is 0.5 * 0.3 = 0.15.\n- There is no draw scenario in this case.\n\nThe winning/lose/draw rates when GoodGuy holds a Jack:\n- If GoodGuy holds a Jack (50% probability), he will likely fold (50% probability). In this case, I will win. So, the winning rate for his Jack is 0.5 * 0.5 = 0.25.\n- If GoodGuy holds a Jack and decides to call (50% probability), I will also win. So, the winning rate for his Jack is 0.5 * 0.5 = 0.25.\n- There is no draw scenario in this case.\n\nPlan1 overall board_game_expert's Winning/Lose/Draw rates:\n- Winning rate for plan 1 is 0.35 (Queen) + 0.15 (Queen) + 0.25 (Jack) + 0.25 (Jack) = 1.0\n- Lose rate for plan 1 is 0.\n- Draw rate for plan 1 is 0.\n\nPlan 2: Fold\n\nIf I fold, I will lose regardless of what card GoodGuy holds. So, 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 would be 24. If win, the winning payoff would be 12. If lose, the lose payoff would be 12.\n- Plan 2: After the fold, chips in the pot would be 20. If win, the winning payoff would be 0 (because I can't win if I fold). If lose, the lose payoff would be 10.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected chips gain = winning rate * winning payoff - lose rate * lose payoff = 1.0 * 12 - 0 * 12 = 12.\n- Plan 2: Expected chips gain = winning rate * winning payoff - lose rate * lose payoff = 0 * 0 - 1 * 10 = -10.\n\nPlan Selection:\n- Plan 1 (Call) has an expected chips gain of 12.\n- Plan 2 (Fold) has an expected chips gain of -10.\n\nTherefore, I should choose Plan 1 (Call) as it has the highest expected chips gain."}}
{"message": "", "2_0": {"plan": "Plan 1: Call\n- If GoodGuy holds 'HQ':\n  - In the 1st round, if I call, GoodGuy would likely call (70%) or raise (30%). If he calls, I have a 50% chance of winning (if the public card is a King or a Queen), a 50% chance of losing (if the public card is a Jack). If he raises, I have a 50% chance of winning (if the public card is a King or a Queen), a 50% chance of losing (if the public card is a Jack).\n  - Overall, the winning rate is 0.33*0.7*0.5 + 0.33*0.3*0.5 = 0.165, the losing rate is 0.33*0.7*0.5 + 0.33*0.3*0.5 = 0.165, and the draw rate is 0.\n- If GoodGuy holds 'SJ' or 'HJ':\n  - In the 1st round, if I call, GoodGuy would likely call (60%) or raise (40%). If he calls, I have a 100% chance of winning (as my card is higher). If he raises, I have a 100% chance of winning (as my card is higher).\n  - Overall, the winning rate is 0.33*0.6*1 + 0.33*0.4*1 = 0.33, the losing rate is 0, and the draw rate is 0.\n- Plan1 overall board_game_expert's Winning/Lose/Draw rates: Winning rate is 0.165 + 0.33 = 0.495, Lose rate is 0.165, Draw rate is 0.\n\nPlan 2: Raise\n- If GoodGuy holds 'HQ':\n  - In the 1st round, if I raise, GoodGuy would likely call (70%) or raise (30%). If he calls, I have a 50% chance of winning (if the public card is a King or a Queen), a 50% chance of losing (if the public card is a Jack). If he raises, I have a 50% chance of winning (if the public card is a King or a Queen), a 50% chance of losing (if the public card is a Jack).\n  - Overall, the winning rate is 0.33*0.7*0.5 + 0.33*0.3*0.5 = 0.165, the losing rate is 0.33*0.7*0.5 + 0.33*0.3*0.5 = 0.165, and the draw rate is 0.\n- If GoodGuy holds 'SJ' or 'HJ':\n  - In the 1st round, if I raise, GoodGuy would likely call (60%) or raise (40%). If he calls, I have a 100% chance of winning (as my card is higher). If he raises, I have a 100% chance of winning (as my card is higher).\n  - Overall, the winning rate is 0.33*0.6*1 + 0.33*0.4*1 = 0.33, the losing rate is 0, and the draw rate is 0.\n- Plan2 overall board_game_expert's Winning/Lose/Draw rates: Winning rate is 0.165 + 0.33 = 0.495, Lose rate is 0.165, Draw rate is 0.\n\nPlan 3: Fold\n- If I fold, I automatically lose the game. So, the winning rate 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- Plan1: 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- Plan2: 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- Plan3: After the action, Chips in the pot: 3. If lose, the lose payoff would be 1.5.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan1: 0.495 * 1.5 - 0.165 * 1.5 = 0.495\n- Plan2: 0.495 * 2.5 - 0.165 * 2.5 = 0.825\n- Plan3: -1.5\n\nPlan Selection:\n- Plan2 (Raise) has the highest estimated expected chips gain, so I should choose this plan."}}
{"message": "", "2_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds 'HQ': \n  - In the 2nd round, if he sees my raise, he will likely call (80%) or fold (20%). If he calls, I will win as my 'SK' outranks his 'HQ'. If he folds, I will also win as he forfeits the game. Therefore, the winning rate is 100%.\n- If GoodGuy holds 'SJ' or 'HJ': \n  - In the 2nd round, if he sees my raise, he will likely fold (70%) or call (30%). If he folds, I will win as he forfeits the game. If he calls, I will lose as his 'SJ'/'HJ' matches the public card. Therefore, the winning rate is 70% and the losing rate is 30%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. Therefore, the losing rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds 'HQ': \n  - In the 2nd round, if he sees my check, he will likely call (80%) or fold (20%). If he calls, I will win as my 'SK' outranks his 'HQ'. If he folds, I will also win as he forfeits the game. Therefore, the winning rate is 100%.\n- If GoodGuy holds 'SJ' or 'HJ': \n  - In the 2nd round, if he sees my check, he will likely call (60%) or raise (40%). If he calls, I will lose as his 'SJ'/'HJ' matches the public card. If he raises, I will also lose as his 'SJ'/'HJ' matches the public card. Therefore, the losing rate is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, chips in the pot: 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 = 0.7 * 4 - 0.3 * 4 = 1.6\n- Plan 2: Expected Chips Gain = -2\n- Plan 3: Expected Chips Gain = 0.7 * 2 - 1 * 2 = -0.6\n\nPlan Selection:\n- Plan 1: Raise\n- Plan 3: Check\n- Plan 2: Fold\n\nBased on the estimated expected chips gain, I should choose Plan 1: Raise."}}
{"message": "", "3_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds 'HQ': \n  - In the 1st round, if I raise, GoodGuy would likely call (probability 80%) or fold (probability 20%). If he calls, the pot would be 8 chips. If he folds, the pot would be 4 chips. \n  - In the 2nd round, if the public card is 'HK' or 'HJ', and I raise, GoodGuy would likely fold (probability 70%) or call (probability 30%). If he folds, the pot would be 12 chips. If he calls, the pot would be 16 chips. \n- If GoodGuy holds 'SJ' or 'HJ': \n  - In the 1st round, if I raise, GoodGuy would likely call (probability 60%) or fold (probability 40%). If he calls, the pot would be 8 chips. If he folds, the pot would be 4 chips. \n  - In the 2nd round, if the public card is 'SK' or 'HK', and I raise, GoodGuy would likely fold (probability 80%) or call (probability 20%). If he folds, the pot would be 12 chips. If he calls, the pot would be 16 chips. \n\nPlan 2: Fold\n- If I fold, the pot would remain at 4 chips. \n\nPlan 3: Check\n- If I check, the pot would remain at 4 chips. \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. If lose, the lose payoff would be half of the pot. \n- Plan 2: If I fold, there would be no payoff. \n- Plan 3: If I check, the payoff would be half of the pot if I win, and half of the pot if I lose. \n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = (Winning Rate * Winning Payoff) - (Lose Rate * Lose Payoff)\n- Plan 2: Expected Chips Gain = 0 (since I fold)\n- Plan 3: Expected Chips Gain = (Winning Rate * Winning Payoff) - (Lose Rate * Lose Payoff)\n\nPlan Selection:\n- If the expected chips gain for Plan 1 is the highest, I would choose Plan 1. \n- If the expected chips gain for Plan 3 is the highest, I would choose Plan 3. \n- I would not choose Plan 2 since the expected chips gain is 0."}}
{"message": "", "5_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (20% probability), he is likely to raise (20%) or call (80%). If he raises, I will lose unless the public card is a Queen. If he calls, I will win if the public card is a Queen, lose if it is a King, and draw if it is a Jack. Overall, my winning rate is 16%, losing rate is 36%, and drawing rate is 48%.\n- If GoodGuy holds a Queen (40% probability), he is likely to raise (40%) or call (60%). If he raises or calls, it will be a draw unless the public card is a King or Jack. Overall, my winning rate is 0%, losing rate is 24%, and drawing rate is 76%.\n- If GoodGuy holds a Jack (40% probability), he is likely to fold (70%) or call (30%). If he folds, I will win. If he calls, I will win unless the public card is a Jack. Overall, my winning rate is 82%, losing rate is 12%, and drawing rate is 6%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (20% probability), he is likely to call (80%) or raise (20%). If he calls or raises, I will lose unless the public card is a Queen. Overall, my winning rate is 16%, losing rate is 64%, and drawing rate is 20%.\n- If GoodGuy holds a Queen (40% probability), 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 King or Jack. Overall, my winning rate is 56%, losing rate is 8%, and drawing rate is 36%.\n- If GoodGuy holds a Jack (40% probability), he is likely to fold (70%) or call (30%). If he folds, I will win. If he calls, I will win unless the public card is a Jack. Overall, my winning rate is 82%, losing rate is 12%, and drawing rate is 6%.\n\nPlan 3: Fold\n- If I fold, I will lose the 2 chips I have already put into the pot. My winning rate is 0%, losing rate is 100%, and drawing rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips. 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 fold, I will lose 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 16% * 3 - 36% * 2 = -0.12 chips\n- Plan 2: 56% * 7 - 8% * 6 = 3.52 chips\n- Plan 3: 0% * 0 - 100% * 2 = -2 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest estimated expected chips gain, so I will choose this plan."}}
{"message": "", "5_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (90% probability), he is likely to raise (90%) or call (10%). If he raises, I will lose as his pair of Kings beats my single Queen. If he calls, I will also lose as his King beats my Queen. Therefore, the winning rate for this plan is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (10% probability), he is likely to call (50%) or fold (50%). If he calls, it will be a draw as we both have a single Queen. If he folds, I will win. Therefore, the winning rate for this plan is 5%, the losing rate is 0%, and the draw rate is 5%.\n\nPlan 2: Fold\n- If I fold, I will automatically lose the game. Therefore, the winning rate for this plan is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King (90% probability), he is likely to raise (90%) or call (10%). If he raises, I will lose as his pair of Kings beats my single Queen. If he calls, I will also lose as his King beats my Queen. Therefore, the winning rate for this plan is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (10% probability), he is likely to call (50%) or fold (50%). If he calls, it will be a draw as we both have a single Queen. If he folds, I will win. Therefore, the winning rate for this plan is 5%, the losing rate is 0%, and the draw rate is 5%.\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 fold, I will lose 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 = 5% * 6 chips - 100% * 6 chips = -5.7 chips\n- Plan 2: Expected Chips Gain = 0% * 6 chips - 100% * 6 chips = -6 chips\n- Plan 3: Expected Chips Gain = 5% * 6 chips - 100% * 6 chips = -5.7 chips\n\nPlan Selection:\n- Plan 1: Rank 2\n- Plan 2: Rank 3\n- Plan 3: Rank 1\n\nConsidering the estimated expected chips gain, I should choose Plan 3: Check. This plan has the highest expected chips gain (-5.7 chips), which is still a loss but less than the other plans. This plan also aligns with my strategy improvement to be more cautious when I have a lower card."}}
{"message": "", "5_5": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (90% probability), he will likely raise (90% probability). If he raises, I will lose as his pair of Kings beats my single Queen. The overall lose rate for his King is 0.9*0.9=0.81.\n- If GoodGuy holds a Queen (10% probability), he will likely call (50% probability) or fold (50% probability). If he calls, it will be a draw as we both have a single Queen. If he folds, I will win. The overall draw rate for his Queen is 0.1*0.5=0.05 and the overall win rate for his Queen is 0.1*0.5=0.05.\n- The overall winning rate for plan 1 is 0.05, the overall lose rate for plan 1 is 0.81, and the overall draw rate for plan 1 is 0.05.\n\nPlan 2: Raise\n- If GoodGuy holds a King (90% probability), he will likely raise (90% probability). If he raises, I will lose as his pair of Kings beats my single Queen. The overall lose rate for his King is 0.9*0.9=0.81.\n- If GoodGuy holds a Queen (10% probability), he will likely call (50% probability) or fold (50% probability). If he calls, it will be a draw as we both have a single Queen. If he folds, I will win. The overall draw rate for his Queen is 0.1*0.5=0.05 and the overall win rate for his Queen is 0.1*0.5=0.05.\n- The overall winning rate for plan 2 is 0.05, the overall lose rate for plan 2 is 0.81, and the overall draw rate for plan 2 is 0.05.\n\nPlan 3: Fold\n- If I fold, I will lose the game and the chips I have already put into the pot. The overall lose rate for plan 3 is 1.\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 (6+10)/2=8 chips. If I lose, the lose payoff would be the chips I have already put into the pot, which is 6 chips.\n- Plan 2: If I win, the winning payoff would be half of the pot, which is (6+10+8)/2=12 chips. If I lose, the lose payoff would be the chips I have already put into the pot, which is 6+8=14 chips.\n- Plan 3: If I lose, the lose payoff would be the chips I have already put into the pot, which is 6 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is 0.05*8-0.81*6=-4.6 chips.\n- Plan 2: The expected chips gain is 0.05*12-0.81*14=-10.26 chips.\n- Plan 3: The expected chips gain is -6 chips.\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain (-4.6 chips), followed by plan 3 (-6 chips), and plan 2 (-10.26 chips). Therefore, I should choose plan 1: Call."}}
{"message": "", "6_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (probability 1/3), he will call (probability 100%) if I call. If the public card is a King, we will draw (probability 1/3). If the public card is a Queen or Jack, I will win (probability 2/3). Overall, the winning rate is 2/9, the losing rate is 0, and the draw rate is 1/9.\n- If GoodGuy holds a Queen (probability 1/3), he will call (probability 30%) or fold (probability 70%) if I call. If he calls and the public card is a Queen, I will lose (probability 1/3). If the public card is a King or Jack, I will win (probability 2/3). If he folds, I will win. Overall, the winning rate is 7/9, the losing rate is 1/9, and the draw rate is 0.\n- If GoodGuy holds a Jack (probability 1/3), he will fold (probability 100%) if I call. I will win. Overall, the winning rate is 1, the losing rate is 0, and the draw rate is 0.\n- Plan 1 overall winning rate is 20/27, losing rate is 1/27, and draw rate is 1/9.\n\nPlan 2: Raise\n- If GoodGuy holds a King (probability 1/3), he will call (probability 100%) if I raise. If the public card is a King, we will draw (probability 1/3). If the public card is a Queen or Jack, I will win (probability 2/3). Overall, the winning rate is 2/9, the losing rate is 0, and the draw rate is 1/9.\n- If GoodGuy holds a Queen (probability 1/3), he will fold (probability 70%) or call (probability 30%) if I raise. If he calls and the public card is a Queen, I will lose (probability 1/3). If the public card is a King or Jack, I will win (probability 2/3). If he folds, I will win. Overall, the winning rate is 7/9, the losing rate is 1/9, and the draw rate is 0.\n- If GoodGuy holds a Jack (probability 1/3), he will fold (probability 100%) if I raise. I will win. Overall, the winning rate is 1, the losing rate is 0, and the draw rate is 0.\n- Plan 2 overall winning rate is 20/27, losing rate is 1/27, and draw rate is 1/9.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of GoodGuy's card. Overall, the winning rate 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 action, chips in the pot: 4. If win, the winning payoff would be 2. If lose, the lose payoff would be 2.\n- Plan 2: After the action, chips in the pot: 6. If win, the winning payoff would be 3. If lose, the lose payoff would be 3.\n- Plan 3: After the action, chips in the pot: 3. If lose, the lose payoff would be 1.5.\n\nEstimated Expected Chips Gain for Each Plan:\n- Plan 1: 20/27 * 2 - 1/27 * 2 = 1.48\n- Plan 2: 20/27 * 3 - 1/27 * 3 = 2.22\n- Plan 3: -1\n\nPlan Selection:\n- Plan 2 > Plan 1 > Plan 3\n- I should choose Plan 2: Raise."}}
{"message": "", "6_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (probability 100% based on my belief), he will call (probability 100% based on his game pattern). Since we both hold a King, it will be a draw. \n- If GoodGuy holds a Queen (probability 0% based on my belief), he will fold (probability 100% based on his game pattern). Since I hold a King and he folds, I will win. \n- If GoodGuy holds a Jack (probability 0% based on my belief), he will fold (probability 100% based on his game pattern). Since I hold a King and he folds, I will win. \n\nPlan 1 overall Winning/Lose/Draw rates: \n- Winning rate for plan 1: 0% (no winning scenarios)\n- Lose rate for plan 1: 0% (no losing scenarios)\n- Draw rate for plan 1: 100% (only draw scenario is when GoodGuy holds a King)\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds.\n\nPlan 2 overall Winning/Lose/Draw rates: \n- Winning rate for plan 2: 0% (no winning scenarios)\n- Lose rate for plan 2: 100% (I lose in all scenarios)\n- Draw rate for plan 2: 0% (no draw scenarios)\n\nPlan 3: Check\n- If GoodGuy holds a King (probability 100% based on my belief), he will call (probability 100% based on his game pattern). Since we both hold a King, it will be a draw. \n- If GoodGuy holds a Queen (probability 0% based on my belief), he will fold (probability 100% based on his game pattern). Since I hold a King and he folds, I will win. \n- If GoodGuy holds a Jack (probability 0% based on my belief), he will fold (probability 100% based on his game pattern). Since I hold a King and he folds, I will win. \n\nPlan 3 overall Winning/Lose/Draw rates: \n- Winning rate for plan 3: 0% (no winning scenarios)\n- Lose rate for plan 3: 0% (no losing scenarios)\n- Draw rate for plan 3: 100% (only draw scenario is when GoodGuy holds a King)\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 4.\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: 0% * 4 - 0% * 4 = 0\n- Plan 2: 0% * 0 - 100% * 4 = -4\n- Plan 3: 0% * 2 - 0% * 2 = 0\n\nPlan Selection:\n- Plan 1 and Plan 3 have the same expected chips gain of 0, which is higher than Plan 2's expected chips gain of -4. Therefore, I should either raise (Plan 1) or check (Plan 3). Considering the strategy improvement, I should raise more aggressively when I have a high card, so I will choose Plan 1: Raise."}}
{"message": "", "6_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a Queen (probability 100% based on my belief), he will win. The winning rate for his Queen is 100%. The lose rate for his Queen is 0%. The draw rate for his Queen is 0%.\n- If GoodGuy holds a King (probability 0% based on my belief), it will be a draw. The winning rate for his King is 0%. The lose rate for his King is 0%. The draw rate for his King is 100%.\n- If GoodGuy holds a Jack (probability 0% based on my belief), I will win. The winning rate for his Jack is 100%. The lose rate for his Jack is 0%. The draw rate for his Jack is 0%.\n\nPlan 1 overall board_game_expert's Winning/Lose/Draw rates: \n- Winning rate for plan 1 is 0% (0% for his Queen + 0% for his King + 100% for his Jack)\n- Lose rate for plan 1 is 100% (100% for his Queen + 0% for his King + 0% for his Jack)\n- Draw Rate for plan 1 is 0% (0% for his Queen + 100% for his King + 0% for his Jack)\n\nPlan 2: Fold\n- If GoodGuy holds a Queen (probability 100% based on my belief), I will lose. The winning rate for his Queen is 0%. The lose rate for his Queen is 100%. The draw rate for his Queen is 0%.\n- If GoodGuy holds a King (probability 0% based on my belief), it will be a draw. The winning rate for his King is 0%. The lose rate for his King is 0%. The draw rate for his King is 100%.\n- If GoodGuy holds a Jack (probability 0% based on my belief), I will lose. The winning rate for his Jack is 0%. The lose rate for his Jack is 100%. The draw rate for his Jack is 0%.\n\nPlan 2 overall board_game_expert's Winning/Lose/Draw rates: \n- Winning rate for plan 2 is 0% (0% for his Queen + 0% for his King + 0% for his Jack)\n- Lose rate for plan 2 is 100% (100% for his Queen + 0% for his King + 100% for his Jack)\n- Draw Rate for plan 2 is 0% (0% for his Queen + 100% for his King + 0% for his Jack)\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 - 100% * 12 = -12\n- Plan 2: 0% * 10 - 100% * 10 = -10\n\nPlan Selection: \n- Plan 1: -12\n- Plan 2: -10\n\nBased on the estimated expected chips gains, Plan 2 (Fold) is the better strategy as it minimizes the potential loss."}}
{"message": "", "7_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (40% probability), he is likely to call (80%) or raise (20%). If he calls, I will win if the public card is a Queen (33.3%) or lose if the public card is a King (33.3%) or a Jack (33.3%). If he raises, I will lose as he has a higher card. \n- If GoodGuy holds a Queen (30% probability), he is likely to call (60%) or fold (40%). If he calls, it will be a draw regardless of the public card. If he folds, I will win. \n- If GoodGuy holds a Jack (30% probability), he is likely to fold (70%) or call (30%). If he folds, I will win. If he calls, I will win if the public card is a Queen (33.3%) or a Jack (33.3%) or lose if the public card is a King (33.3%).\n\nPlan 2: Fold\n- If I fold, I will lose the 2 chips in the pot regardless of GoodGuy's card or the public card.\n\nPlan 3: Check\n- If GoodGuy holds a King (40% probability), he is likely to raise (100%). I will lose as he has a higher card. \n- If GoodGuy holds a Queen (30% probability), he is likely to call (60%) or fold (40%). If he calls, it will be a draw regardless of the public card. If he folds, I will win. \n- If GoodGuy holds a Jack (30% probability), he is likely to fold (70%) or call (30%). If he folds, I will win. If he calls, I will win if the public card is a Queen (33.3%) or a Jack (33.3%) or lose if the public card is a King (33.3%).\n\nWinning/Lose Payoffs:\n- Plan 1: If I win, the pot will be 8 chips and the winning payoff would be 4 chips. If I lose, the pot will be 8 chips and the lose payoff would be 4 chips.\n- Plan 2: If I fold, I will lose the 2 chips in the pot.\n- Plan 3: If I win, the pot will be 4 chips and the winning payoff would be 2 chips. If I lose, the pot will be 4 chips and the lose payoff would be 2 chips.\n\nExpected Chips Gain:\n- Plan 1: Expected gain = 0.4*(0.8*4 - 0.2*4) + 0.3*(0.6*4 - 0.4*4) + 0.3*(0.7*4 - 0.3*4) = 0.8 chips\n- Plan 2: Expected gain = -2 chips\n- Plan 3: Expected gain = 0.4*(-4) + 0.3*(0.6*2 - 0.4*2) + 0.3*(0.7*2 - 0.3*2) = -0.8 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I will choose to raise."}}
{"message": "", "8_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (50% probability), he will likely raise in the 2nd round if the public card is a King (33.33% probability). If the public card is not a King, he will likely call (70% probability) or fold (30% probability). Therefore, the winning rate for this plan is 16.67% (50% * 33.33%), the losing rate is 35% (50% * 70%), and the draw rate is 15% (50% * 30%).\n- If GoodGuy holds a Queen (30% probability), he will likely raise in the 2nd round if the public card is a Queen (33.33% probability). If the public card is not a Queen, he will likely call (50% probability) or fold (50% probability). Therefore, the winning rate for this plan is 10% (30% * 33.33%), the losing rate is 15% (30% * 50%), and the draw rate is 15% (30% * 50%).\n- If GoodGuy holds a Jack (20% probability), he will likely raise in the 2nd round if the public card is a Jack (33.33% probability). If the public card is not a Jack, he will likely fold (80% probability) or call (20% probability). Therefore, the winning rate for this plan is 6.67% (20% * 33.33%), the losing rate is 4% (20% * 20%), and the draw rate is 16% (20% * 80%).\n\nPlan 2: Raise\n- If GoodGuy holds a King (50% probability), he will likely call in the 2nd round if the public card is a King (33.33% probability). If the public card is not a King, he will likely call (70% probability) or fold (30% probability). Therefore, the winning rate for this plan is 16.67% (50% * 33.33%), the losing rate is 35% (50% * 70%), and the draw rate is 15% (50% * 30%).\n- If GoodGuy holds a Queen (30% probability), he will likely fold in the 2nd round if the public card is not a Queen (66.67% probability). If the public card is a Queen, he will likely raise (100% probability). Therefore, the winning rate for this plan is 20% (30% * 66.67%), the losing rate is 10% (30% * 33.33%), and the draw rate is 0%.\n- If GoodGuy holds a Jack (20% probability), he will likely fold in the 2nd round if the public card is not a Jack (66.67% probability). If the public card is a Jack, he will likely raise (100% probability). Therefore, the winning rate for this plan is 13.33% (20% * 66.67%), the losing rate is 6.67% (20% * 33.33%), and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card. 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 I win, the winning payoff would be 4 chips (half of the pot). If I lose, the losing payoff would be 2 chips (half of the pot).\n- Plan 2: If I win, the winning payoff would be 6 chips (half of the pot). If I lose, the losing payoff would be 3 chips (half of the pot).\n- Plan 3: If I fold, I will lose 2 chips (my initial bet).\n\nThe expected chips gain for each plan:\n- Plan 1: 16.67% * 4 - 35% * 2 = -0.33 chips\n- Plan 2: 50% * 6 - 51.67% * 3 = -0.5 chips\n- Plan 3: 0% * 0 - 100% * 2 = -2 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain (-0.33 chips), followed by Plan 2 (-0.5 chips), and Plan 3 (-2 chips). Therefore, I should choose Plan 1: Call."}}
{"message": "", "8_3": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (60% probability), he will likely raise (100% probability). If I call, I will lose as his pair of Kings beats my single Queen. \n- If GoodGuy holds a Queen (20% probability), he will likely call (50% probability) or fold (50% probability). If I call and he calls, it will be a draw as we both have a single Queen. If he folds, I will win.\n- If GoodGuy holds a Jack (20% probability), he will likely fold (80% probability) or call (20% probability). If I call and he folds, I will win. If he calls, I will win as my single Queen beats his single Jack.\n\nPlan 2: Raise\n- If GoodGuy holds a King (60% probability), he will likely raise (100% probability). If I raise, I will lose as his pair of Kings beats my single Queen.\n- If GoodGuy holds a Queen (20% probability), he will likely call (50% probability) or fold (50% probability). If I raise and he calls, it will be a draw as we both have a single Queen. If he folds, I will win.\n- If GoodGuy holds a Jack (20% probability), he will likely fold (80% probability) or call (20% probability). If I raise and he folds, I will win. If he calls, I will win as my single Queen beats his single Jack.\n\nPlan 3: Fold\n- If I fold, I will lose the game and any chips I have already put into the pot.\n\nWinning/Lose Payoffs for Each Plan:\n- Plan 1: If I win, the winning payoff would be half of the pot (12 chips). If I lose, the losing payoff would be half of the pot (12 chips).\n- Plan 2: If I win, the winning payoff would be half of the pot (16 chips). If I lose, the losing payoff would be half of the pot (16 chips).\n- Plan 3: If I fold, I will lose the 4 chips I have already put into the pot.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.4 * 12 - 0.6 * 12 = -2.4 chips\n- Plan 2: Expected Chips Gain = 0.4 * 16 - 0.6 * 16 = -3.2 chips\n- Plan 3: Expected Chips Gain = -4 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I will choose to call."}}
{"message": "", "10_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King, he will likely call (60%) or raise (40%). If he raises, I will lose unless the public card is a Queen. If he calls, I will win if the public card is a Queen, and lose if it is a King or Jack. The overall winning rate is 20%, losing rate is 70%, and drawing rate is 10%.\n- If GoodGuy holds a Queen, he will likely call (60%) or fold (40%). If he folds, I will win. If he calls, I will draw unless the public card is a King or Jack. The overall winning rate is 40%, losing rate is 20%, and drawing rate is 40%.\n- If GoodGuy holds a Jack, he will likely fold (70%) or call (30%). If he folds, I will win. If he calls, I will win unless the public card is a Jack. The overall winning rate is 70%, losing rate is 10%, and drawing rate is 20%.\n\nPlan 2: Raise\n- If GoodGuy holds a King, he will likely call (70%) or raise (30%). If he raises, I will lose unless the public card is a Queen. If he calls, I will win if the public card is a Queen, and lose if it is a King or Jack. The overall winning rate is 20%, losing rate is 70%, and drawing rate is 10%.\n- If GoodGuy holds a Queen, he will likely call (60%) or fold (40%). If he folds, I will win. If he calls, I will draw unless the public card is a King or Jack. The overall winning rate is 40%, losing rate is 20%, and drawing rate is 40%.\n- If GoodGuy holds a Jack, he will likely fold (70%) or call (30%). If he folds, I will win. If he calls, I will win unless the public card is a Jack. The overall winning rate is 70%, losing rate is 10%, and drawing rate is 20%.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card. The overall winning rate is 0%, losing rate is 100%, and drawing rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, chips in the pot: 3. If win, the winning payoff would be 1.5. 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 = 0.2 * 1.5 - 0.7 * 1.5 = -0.75\n- Plan 2: Expected chips gain = 0.2 * 2.5 - 0.7 * 2.5 = -1.25\n- Plan 3: Expected chips gain = -0.5\n\nPlan Selection:\n- Plan 1: Rank 1\n- Plan 2: Rank 2\n- Plan 3: Rank 3\n\nBased on the above analysis, I should choose Plan 1 (Call) as it has the highest expected chips gain."}}
{"message": "", "10_2": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (30% chance), he will likely raise (80%) or call (20%) in the 2nd round. If the public card is a Queen, I will win (probability = 30% * 20% = 6%). If the public card is a King or Jack, I will lose (probability = 30% * 80% = 24%).\n- If GoodGuy holds a Queen (40% chance), he will likely call (70%) or raise (30%) in the 2nd round. If the public card is a Queen, it will be a draw (probability = 40% * 70% = 28%). If the public card is a King or Jack, I will lose (probability = 40% * 30% = 12%).\n- If GoodGuy holds a Jack (30% chance), he will likely fold (70%) or call (30%) in the 2nd round. If the public card is a Queen, I will win (probability = 30% * 70% = 21%). If the public card is a King or Jack, I will lose (probability = 30% * 30% = 9%).\n\nPlan 2: Raise\n- If GoodGuy holds a King (30% chance), he will likely raise (80%) or call (20%) in the 2nd round. If the public card is a Queen, I will win (probability = 30% * 20% = 6%). If the public card is a King or Jack, I will lose (probability = 30% * 80% = 24%).\n- If GoodGuy holds a Queen (40% chance), he will likely fold (60%) or call (40%) in the 2nd round. If the public card is a Queen, it will be a draw (probability = 40% * 40% = 16%). If the public card is a King or Jack, I will win (probability = 40% * 60% = 24%).\n- If GoodGuy holds a Jack (30% chance), he will likely fold (70%) or call (30%) in the 2nd round. If the public card is a Queen, I will win (probability = 30% * 70% = 21%). If the public card is a King or Jack, I will lose (probability = 30% * 30% = 9%).\n\nPlan 3: Fold\n- If I fold, I will lose the pot, 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 6 chips. If I lose, the loss would be 4 chips.\n- Plan 2: If I win, the winning payoff would be 10 chips. If I lose, the loss would be 8 chips.\n- Plan 3: If I fold, the loss would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected gain = 6 * 27% - 4 * 45% = -0.18 chips\n- Plan 2: Expected gain = 10 * 51% - 8 * 33% = 2.18 chips\n- Plan 3: Expected gain = -2 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I should choose this plan."}}
{"message": "", "10_4": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (70% probability), he will likely raise (80%) or call (20%). If he raises, I will lose as his King matches the public card. If he calls, I will also lose as his King is higher than my Queen. So, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (30% probability), he will likely call (70%) or raise (30%). If he calls or raises, it will be a draw as we both hold a Queen. So, the winning rate is 0%, the losing rate is 0%, and the draw rate is 100%.\n\nPlan 2: Fold\n- If I fold, I will lose the chips in the pot regardless of GoodGuy's card. 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 King (70% probability), he will likely raise (80%) or call (20%). If he raises, I will lose as his King matches the public card. If he calls, I will also lose as his King is higher than my Queen. So, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (30% probability), he will likely call (70%) or raise (30%). If he calls or raises, it will be a draw as we both hold a Queen. So, 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: If I win, the winning payoff would be half of the pot (6 chips) plus my raise (8 chips), so 14 chips. If I lose, the losing payoff would be my raise (8 chips).\n- Plan 2: If I fold, I will lose the chips I have already put in the pot (6 chips).\n- Plan 3: If I win, the winning payoff would be half of the pot (6 chips). If I lose, the losing payoff would be the chips I have already put in the pot (6 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0% * 14 chips - 100% * 8 chips = -8 chips\n- Plan 2: Expected Chips Gain = 0% * 0 chips - 100% * 6 chips = -6 chips\n- Plan 3: Expected Chips Gain = 0% * 6 chips - 100% * 6 chips = -6 chips\n\nPlan Selection:\n- Plan 1: -8 chips\n- Plan 2: -6 chips\n- Plan 3: -6 chips\n\nBased on the expected chips gain, Plan 2 and Plan 3 are the best strategies. However, considering the strategy improvement, Plan 2 (Fold) is the best strategy as it minimizes my losses when the public card does not match my card and GoodGuy raises."}}
{"message": "", "11_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King, he will likely call (70%) or raise (30%). 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 lose if it's a Queen. The overall winning rate is 30%, losing rate is 70%.\n- If GoodGuy holds a Queen, he will likely call (60%) or fold (40%). 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 40%, losing rate is 60%.\n- If GoodGuy holds a Jack, he will likely fold (70%) or call (30%). If the public card is a Jack, it's a draw. If the public card is not a Jack, I will win if it's a King and lose if it's a Queen. The overall winning rate is 35%, losing rate is 35%, draw rate is 30%.\n\nPlan 2: Fold\n- If I fold, I will lose the chips in the pot regardless of GoodGuy's card or the public card. The overall losing rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King, he will likely call (70%) or raise (30%). 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 lose if it's a Queen. The overall winning rate is 30%, losing rate is 70%.\n- If GoodGuy holds a Queen, he will likely call (60%) or fold (40%). 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 40%, losing rate is 60%.\n- If GoodGuy holds a Jack, he will likely fold (70%) or call (30%). If the public card is a Jack, it's a draw. If the public card is not a Jack, I will win if it's a King and lose if it's a Queen. The overall winning rate is 35%, losing rate is 35%, draw rate is 30%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 4 chips. If lose, the lose payoff would be 2 chips.\n- Plan 2: If 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: 30% * 4 - 70% * 2 = -0.8 chips\n- Plan 2: -100% * 2 = -2 chips\n- Plan 3: 35% * 2 - 35% * 2 = 0 chips\n\nPlan Selection:\n- Plan 1: -0.8 chips\n- Plan 2: -2 chips\n- Plan 3: 0 chips\n\nBased on the estimated expected chips gain, Plan 3 (Check) is the best strategy to use in this situation."}}
{"message": "", "11_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (41.18% chance), he will likely raise (80% chance) or call (20% chance). If he raises, I will lose (100% chance). If he calls, I will lose (100% chance). Overall, I will lose with a probability of 41.18%.\n- If GoodGuy holds a Queen (35.29% chance), he will likely call (50% chance) or fold (50% chance). If he calls, I will win (100% chance). If he folds, I will win (100% chance). Overall, I will win with a probability of 35.29%.\n- If GoodGuy holds a Jack (23.53% chance), he will likely fold (80% chance) or call (20% chance). If he folds, I will win (100% chance). If he calls, it will be a draw (100% chance). Overall, I will win with a probability of 18.82% and draw with a probability of 4.71%.\n\nPlan 2: Fold\n- If I fold, I will lose the current pot (2 chips). The probability of this happening is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (41.18% chance), he will likely raise (80% chance) or check (20% chance). If he raises, I will lose (100% chance). If he checks, I will lose (100% chance). Overall, I will lose with a probability of 41.18%.\n- If GoodGuy holds a Queen (35.29% chance), he will likely check (50% chance) or fold (50% chance). If he checks, I will win (100% chance). If he folds, I will win (100% chance). Overall, I will win with a probability of 35.29%.\n- If GoodGuy holds a Jack (23.53% chance), he will likely fold (80% chance) or check (20% chance). If he folds, I will win (100% chance). If he checks, it will be a draw (100% chance). Overall, I will win with a probability of 18.82% and draw with a probability of 4.71%.\n\nWinning/Lose Payoffs:\n- Plan 1: If I win, the pot will be 6 chips, so I will gain 3 chips. If I lose, I will lose 2 chips.\n- Plan 2: If I fold, I will lose 2 chips.\n- Plan 3: If I win, the pot will be 4 chips, so I will gain 2 chips. If I lose, I will lose 2 chips.\n\nExpected Chips Gain:\n- Plan 1: (35.29% * 3) - (41.18% * 2) = 0.53 chips\n- Plan 2: -2 chips\n- Plan 3: (35.29% * 2) - (41.18% * 2) = -0.12 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I will choose to raise."}}
{"message": "", "12_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (33.33% probability), he will likely call (70%) or raise (30%). If the public card is a King or Queen, I will lose. If the public card is a Jack, it's a draw. \n- If GoodGuy holds a Queen (33.33% probability), he will likely call (60%) or fold (40%). If the public card is a Queen, it's a draw. If the public card is a King or Jack, I will win.\n- If GoodGuy holds a Jack (33.33% probability), he will likely fold (70%) or call (30%). If the public card is a Jack, I will lose. If the public card is a Queen or King, I will win.\n\nPlan 2: Raise\n- If GoodGuy holds a King (33.33% probability), he will likely call (70%) or raise (30%). If the public card is a King or Queen, I will lose. If the public card is a Jack, it's a draw. \n- If GoodGuy holds a Queen (33.33% probability), he will likely fold (40%) or call (60%). If the public card is a Queen, it's a draw. If the public card is a King or Jack, I will win.\n- If GoodGuy holds a Jack (33.33% probability), he will likely fold (70%) or call (30%). If the public card is a Jack, I will lose. If the public card is a Queen or King, I will win.\n\nPlan 3: Fold\n- If I fold, I will lose the pot, 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 half of the pot (3 chips). If I lose, the lose payoff would be half of the pot (3 chips).\n- Plan 2: If I win, the winning payoff would be half of the pot (4 chips). If I lose, the lose payoff would be half of the pot (4 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 = 0.33*(0.7*3 + 0.3*3) - 0.33*(0.7*3 + 0.3*3) = 0\n- Plan 2: Expected Chips Gain = 0.33*(0.7*4 + 0.3*4) - 0.33*(0.7*4 + 0.3*4) = 0\n- Plan 3: Expected Chips Gain = -1\n\nPlan Selection:\n- Plan 1 and Plan 2 have the same expected chips gain, which is higher than Plan 3. Therefore, I should either call or raise. Considering the strategy improvement, I should raise more aggressively when I hold a Queen and the public card is a Queen or King. Therefore, I choose Plan 2: Raise."}}
{"message": "", "12_2": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (100% probability based on my belief), he will likely raise (80%) or call (20%) in the second round. If the public card is a Queen, I will win (probability = 0.8 * 0.5 = 0.4), draw (probability = 0.2 * 0.5 = 0.1), or lose (probability = 0.5). Overall, the winning rate is 0.4, the draw rate is 0.1, and the losing rate is 0.5.\n- After the call, the chips in the pot would be 12. If I win, the winning payoff would be 6 chips. If I lose, the loss would be 6 chips.\n- The expected chips gain for Plan 1 is 0.4 * 6 - 0.5 * 6 = -0.6 chips.\n\nPlan 2: Fold\n- If I fold, I will lose the round regardless of GoodGuy's card. The losing rate is 1.\n- After the fold, the chips in the pot would be 10. The loss would be 5 chips.\n- The expected chips gain for Plan 2 is -1 * 5 = -5 chips.\n\nPlan Selection:\n- The estimated expected chips gains for Plan 1 and Plan 2 are -0.6 chips and -5 chips, respectively.\n- Therefore, I should select Plan 1 (Call) as it has the highest estimated expected chips gain."}}
{"message": "", "12_4": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (30% chance), he will likely call (70%) or raise (30%). If he calls, I will win as my Queen matches the public card. If he raises, I will still win. Therefore, the winning rate is 100%.\n- If GoodGuy holds a Queen (70% chance), it will be a draw as both our cards match the public card. Therefore, the draw rate is 100%.\n- Overall, the winning rate for Plan 1 is 30% (30% chance of GoodGuy holding a King * 100% winning rate), the draw rate is 70% (70% chance of GoodGuy holding a Queen * 100% draw rate), and the losing rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. Therefore, the losing rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (30% chance), he will likely call (70%) or raise (30%). If he calls, I will win as my Queen matches the public card. If he raises, I will still win. Therefore, the winning rate is 100%.\n- If GoodGuy holds a Queen (70% chance), it will be a draw as both our cards match the public card. Therefore, the draw rate is 100%.\n- Overall, the winning rate for Plan 3 is 30% (30% chance of GoodGuy holding a King * 100% winning rate), the draw rate is 70% (70% chance of GoodGuy holding a Queen * 100% draw rate), 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 (6 chips) plus my raise (4 chips), so 10 chips. If I lose, the lose payoff would be my raise (4 chips).\n- Plan 2: If I fold, I will lose my current stake in the pot (6 chips).\n- Plan 3: If I win, the winning payoff would be half of the pot (6 chips). If I lose, there is no additional loss as I did not raise.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected gain is winning rate * winning payoff - losing rate * losing payoff = 30% * 10 chips - 0% * 4 chips = 3 chips.\n- Plan 2: Expected loss is 100% * 6 chips = -6 chips.\n- Plan 3: Expected gain is winning rate * winning payoff - losing rate * losing payoff = 30% * 6 chips - 0% * 0 chips = 1.8 chips.\n\nPlan Selection:\n- Plan 1 (Raise) has the highest expected chips gain (3 chips), followed by Plan 3 (Check) with 1.8 chips, and Plan 2 (Fold) with -6 chips. Therefore, I should choose Plan 1: Raise."}}
{"message": "", "13_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King, he is likely to raise (70%) or call (30%). If he raises, I will lose unless the public card is a Jack. If he calls, I have a chance to win if the public card is a Jack. The winning rate is 30% * 1/3 = 10%, the losing rate is 70% * 2/3 + 30% * 2/3 = 60%, and the draw rate is 30%.\n- If GoodGuy holds a Queen, he is likely to call (60%) or fold (40%). If he calls, I have a chance to win if the public card is a Jack. The winning rate is 60% * 1/3 = 20%, the losing rate is 60% * 2/3 = 40%, and the draw rate is 40%.\n- If GoodGuy holds a Jack, he is likely to fold (70%) or call (30%). If he calls, it will be a draw. The winning rate is 0%, the losing rate is 0%, and the draw rate is 100%.\n\nPlan 2: Raise\n- If GoodGuy holds a King, he is likely to raise (70%) or call (30%). If he raises, I will lose unless the public card is a Jack. If he calls, I have a chance to win if the public card is a Jack. The winning rate is 30% * 1/3 = 10%, the losing rate is 70% * 2/3 + 30% * 2/3 = 60%, and the draw rate is 30%.\n- If GoodGuy holds a Queen, he is likely to fold (40%) or call (60%). If he folds, I will win. If he calls, I have a chance to win if the public card is a Jack. The winning rate is 40% + 60% * 1/3 = 60%, the losing rate is 60% * 2/3 = 40%, and the draw rate is 0%.\n- If GoodGuy holds a Jack, he is likely to fold (70%) or call (30%). If he folds, I will win. If he calls, it will be a draw. The winning rate is 70%, the losing rate is 0%, and the draw rate is 30%.\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 5 chips. If I lose, the losing payoff would be 3 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: 10% * 3 - 60% * 1 = -0.3 chips\n- Plan 2: 60% * 5 - 40% * 3 = 1.8 chips\n- Plan 3: -1 chip\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain, so I should choose Plan 2: Raise."}}
{"message": "", "13_2": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he is likely to raise (80%) or call (20%) in the second round. If the public card is a King, I will lose. If the public card is not a King, I have a 50% chance of winning (if the public card is a Jack) or losing (if the public card is a Queen). Overall, the winning rate for this plan is 35%, the losing rate is 65%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (30% probability), he is likely to raise (70%) or call (30%) in the second round. If the public card is a Queen, I will lose. If the public card is not a Queen, I have a 50% chance of winning (if the public card is a Jack) or losing (if the public card is a King). Overall, the winning rate for this plan is 15%, the losing rate is 85%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose the round regardless of GoodGuy's card or the public card. 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: After the action, there will be 10 chips in the pot. If I win, the winning payoff would be 5 chips. If I lose, the lose payoff would be 5 chips.\n- Plan 2: After the action, there will be 6 chips in the pot. If I lose, the lose payoff would be 3 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is 35% * 5 chips - 65% * 5 chips = -1.5 chips.\n- Plan 2: The expected chips gain is 0% * 0 chips - 100% * 3 chips = -3 chips.\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain than Plan 2. Therefore, I should choose Plan 1 and call."}}
{"message": "", "13_4": {"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 Jack). If he folds, I will win. The overall winning rate is 40%, losing rate is 60%, and draw rate is 0%.\n- If GoodGuy holds a Queen, he is likely to call (50%) or fold (50%). If he calls, it will be a draw (as the public card is a Queen). If he folds, I will win. The overall winning rate is 50%, losing rate is 0%, and draw rate is 50%.\n- If GoodGuy holds a Jack, he is likely to fold (80%) or call (20%). If he folds, I will win. If he calls, it will be a draw (as we both hold Jacks). The overall winning rate is 80%, losing rate is 0%, and draw rate is 20%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. The overall winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King, he is likely to raise (80%) or check (20%). If he raises, I will lose (as King is higher than Jack). If he checks, it will be a draw (as the public card is a Queen). The overall winning rate is 0%, losing rate is 80%, and draw rate is 20%.\n- If GoodGuy holds a Queen, he is likely to raise (70%) or check (30%). If he raises, it will be a draw (as the public card is a Queen). If he checks, it will be a draw. The overall winning rate is 0%, losing rate is 0%, and draw rate is 100%.\n- If GoodGuy holds a Jack, he is likely to raise (60%) or check (40%). If he raises, it will be a draw (as we both hold Jacks). If he checks, it will be a draw. The overall winning rate is 0%, losing rate is 0%, and draw rate is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 6 chips (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 = 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 * 6 = 0 chips\n\nPlan Selection:\n- Plan 1: -1.2 chips\n- Plan 2: -6 chips\n- Plan 3: 0 chips\n\nBased on the estimated expected chips gain, Plan 3 (Check) is the best strategy to use in this situation."}}
{"message": "", "15_1": {"plan": "Plan 1: Check\n- If GoodGuy holds a King (20% probability), he will likely raise (80% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I have a chance to win if I raise in the next round. \n- If GoodGuy holds a Queen (60% probability), he will likely call (60% probability). If the public card is a Queen, I will lose. If the public card is a King or Jack, I have a chance to win if I raise in the next round. \n- If GoodGuy holds a Jack (20% probability), he will likely fold (70% probability). If the public card is a Jack, I will win. If the public card is a King or Queen, I have a chance to win if I raise in the next round. \n\nPlan 2: Raise\n- If GoodGuy holds a King (20% probability), he will likely call (20% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I have a chance to win if I raise in the next round. \n- If GoodGuy holds a Queen (60% probability), he will likely fold (40% probability). If the public card is a Queen, I will lose. If the public card is a King or Jack, I have a chance to win if I raise in the next round. \n- If GoodGuy holds a Jack (20% probability), he will likely fold (70% probability). If the public card is a Jack, I will win. If the public card is a King or Queen, I have a chance to win if I raise in the next round. \n\nPlan 3: Fold\n- If I fold, I will lose the chips in the pot, but I will not lose any more chips in this round. \n\nWinning/Lose Payoffs for Each Plan:\n- Plan 1: If I win, the winning payoff would be 2 chips. If I lose, the losing payoff would be 2 chips.\n- Plan 2: If I win, the winning payoff would be 6 chips. If I lose, the losing payoff would be 6 chips.\n- Plan 3: If I fold, I will lose 2 chips.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.2 * 2 - 0.8 * 2 = -1.2 chips\n- Plan 2: Expected Chips Gain = 0.2 * 6 - 0.8 * 6 = -3.6 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- Based on the expected chips gain, Plan 1 (Check) is the best strategy to follow in this round."}}
{"message": "", "15_3": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (45% probability), he will likely raise (90% probability). If he raises, I will lose as a King is higher than my Jack. The losing rate for this scenario is 0.45*0.9 = 0.405.\n- If GoodGuy holds a Queen (55% probability), he will likely call (60% probability). If he calls, I will lose as a pair of Queens is higher than my single Jack. The losing rate for this scenario is 0.55*0.6 = 0.33.\n- The overall losing rate for Plan 1 is 0.405 + 0.33 = 0.735. The winning rate is 0 as I will lose in both scenarios. The draw rate is 0.265.\n\nPlan 2: Raise\n- If GoodGuy holds a King (45% probability), he will likely raise (90% probability). If he raises, I will lose as a King is higher than my Jack. The losing rate for this scenario is 0.45*0.9 = 0.405.\n- If GoodGuy holds a Queen (55% probability), he might fold (40% probability). If he folds, I will win. The winning rate for this scenario is 0.55*0.4 = 0.22.\n- The overall winning rate for Plan 2 is 0.22. The losing rate is 0.405. The draw rate is 0.375.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put into the pot. The losing rate is 1. The winning rate and draw rate are both 0.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips (half of the pot). If I lose, the losing payoff would be 4 chips.\n- Plan 2: If I win, the winning payoff would be 7 chips (half of the pot). If I lose, the losing payoff would be 7 chips.\n- Plan 3: If I lose, the losing payoff would be 2 chips (the chips I have already put into the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0*4 - 0.735*4 = -2.94 chips\n- Plan 2: Expected Chips Gain = 0.22*7 - 0.405*7 = -1.295 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- Plan 1: -2.94 chips\n- Plan 2: -1.295 chips\n- Plan 3: -2 chips\n\nThe rank of estimated expected chips gains for every plan is: Plan 2 > Plan 3 > Plan 1. Therefore, I should choose Plan 2: Raise."}}
{"message": "", "16_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a Jack, he will likely fold (70%) or call (30%). If he folds, I win the pot. If he calls, the outcome depends on the public card. If the public card is a Jack, I win. If the public card is a Queen or King, I lose. \n- If GoodGuy holds a Queen, he will likely call (60%) or raise (40%). If he calls, the outcome depends on the public card. If the public card is a Jack or Queen, I lose. If the public card is a King, I win. If he raises, I can choose to fold, call, or raise in the next round.\n- If GoodGuy holds a King, he will likely raise (80%) or call (20%). If he raises, I can choose to fold, call, or raise in the next round. If he calls, the outcome depends on the public card. If the public card is a Jack or King, I lose. If the public card is a Queen, I win.\n\nPlan 2: Raise\n- If GoodGuy holds a Jack, he will likely fold (70%) or call (30%). If he folds, I win the pot. If he calls, the outcome depends on the public card. If the public card is a Jack, I win. If the public card is a Queen or King, I lose. \n- If GoodGuy holds a Queen, he will likely call (60%) or raise (40%). If he calls, the outcome depends on the public card. If the public card is a Jack or Queen, I lose. If the public card is a King, I win. If he raises, I can choose to fold, call, or raise in the next round.\n- If GoodGuy holds a King, he will likely raise (80%) or call (20%). If he raises, I can choose to fold, call, or raise in the next round. If he calls, the outcome depends on the public card. If the public card is a Jack or King, I lose. If the public card is a Queen, I win.\n\nPlan 3: Fold\n- If I fold, I lose the pot regardless of GoodGuy's card.\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: Expected Chips Gain = 0.3 * 1.5 - 0.7 * 1.5 = -0.6\n- Plan 2: Expected Chips Gain = 0.3 * 2.5 - 0.7 * 2.5 = -1\n- Plan 3: Expected Chips Gain = -1\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I will choose Plan 1: Call."}}
{"message": "", "16_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (70% probability), he will likely raise (80%) or call (20%). If he raises, I will lose as King is higher than Jack. If he calls, the outcome will depend on the public card in the next round. If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. So, the overall winning rate for this plan is 0.7 * 0.2 * 0.25 = 0.035 (3.5%), and the overall losing rate is 0.7 * (0.8 + 0.2 * 0.75) = 0.665 (66.5%). The draw rate is 0.\n- If GoodGuy holds a Queen (20% probability), he will likely call (60%) or raise (40%). If he calls, the outcome will depend on the public card in the next round. If the public card is a King, I will win. If the public card is a Queen or Jack, I will lose. So, the overall winning rate for this plan is 0.2 * 0.6 * 0.5 = 0.06 (6%), and the overall losing rate is 0.2 * (0.4 + 0.6 * 0.5) = 0.14 (14%). The draw rate is 0.\n- If GoodGuy holds a Jack (10% probability), he will likely fold (70%) or call (30%). If he folds, I will win. If he calls, the outcome will depend on the public card in the next round. If the public card is a King or Queen, I will win. If the public card is a Jack, it will be a draw. So, the overall winning rate for this plan is 0.1 * (0.7 + 0.3 * 0.75) = 0.0925 (9.25%), and the overall losing rate is 0. The draw rate is 0.1 * 0.3 * 0.25 = 0.0075 (0.75%).\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card. So, the overall winning rate for this plan is 0, and the overall losing rate is 1 (100%). The draw rate is 0.\n\nPlan 3: Check\n- If GoodGuy holds a King (70% probability), he will likely raise (90%) or call (10%). If he raises, I will lose as King is higher than Jack. If he calls, the outcome will depend on the public card in the next round. If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. So, the overall winning rate for this plan is 0.7 * 0.1 * 0.25 = 0.0175 (1.75%), and the overall losing rate is 0.7 * (0.9 + 0.1 * 0.75) = 0.6825 (68.25%). The draw rate is 0.\n- If GoodGuy holds a Queen (20% probability), he will likely raise (40%) or call (60%). If he raises, I will lose as Queen is higher than Jack. If he calls, the outcome will depend on the public card in the next round. If the public card is a King, I will win. If the public card is a Queen or Jack, I will lose. So, the overall winning rate for this plan is 0.2 * 0.6 * 0.5 = 0.06 (6%), and the overall losing rate is 0.2 * (0.4 + 0.6 * 0.5) = 0.14 (14%). The draw rate is 0.\n- If GoodGuy holds a Jack (10% probability), he will likely fold (70%) or call (30%). If he folds, I will win. If he calls, the outcome will depend on the public card in the next round. If the public card is a King or Queen, I will win. If the public card is a Jack, it will be a draw. So, the overall winning rate for this plan is 0.1 * (0.7 + 0.3 * 0.75) = 0.0925 (9.25%), and the overall losing rate is 0. The draw rate is 0.1 * 0.3 * 0.25 = 0.0075 (0.75%).\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 4 chips (half of the pot).\n- Plan 2: If I fold, I will lose 2 chips (my initial bet).\n- Plan 3: If I win, the winning payoff would be 4 chips (half of the pot). If I lose, the lose payoff would be 2 chips (my initial bet).\n\nThe estimated expected chips gain for each plan:\n- Plan 1: 0.035 * 6 - 0.665 * 4 = -2.39 chips\n- Plan 2: -2 chips\n- Plan 3: 0.0175 * 4 - 0.6825 * 2 = -1.25 chips\n\nPlan Selection:\n- Plan 1: -2.39 chips\n- Plan 2: -2 chips\n- Plan 3: -1.25 chips\n\nSo, the best plan is Plan 3 (Check), followed by Plan 2 (Fold), and the worst plan is Plan 1 (Raise)."}}
{"message": "", "17_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Jack, he will likely fold (70% probability) or call (30% probability). If he folds, I win the pot. If he calls, my winning rate is 50% (if the public card is a Queen or King), my losing rate is 50% (if the public card is a Jack), and my draw rate is 0%. \n- If GoodGuy holds a Queen, he will likely call (60% probability) or raise (40% probability). If he calls or raises, my winning rate is 50% (if the public card is a Queen), my losing rate is 50% (if the public card is a King), and my draw rate is 0% (if the public card is a Jack).\n- If GoodGuy holds a King, he will likely raise (80% probability) or call (20% probability). If he raises or calls, my winning rate is 0% (if the public card is a King), my losing rate is 100%, and my draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I lose the pot regardless of GoodGuy's card. My winning rate is 0%, my losing rate is 100%, and my draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a Jack, he will likely check (70% probability) or raise (30% probability). If he checks, my winning rate is 50% (if the public card is a Queen or King), my losing rate is 50% (if the public card is a Jack), and my draw rate is 0%. If he raises, I can choose to call or fold.\n- If GoodGuy holds a Queen, he will likely raise (60% probability) or check (40% probability). If he raises, I can choose to call or fold. If he checks, my winning rate is 50% (if the public card is a Queen), my losing rate is 50% (if the public card is a King), and my draw rate is 0%.\n- If GoodGuy holds a King, he will likely raise (90% probability) or check (10% probability). If he raises, I can choose to fold. If he checks, my winning rate is 0% (if the public card is a King), my losing rate is 100%, and my 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 the pot of 2 chips.\n- Plan 3: If I win, the winning payoff would be 2 chips. If I lose, the losing payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.5 * 4 - 0.5 * 4 = 0\n- Plan 2: Expected Chips Gain = 0 - 1 * 2 = -2\n- Plan 3: Expected Chips Gain = 0.5 * 2 - 0.5 * 2 = 0\n\nPlan Selection:\n- Plan 1 and Plan 3 have the same expected chips gain, but Plan 1 has a higher potential payoff if I win. Therefore, I will choose Plan 1: Raise."}}
{"message": "", "18_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (35% probability), he will likely raise (70%) or call (30%). If he raises, I will lose as my Jack is lower than his King. If he calls, the outcome 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 (35% probability), he will likely call (60%) or raise (40%). If he raises, I will lose as my Jack is lower than his Queen. If he calls, the outcome 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 Jack (30% probability), he will likely fold (60%) or call (40%). If he folds, I will win. If he calls, the outcome 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: Raise\n- If GoodGuy holds a King (35% probability), he will likely raise (70%) or call (30%). If he raises, I will lose as my Jack is lower than his King. If he calls, the outcome 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 (35% probability), he will likely call (60%) or raise (40%). If he raises, I will lose as my Jack is lower than his Queen. If he calls, the outcome 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 Jack (30% probability), he will likely fold (60%) or call (40%). If he folds, I will win. If he calls, the outcome 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 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 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 the 1 chip I have already put in the pot. \n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.35*(0.7*(-1.5) + 0.3*(1.5)) + 0.35*(0.6*(-1.5) + 0.4*(1.5)) + 0.3*(0.6*(1.5) + 0.4*(-1.5)) = -0.45 chips\n- Plan 2: Expected Chips Gain = 0.35*(0.7*(-3.5) + 0.3*(3.5)) + 0.35*(0.6*(-3.5) + 0.4*(3.5)) + 0.3*(0.6*(3.5) + 0.4*(-3.5)) = -1.05 chips\n- Plan 3: Expected Chips Gain = -1 chip\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain (-0.45 chips), followed by Plan 3 (-1 chip), and Plan 2 (-1.05 chips). Therefore, I should choose Plan 1: Call."}}
{"message": "", "18_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Jack (60% probability), he will likely fold (70%) or call (30%). If he folds, I win the pot. If he calls, I lose unless the public card is a Jack. The winning rate is 70%, the losing rate is 30% * (1 - 1/3) = 20%, and the draw rate is 30% * 1/3 = 10%.\n- If GoodGuy holds a Queen (40% probability), he will likely call (70%) or raise (30%). If he calls, I lose unless the public card is a Jack. If he raises, I lose unless the public card is a Jack. The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I lose the pot 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 Jack (60% probability), he will likely call (80%) or raise (20%). If he calls, I lose unless the public card is a Jack. If he raises, I lose unless the public card is a Jack. The winning rate is 20% * 1/3 = 6.67%, the losing rate is 80% + 20% * (1 - 1/3) = 93.33%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (40% probability), he will likely raise (60%) or call (40%). If he raises, I lose unless the public card is a Jack. If he calls, I lose unless the public card is a 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 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: Expected gain = 0.7 * 4 - 0.2 * 4 = 2 chips\n- Plan 2: Expected gain = -2 chips\n- Plan 3: Expected gain = 0.067 * 2 - 0.933 * 2 = -1.73 chips\n\nPlan Selection:\n- Plan 1: 2 chips\n- Plan 2: -2 chips\n- Plan 3: -1.73 chips\n\nBased on the expected chips gain, I should choose Plan 1 (Raise) as it has the highest expected gain."}}
{"message": "", "20_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (33.3% chance), he will likely raise (80% chance) or call (20% chance). If he raises, I will lose as we both have a King but he has more chips in the pot. If he calls, it will be a draw. So, the winning rate is 0%, losing rate is 26.6% (33.3% * 80%), and draw rate is 6.6% (33.3% * 20%).\n- If GoodGuy holds a Queen (33.3% chance), he will likely call (70% chance) or raise (30% chance). In either case, I will win as I have a King. So, the winning rate is 33.3%, losing rate is 0%, and draw rate is 0%.\n- If GoodGuy holds a Jack (33.3% chance), he will likely call (60% chance) or raise (40% chance). In either case, I will win as I have a King. So, the winning rate is 33.3%, losing rate is 0%, and draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (33.3% chance), he will likely raise (70% chance) or call (30% chance). If he raises, it will be a draw as we both have a King. If he calls, I will win as I have more chips in the pot. So, the winning rate is 10% (33.3% * 30%), losing rate is 0%, and draw rate is 23.3% (33.3% * 70%).\n- If GoodGuy holds a Queen (33.3% chance), he will likely call (60% chance) or fold (40% chance). In either case, I will win as I have a King. So, the winning rate is 33.3%, losing rate is 0%, and draw rate is 0%.\n- If GoodGuy holds a Jack (33.3% chance), he will likely call (30% chance) or fold (70% chance). In either case, I will win as I have a King. So, the winning rate is 33.3%, losing rate is 0%, and draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. So, the winning rate is 0%, 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 (half of the pot). If I lose, the losing payoff would be 1 chip (my current 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 current bet).\n- Plan 3: If I fold, I will lose 1 chip (my current bet).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 66.6% * 3 - 26.6% * 1 = 1.4 chips\n- Plan 2: Expected Chips Gain = 76.6% * 5 - 0% * 2 = 3.83 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": "", "20_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (30% chance), he will likely raise (40% chance) or call (60% chance). If he raises, I will lose (0% chance of winning, 100% chance of losing, 0% chance of draw). If he calls, I will win (100% chance of winning, 0% chance of losing, 0% chance of draw).\n- If GoodGuy holds a Queen (60% chance), he will likely call (70% chance) or fold (30% chance). If he calls or folds, I will win (100% chance of winning, 0% chance of losing, 0% chance of draw).\n- If GoodGuy holds a Jack (10% chance), he will likely raise (70% chance) or call (30% chance). If he raises, I will lose (0% chance of winning, 100% chance of losing, 0% chance of draw). If he calls, I will lose (0% chance of winning, 100% chance of losing, 0% chance of draw).\n- Overall, the winning rate for Plan 1 is 63%, the losing rate is 37%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what GoodGuy does. 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 (30% chance), he will likely raise (40% chance) or call (60% chance). If he raises, I will lose (0% chance of winning, 100% chance of losing, 0% chance of draw). If he calls, I will win (100% chance of winning, 0% chance of losing, 0% chance of draw).\n- If GoodGuy holds a Queen (60% chance), he will likely call (70% chance) or fold (30% chance). If he calls or folds, I will win (100% chance of winning, 0% chance of losing, 0% chance of draw).\n- If GoodGuy holds a Jack (10% chance), he will likely raise (70% chance) or call (30% chance). If he raises, I will lose (0% chance of winning, 100% chance of losing, 0% chance of draw). If he calls, I will lose (0% chance of winning, 100% chance of losing, 0% chance of draw).\n- Overall, the winning rate for Plan 3 is 63%, the losing rate is 37%, 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 lose, the losing payoff would be 4 chips.\n- Plan 3: If I win, the winning payoff would be 4 chips. If I lose, the losing payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.63 * 4 - 0.37 * 4 = 1.04 chips\n- Plan 2: Expected Chips Gain = 0 * 4 - 1 * 4 = -4 chips\n- Plan 3: Expected Chips Gain = 0.63 * 4 - 0.37 * 4 = 1.04 chips\n\nPlan Selection:\n- Plan 1: 1.04 chips\n- Plan 2: -4 chips\n- Plan 3: 1.04 chips\n\nBased on the estimated expected chips gains, Plan 1 and Plan 3 are the best strategies to follow. However, considering the strategy improvement, I should choose Plan 1 (raise) to exploit GoodGuy's game pattern."}}
{"message": "", "21_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he will likely raise (70%) or call (30%). If he raises, I will lose as King is higher than Queen. If he calls, the outcome will depend on the public card. If the public card is a Queen, I will win. If the public card is a King or Jack, I will lose. \n- If GoodGuy holds a Queen (30% probability), he will likely call (60%) or fold (40%). If he calls, the outcome will depend on the public card. If the public card is a Queen, it will be a draw. If the public card is a King or Jack, I will lose. If he folds, I will win.\n- If GoodGuy holds a Jack (30% probability), he will likely fold (70%) or call (30%). If he folds, I will win. If he calls, the outcome will depend on the public card. If the public card is a Queen, I will win. If the public card is a King or Jack, I will lose. \n\nPlan 2: Raise\n- If GoodGuy holds a King (70% probability), he will likely raise (70%) or call (30%). If he raises, I will lose as King is higher than Queen. If he calls, the outcome will depend on the public card. If the public card is a Queen, I will win. If the public card is a King or Jack, I will lose. \n- If GoodGuy holds a Queen (30% probability), he will likely fold (60%) or call (40%). If he folds, I will win. If he calls, the outcome will depend on the public card. If the public card is a Queen, it will be a draw. If the public card is a King or Jack, I will lose. \n- If GoodGuy holds a Jack (30% probability), he will likely fold (70%) or call (30%). If he folds, I will win. If he calls, the outcome will depend on the public card. If the public card is a Queen, I will win. If the public card is a King or Jack, I will lose. \n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips (half of the pot). If I lose, the lose payoff would be 1 chip (half of the pot).\n- Plan 2: If I win, the winning payoff would be 5 chips (half of the pot). If I lose, the lose payoff would be 3 chips (half of the pot).\n- Plan 3: If I fold, the lose payoff would be 1 chip (half of the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.3 * 3 - 0.7 * 1 = 0.2 chips\n- Plan 2: Expected Chips Gain = 0.3 * 5 - 0.7 * 3 = -0.1 chips\n- Plan 3: Expected Chips Gain = -1 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I will choose Plan 1: Call."}}
{"message": "", "21_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (probability 33%): \n  - He will raise (probability 80%). I will lose as his King matches the public card. \n  - He will call (probability 20%). I will lose as his King matches the public card. \n  - Overall, I will lose (probability 33%).\n- If GoodGuy holds a Queen (probability 33%): \n  - He will fold (probability 60%). I will win as he folds. \n  - He will call (probability 40%). I will win as my Queen is higher than his Queen. \n  - Overall, I will win (probability 33%).\n- If GoodGuy holds a Jack (probability 33%): \n  - He will fold (probability 80%). I will win as he folds. \n  - He will call (probability 20%). I will win as my Queen is higher than his Jack. \n  - Overall, I will win (probability 33%).\n\nPlan 2: Fold\n- If GoodGuy holds a King (probability 33%): \n  - I will lose as I fold. \n- If GoodGuy holds a Queen (probability 33%): \n  - I will lose as I fold. \n- If GoodGuy holds a Jack (probability 33%): \n  - I will lose as I fold. \n\nPlan 3: Check\n- If GoodGuy holds a King (probability 33%): \n  - He will raise (probability 80%). I will lose as his King matches the public card. \n  - He will call (probability 20%). I will lose as his King matches the public card. \n  - Overall, I will lose (probability 33%).\n- If GoodGuy holds a Queen (probability 33%): \n  - He will fold (probability 60%). I will win as he folds. \n  - He will call (probability 40%). I will win as my Queen is higher than his Queen. \n  - Overall, I will win (probability 33%).\n- If GoodGuy holds a Jack (probability 33%): \n  - He will fold (probability 80%). I will win as he folds. \n  - He will call (probability 20%). I will win as my Queen is higher than his Jack. \n  - Overall, I will win (probability 33%).\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 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: (33% * 3 chips) - (33% * 2 chips) = 0.33 chips\n- Plan 2: (0% * 0 chips) - (100% * 2 chips) = -2 chips\n- Plan 3: (66% * 2 chips) - (33% * 2 chips) = 0.66 chips\n\nPlan Selection:\n- Plan 1: 0.33 chips\n- Plan 2: -2 chips\n- Plan 3: 0.66 chips\n\nThe rank of estimated expected chips gains for every plan is: Plan 3 > Plan 1 > Plan 2. Therefore, I should choose Plan 3: Check."}}
{"message": "", "23_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (40% chance), he will likely raise (70%) or call (30%). If he raises, I will lose unless the public card is a Queen. If he calls, I will win if the public card is a Queen, lose if it's a King, and draw if it's a Jack. Overall, my winning rate is 12%, losing rate is 28%, and drawing rate is 0%.\n- If GoodGuy holds a Queen (40% chance), he will likely call (60%) or raise (40%). If he raises, I will lose unless the public card is a Queen. If he calls, I will win if the public card is a Queen, lose if it's a King, and draw if it's a Jack. Overall, my winning rate is 24%, losing rate is 16%, and drawing rate is 0%.\n- If GoodGuy holds a Jack (20% chance), he will likely call (50%) or fold (50%). If he calls, I will win if the public card is a Queen or King, and lose if it's a Jack. If he folds, I will win. Overall, my winning rate is 20%, losing rate is 0%, and drawing rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (40% chance), he will likely raise (70%) or call (30%). If he raises, I will lose unless the public card is a Queen. If he calls, I will win if the public card is a Queen, lose if it's a King, and draw if it's a Jack. Overall, my winning rate is 12%, losing rate is 28%, and drawing rate is 0%.\n- If GoodGuy holds a Queen (40% chance), he will likely call (60%) or raise (40%). If he raises, I will lose unless the public card is a Queen. If he calls, I will win if the public card is a Queen, lose if it's a King, and draw if it's a Jack. Overall, my winning rate is 24%, losing rate is 16%, and drawing rate is 0%.\n- If GoodGuy holds a Jack (20% chance), he will likely fold (70%) or call (30%). If he folds, I will win. If he calls, I will win if the public card is a Queen or King, and lose if it's a Jack. Overall, my winning rate is 20%, losing rate is 0%, and drawing rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose 1 chip regardless of GoodGuy's card or action. My winning rate is 0%, losing rate is 100%, and drawing rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips. If I lose, the losing payoff would be 1 chip.\n- Plan 2: If I win, the winning payoff would be 5 chips. If I lose, the losing payoff would be 3 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 = 0.56 chips\n- Plan 2: Expected Chips Gain = 0.8 chips\n- Plan 3: Expected Chips Gain = -1 chip\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I will choose this plan."}}
{"message": "", "23_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (probability 1/3), he will likely raise (80%) or call (20%). If he raises, I will lose (probability 1) as his King pairs with the public card. If he calls, I will also lose (probability 1) as his King is higher than my Queen. Overall, the winning rate is 0, the losing rate is 1, and the draw rate is 0.\n- If GoodGuy holds a Queen (probability 1/3), he will likely check (50%) or call (50%). Regardless of his action, it will be a draw (probability 1) as we both hold a Queen. Overall, the winning rate is 0, the losing rate is 0, and the draw rate is 1.\n- If GoodGuy holds a Jack (probability 1/3), he will likely fold (70%) or check (30%). If he folds, I will win (probability 1) as he forfeits the game. If he checks, I will also win (probability 1) as my Queen is higher than his Jack. Overall, the winning rate is 1, 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. The winning rate is 0, the losing rate is 1, and the draw rate is 0.\n\nPlan 3: Check\n- This plan has the same outcomes as Plan 1, as GoodGuy's actions and the game outcomes do not depend on whether I check or raise.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 (half of the pot). If I lose, the losing payoff would be 4 (half of the pot).\n- Plan 2: If I fold, I will lose 4 chips.\n- Plan 3: If I win, the winning payoff would be 4 (half of the pot). If I lose, the losing payoff would be 4 (half of the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = winning rate * Winning Payoff - losing rate * Losing Payoff = (1/3 * 4) - (1/3 * 4) = 0\n- Plan 2: Expected Chips Gain = -4 (as I will lose 4 chips if I fold)\n- Plan 3: Expected Chips Gain = (1/3 * 4) - (1/3 * 4) = 0\n\nPlan Selection:\n- Plan 1 and Plan 3 have the same expected chips gain of 0, which is higher than Plan 2's expected chips gain of -4. Therefore, I should either raise (Plan 1) or check (Plan 3). Considering the strategy improvement, I should choose Plan 1 (raise) to be more aggressive when I have a Queen, as GoodGuy likely expects me to call."}}
{"message": "", "23_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (80% probability), he will likely raise (80% probability). In this case, I will lose as his pair of Kings beats my single Queen. The overall losing rate for this card is 64% (0.8*0.8).\n- If GoodGuy holds a Queen (20% probability), he will likely check (50% probability) or call (50% probability). In this case, it will be a draw as we both have a single Queen. The overall draw rate for this card is 20% (0.2*1).\n\nPlan 2: Fold\n- If GoodGuy holds a King (80% probability), he will likely raise (80% probability). In this case, I will lose as I forfeit the game. The overall losing rate for this card is 64% (0.8*0.8).\n- If GoodGuy holds a Queen (20% probability), he will likely check (50% probability) or call (50% probability). In this case, I will lose as I forfeit the game. The overall losing rate for this card is 20% (0.2*1).\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 10 chips (half of the pot). If I lose, the losing payoff would be 8 chips (the number of chips I have put in the pot).\n- Plan 2: If I win, the winning payoff would be 0 chips (as I forfeit the game). If I lose, the losing payoff would be 8 chips (the number of chips I have put in the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is 0 * winning rate - 8 * losing rate = -8 * 0.64 = -5.12 chips.\n- Plan 2: The expected chips gain is 0 * winning rate - 8 * losing rate = -8 * 0.84 = -6.72 chips.\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain (-5.12 chips) than Plan 2 (-6.72 chips). Therefore, I should choose Plan 1: Call."}}
{"message": "", "24_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (41.18% probability), he will likely raise (70%) or call (30%). If he raises, I will lose as his King is higher than my Queen. If he calls, the outcome will depend on the public card. If the public card is a Queen, I will win. If the public card is a King or Jack, I will lose. Therefore, the winning rate for this plan is 30% * 33.33% = 10%, the losing rate is 70% + 30% * 66.67% = 90%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (23.53% probability), he will likely raise (40%) or call (60%). If he raises or calls, the outcome will depend on the public card. If the public card is a Queen, it will be a draw. If the public card is a King or Jack, I will win. Therefore, the winning rate for this plan is 100% - 33.33% = 66.67%, the losing rate is 0%, and the draw rate is 33.33%.\n- If GoodGuy holds a Jack (35.29% probability), he will likely call (50%) or fold (50%). If he calls or folds, I will win unless the public card is a Jack. Therefore, the winning rate for this plan is 100% - 33.33% = 66.67%, the losing rate is 33.33%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (41.18% probability), he will likely raise (70%) or call (30%). If he raises or calls, I will lose unless the public card is a Queen. Therefore, the winning rate for this plan is 33.33%, the losing rate is 66.67%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (23.53% probability), he will likely raise (40%) or call (60%). If he raises or calls, the outcome will depend on the public card. If the public card is a Queen, it will be a draw. If the public card is a King or Jack, I will win. Therefore, the winning rate for this plan is 66.67%, the losing rate is 0%, and the draw rate is 33.33%.\n- If GoodGuy holds a Jack (35.29% probability), he will likely fold (50%) or call (50%). If he folds, I will win. If he calls, I will win unless the public card is a Jack. Therefore, the winning rate for this plan is 100% - 33.33% = 66.67%, the losing rate is 33.33%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of GoodGuy's card. 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 I win, the winning payoff would be 6 chips. If I lose, the lose payoff would be 2 chips.\n- Plan 2: If I win, the winning payoff would be 8 chips. If I lose, the lose payoff would be 4 chips.\n- Plan 3: If I lose, the lose payoff would be 2 chips.\n\nThe expected chips gain for each plan:\n- Plan 1: 10% * 6 - 90% * 2 = -1.2 chips\n- Plan 2: 66.67% * 8 - 33.33% * 4 = 3.33 chips\n- Plan 3: 0% * 0 - 100% * 2 = -2 chips\n\nPlan Selection:\n- Plan 1: -1.2 chips\n- Plan 2: 3.33 chips\n- Plan 3: -2 chips\n\nTherefore, I should choose Plan 2 (Raise) as it has the highest expected chips gain."}}
{"message": "", "24_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (33% chance), he will likely call (60% chance) or check (40% chance). If he calls, I will win (100% chance) as my Queen matches the public card. If he checks, I will also win (100% chance). So, the overall winning rate for this plan if GoodGuy holds a King is 100%.\n- If GoodGuy holds a Queen (33% chance), it will be a draw (100% chance) as we both have a Queen.\n- If GoodGuy holds a Jack (33% chance), he will likely check (70% chance) or fold (30% chance). If he checks, I will win (100% chance). If he folds, I will also win (100% chance). So, the overall winning rate for this plan if GoodGuy holds a Jack is 100%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. So, the overall losing rate for this plan is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (33% chance), he will likely call (60% chance) or check (40% chance). If he calls, I will win (100% chance) as my Queen matches the public card. If he checks, I will also win (100% chance). So, the overall winning rate for this plan if GoodGuy holds a King is 100%.\n- If GoodGuy holds a Queen (33% chance), it will be a draw (100% chance) as we both have a Queen.\n- If GoodGuy holds a Jack (33% chance), he will likely check (70% chance) or fold (30% chance). If he checks, I will win (100% chance). If he folds, I will also win (100% chance). So, the overall winning rate for this plan if GoodGuy holds a Jack is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the raise, chips in the pot will be 14. If win, the winning payoff would be 7. If lose, the lose payoff would be 7.\n- Plan 2: If fold, there will be no change in chips in the pot. The lose payoff would be 3 (the amount I have already put in the pot).\n- Plan 3: After the check, chips in the pot will remain 12. If win, the winning payoff would be 6. If lose, the lose payoff would be 6.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 100% * 7 - 0% * 7 = 7\n- Plan 2: Expected Chips Gain = 0% * 0 - 100% * 3 = -3\n- Plan 3: Expected Chips Gain = 100% * 6 - 0% * 6 = 6\n\nPlan Selection:\n- Plan 1: Raise (Expected Chips Gain = 7)\n- Plan 3: Check (Expected Chips Gain = 6)\n- Plan 2: Fold (Expected Chips Gain = -3)\n\nBased on the estimated expected chips gains, I should choose Plan 1: Raise."}}
{"message": "", "25_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (35% probability), he will likely raise (70% probability). If he raises, I will lose as King is higher than my Queen. The losing rate for this scenario is 0.35*0.7=0.245. If he calls (30% probability), it will be a draw as we both have the same amount of chips in the pot. The draw rate for this scenario is 0.35*0.3=0.105.\n- If GoodGuy holds a Queen (35% probability), he will likely call (60% probability). If he calls, it will be a draw as we both have the same card. The draw rate for this scenario is 0.35*0.6=0.21. If he raises (40% probability), I will lose as he will have more chips in the pot. The losing rate for this scenario is 0.35*0.4=0.14.\n- If GoodGuy holds a Jack (30% probability), he will likely fold (60% probability). If he folds, I will win as he forfeits the game. The winning rate for this scenario is 0.3*0.6=0.18. If he calls (40% probability), I will win as my Queen is higher than his Jack. The winning rate for this scenario is 0.3*0.4=0.12.\n- The overall winning rate for Plan 1 is 0.18+0.12=0.3, the overall losing rate is 0.245+0.14=0.385, and the overall draw rate is 0.105+0.21=0.315.\n\nPlan 2: Raise\n- If GoodGuy holds a King (35% probability), he will likely raise (70% probability). If he raises, I will lose as King is higher than my Queen. The losing rate for this scenario is 0.35*0.7=0.245. If he calls (30% probability), it will be a draw as we both have the same amount of chips in the pot. The draw rate for this scenario is 0.35*0.3=0.105.\n- If GoodGuy holds a Queen (35% probability), he will likely raise (40% probability). If he raises, it will be a draw as we both have the same card and the same amount of chips in the pot. The draw rate for this scenario is 0.35*0.4=0.14. If he calls (60% probability), I will win as I will have more chips in the pot. The winning rate for this scenario is 0.35*0.6=0.21.\n- If GoodGuy holds a Jack (30% probability), he will likely fold (60% probability). If he folds, I will win as he forfeits the game. The winning rate for this scenario is 0.3*0.6=0.18. If he calls (40% probability), I will win as my Queen is higher than his Jack. The winning rate for this scenario is 0.3*0.4=0.12.\n- The overall winning rate for Plan 2 is 0.21+0.18+0.12=0.51, the overall losing rate is 0.245, and the overall draw rate is 0.105+0.14=0.245.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of GoodGuy's card. The overall losing rate for Plan 3 is 1.\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 lose, the losing payoff would be 1 chip (half of the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0.3*3 - 0.385*2 = -0.27 chips\n- Plan 2: 0.51*4 - 0.245*3 = 1.035 chips\n- Plan 3: -1*1 = -1 chips\n\nPlan Selection:\n- Plan 2 has the highest estimated expected chips gain, so I should choose Plan 2: Raise."}}
{"message": "", "25_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (probability 1/3), he will likely raise (80%) or call (20%). If he raises, I will lose (as King is higher than Queen). If he calls, I will win (as Queen is higher than public card Jack). Overall, the winning rate is 20%, the losing rate is 80%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (probability 1/3), it will be a draw regardless of his action. So, the winning rate is 0%, the losing rate is 0%, and the draw rate is 100%.\n- If GoodGuy holds a Jack (probability 1/3), he will likely fold (70%) or call (30%). If he folds, I will win. If he calls, I will win (as Queen is higher than Jack). Overall, 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 regardless of GoodGuy's card. 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 King (probability 1/3), he will likely raise (80%) or call (20%). If he raises, I will lose. If he calls, I will win. Overall, the winning rate is 20%, the losing rate is 80%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (probability 1/3), it will be a draw regardless of his action. So, the winning rate is 0%, the losing rate is 0%, and the draw rate is 100%.\n- If GoodGuy holds a Jack (probability 1/3), he will likely raise (30%) or call (70%). If he raises, I will lose. If he calls, I will 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 win, the winning payoff would be half of the pot (8 chips). If lose, the lose payoff would be half of the pot (8 chips).\n- Plan 2: If lose, the lose payoff would be half of the pot (4 chips).\n- Plan 3: If win, the winning payoff would be half of the pot (8 chips). If lose, the lose payoff would be half of the pot (8 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.6 * 8 - 0.4 * 8 = 1.6 chips\n- Plan 2: Expected Chips Gain = -4 chips\n- Plan 3: Expected Chips Gain = 0.45 * 8 - 0.35 * 8 = 0.8 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I will choose Plan 1: Raise."}}
{"message": "", "26_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he will likely raise (70%) or call (30%). If he raises, I will lose unless the public card is a Jack. If he calls, I will win if the public card is a Jack, and lose otherwise. The overall winning rate for this plan is 0.7*0.3*1/3 = 7%, the losing rate is 0.7*0.7 + 0.7*0.3*2/3 = 77%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (30% probability), he will likely check (70%) or call (30%). If he checks, I will win if the public card is a Jack, and lose otherwise. If he calls, I will win if the public card is a Jack, and lose otherwise. The overall winning rate for this plan is 0.3*1*1/3 = 10%, the losing rate is 0.3*1*2/3 = 20%, and the draw rate is 0%.\n- The overall winning rate for Plan 1 is 7% + 10% = 17%, the losing rate is 77% + 20% = 97%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (70% probability), he will likely raise (70%) or call (30%). If he raises, I will lose unless the public card is a Jack. If he calls, I will win if the public card is a Jack, and lose otherwise. The overall winning rate for this plan is 0.7*0.3*1/3 = 7%, the losing rate is 0.7*0.7 + 0.7*0.3*2/3 = 77%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (30% probability), he will likely check (70%) or call (30%). If he checks, I will win if the public card is a Jack, and lose otherwise. If he calls, I will win if the public card is a Jack, and lose otherwise. The overall winning rate for this plan is 0.3*1*1/3 = 10%, the losing rate is 0.3*1*2/3 = 20%, and the draw rate is 0%.\n- The overall winning rate for Plan 2 is 7% + 10% = 17%, the losing rate is 77% + 20% = 97%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of GoodGuy's cards. 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 6 chips. If I lose, the losing payoff would be 2 chips.\n- Plan 2: If I win, the winning payoff would be 8 chips. If I lose, the losing payoff would be 4 chips.\n- Plan 3: If I fold, I will lose 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is 17% * 6 - 97% * 2 = -1.38 chips.\n- Plan 2: The expected chips gain is 17% * 8 - 97% * 4 = -3.36 chips.\n- Plan 3: The expected chips gain is -2 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: Call."}}
{"message": "", "26_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (30% probability), he will likely call (60%) or check (40%). If he calls, I will likely lose (as a King beats a Jack), but if he checks, the game will continue to the next round. The overall winning rate for this plan is 0% (as I cannot beat a King with a Jack), the losing rate is 60% (probability of him holding a King * probability of him calling), and the draw rate is 40% (probability of him holding a King * probability of him checking).\n- If GoodGuy holds a Queen (40% probability), he will likely check (70%) or call (30%). If he checks, the game will continue to the next round. If he calls, I will likely lose (as a Queen beats a Jack). The overall winning rate for this plan is 0% (as I cannot beat a Queen with a Jack), the losing rate is 30% (probability of him holding a Queen * probability of him calling), and the draw rate is 70% (probability of him holding a Queen * probability of him checking).\n- If GoodGuy holds a Jack (30% probability), he will likely check (80%) or fold (20%). If he checks, the game will continue to the next round. If he folds, I will win. The overall winning rate for this plan is 20% (probability of him holding a Jack * probability of him folding), the losing rate is 0% (as a Jack cannot beat another Jack), and the draw rate is 80% (probability of him holding a Jack * probability of him checking).\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of what card GoodGuy holds. The overall winning rate for this plan is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King (30% probability), he will likely call (60%) or check (40%). If he calls, I will likely lose (as a King beats a Jack), but if he checks, the game will continue to the next round. The overall winning rate for this plan is 0% (as I cannot beat a King with a Jack), the losing rate is 60% (probability of him holding a King * probability of him calling), and the draw rate is 40% (probability of him holding a King * probability of him checking).\n- If GoodGuy holds a Queen (40% probability), he will likely check (70%) or call (30%). If he checks, the game will continue to the next round. If he calls, I will likely lose (as a Queen beats a Jack). The overall winning rate for this plan is 0% (as I cannot beat a Queen with a Jack), the losing rate is 30% (probability of him holding a Queen * probability of him calling), and the draw rate is 70% (probability of him holding a Queen * probability of him checking).\n- If GoodGuy holds a Jack (30% probability), he will likely check (80%) or fold (20%). If he checks, the game will continue to the next round. If he folds, I will win. The overall winning rate for this plan is 20% (probability of him holding a Jack * probability of him folding), the losing rate is 0% (as a Jack cannot beat another Jack), and the draw rate is 80% (probability of him holding a Jack * probability of him checking).\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips (half of the pot). If I lose, the losing payoff would be 4 chips.\n- Plan 2: If I fold, I will lose 4 chips (my current bet in the pot).\n- Plan 3: If I win, the winning payoff would be 4 chips (half of the pot). If I lose, the losing payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 20% * 4 - 90% * 4 = -2.8 chips\n- Plan 2: Expected Chips Gain = 0% * 4 - 100% * 4 = -4 chips\n- Plan 3: Expected Chips Gain = 20% * 4 - 90% * 4 = -2.8 chips\n\nPlan Selection:\nBased on the estimated expected chips gains, Plan 1 and Plan 3 are the best strategies, as they both have the highest expected chips gain (-2.8 chips). However, considering the strategy improvement, Plan 1 (Raise) might be a better choice as it could potentially confuse GoodGuy and make him make mistakes."}}
{"message": "", "26_5": {"plan": "Plan 1: 'Call'\n- If GoodGuy holds a Queen (80% probability), he will likely raise (80%). If I call, I will lose as his pair of Queens beats my single Jack. The losing rate is 64% (80% * 80%).\n- If GoodGuy holds a King (10% probability), he will likely call (60%) or check (40%). If I call, I will win as my Jack beats his King. The winning rate is 6% (10% * 60%).\n- If GoodGuy holds a Jack (10% probability), he will likely check (80%) or fold (20%). If I call, it will be a draw as we both have a single Jack. The draw rate is 8% (10% * 80%).\n\nPlan 2: 'Fold'\n- If GoodGuy holds a Queen (80% probability), he will likely raise (80%). If I fold, I will lose. The losing rate is 64% (80% * 80%).\n- If GoodGuy holds a King (10% probability), he will likely call (60%) or check (40%). If I fold, I will lose. The losing rate is 10% (10% * 100%).\n- If GoodGuy holds a Jack (10% probability), he will likely check (80%) or fold (20%). If I fold, I will lose. The losing rate is 10% (10% * 100%).\n\nPlan 1 Winning/Lose/Draw rates: Winning rate: 6%, Lose rate: 64%, Draw rate: 8%\nPlan 2 Winning/Lose/Draw rates: Winning rate: 0%, Lose rate: 84%, Draw rate: 0%\n\nPlan 1 Payoffs: \n- If win, the winning payoff would be half of the pot (20 chips) = 10 chips.\n- If lose, the lose payoff would be half of the pot (20 chips) = 10 chips.\n\nPlan 2 Payoffs: \n- If win, the winning payoff would be 0 chips (as I fold).\n- If lose, the lose payoff would be half of the pot (12 chips) = 6 chips.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: 6% * 10 chips - 64% * 10 chips = -5.4 chips\n- Plan 2: 0% * 0 chips - 84% * 6 chips = -5.04 chips\n\nPlan Selection: \n- Plan 1: -5.4 chips\n- Plan 2: -5.04 chips\n\nBased on the expected chips gain, Plan 2 ('Fold') is the better strategy as it results in a smaller loss of chips."}}
{"message": "", "29_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (50% probability), he will raise (100% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, it will be a draw. Overall, the winning rate is 0%, the losing rate is 50%, and the draw rate is 50%.\n- If GoodGuy holds a Queen (30% probability), he will raise (100% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. Overall, the winning rate is 30%, the losing rate is 30%, and the draw rate is 40%.\n- If GoodGuy holds a Jack (20% probability), he will call (30% probability) or fold (70% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. Overall, the winning rate is 20%, the losing rate is 20%, and the draw rate is 60%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (50% probability), he will call (100% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, it will be a draw. Overall, the winning rate is 0%, the losing rate is 50%, and the draw rate is 50%.\n- If GoodGuy holds a Queen (30% probability), he will call (60% probability) or raise (40% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. Overall, the winning rate is 30%, the losing rate is 30%, and the draw rate is 40%.\n- If GoodGuy holds a Jack (20% probability), he will fold (70% probability) or call (30% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. Overall, the winning rate is 20%, the losing rate is 20%, and the draw rate is 60%.\n\nPlan 3: Fold\n- If I fold, I will lose 1 chip 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. If I lose, the losing payoff would be 1 chip.\n- Plan 2: If I win, the winning payoff would be 7 chips. If I lose, the losing payoff would be 5 chips.\n- Plan 3: If I lose, the losing payoff would be 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0% * 3 - 50% * 1 = -0.5 chips\n- Plan 2: 30% * 7 - 50% * 5 = -1.1 chips\n- Plan 3: 0% * 0 - 100% * 1 = -1 chip\n\nPlan Selection:\nBased on the estimated expected chips gains, Plan 1 (Call) is the best strategy."}}
{"message": "", "29_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Jack (70% probability), he tends to fold (70% probability) when I raise. So, I would win the pot (49% overall probability). If he calls (30% probability), we would go to the second round and the result would depend on the public card (21% overall probability).\n- If GoodGuy holds a Queen (20% probability), he tends to call (60% probability) or raise (40% probability) when I raise. So, we would go to the second round and the result would depend on the public card (12% overall probability for call, 8% overall probability for raise).\n- If GoodGuy holds a King (10% probability), he tends to raise (100% probability) when I raise. So, we would go to the second round and the result would depend on the public card (10% overall probability).\n\nPlan 2: Fold\n- If I fold, I would lose the pot regardless of GoodGuy's card.\n\nPlan 3: Check\n- If GoodGuy holds a Jack (70% probability), he tends to call (30% probability) when I check. So, we would go to the second round and the result would depend on the public card (21% overall probability).\n- If GoodGuy holds a Queen (20% probability), he tends to raise (100% probability) when I check. So, we would go to the second round and the result would depend on the public card (20% overall probability).\n- If GoodGuy holds a King (10% probability), he tends to raise (100% probability) when I check. So, we would go to the second round and the result would depend on the public card (10% overall probability).\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 lose payoff would be half of the pot, so 2 chips.\n- Plan 2: If I fold, I would lose the pot, so the lose payoff would be 2 chips.\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 lose payoff would be half of the pot, so 2 chips.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected chips gain = winning rate * winning payoff - lose rate * lose payoff = 49% * 2 chips - 51% * 2 chips = -0.04 chips.\n- Plan 2: Expected chips gain = -2 chips (as I would lose the pot).\n- Plan 3: Expected chips gain = winning rate * winning payoff - lose rate * lose payoff = 21% * 2 chips - 79% * 2 chips = -1.16 chips.\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain (-0.04 chips), followed by Plan 3 (-1.16 chips) and Plan 2 (-2 chips). So, I should choose Plan 1: Raise."}}
{"message": "", "29_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a Jack (15% probability), he will likely fold (70% probability). I will win the pot, which is currently 16 chips. The expected gain is 0.15 * 0.7 * 16 = 1.68 chips.\n- If GoodGuy holds a Queen (42.5% probability), he will likely raise (100% probability). I will lose the pot, which will be 24 chips after my call. The expected loss is 0.425 * 24 = 10.2 chips.\n- If GoodGuy holds a King (42.5% probability), he will likely raise (100% probability). I will lose the pot, which will be 24 chips after my call. The expected loss is 0.425 * 24 = 10.2 chips.\n- Overall, the expected gain for Plan 1 is 1.68 - 10.2 - 10.2 = -18.72 chips.\n\nPlan 2: Fold\n- If GoodGuy holds a Jack (15% probability), he will likely fold (70% probability). I will lose the pot, which is currently 6 chips. The expected loss is 0.15 * 0.7 * 6 = 0.63 chips.\n- If GoodGuy holds a Queen (42.5% probability), he will likely raise (100% probability). I will lose the pot, which is currently 6 chips. The expected loss is 0.425 * 6 = 2.55 chips.\n- If GoodGuy holds a King (42.5% probability), he will likely raise (100% probability). I will lose the pot, which is currently 6 chips. The expected loss is 0.425 * 6 = 2.55 chips.\n- Overall, the expected loss for Plan 2 is 0.63 + 2.55 + 2.55 = 5.73 chips.\n\nPlan Selection:\n- Plan 1 (Call) has an expected gain of -18.72 chips.\n- Plan 2 (Fold) has an expected loss of 5.73 chips.\n- Therefore, Plan 2 (Fold) is the better strategy as it minimizes my expected loss."}}
{"message": "", "30_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he will likely raise (80% probability). If the public card is a King, it will be a draw. If the public card is a Queen or a Jack, I will win. Overall, the winning rate is 56%, the losing rate is 0%, and the draw rate is 14%.\n- If GoodGuy holds a Queen (30% probability), he will likely call (70% probability). If the public card is a Queen, I will lose. If the public card is a King or a Jack, I will win. Overall, the winning rate is 21%, the losing rate is 9%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (70% probability), he will likely raise (80% probability). If the public card is a King, it will be a draw. If the public card is a Queen or a Jack, I will win. Overall, the winning rate is 56%, the losing rate is 0%, and the draw rate is 14%.\n- If GoodGuy holds a Queen (30% probability), he will likely fold (40% probability). If the public card is a Queen, I will lose. If the public card is a King or a Jack, I will win. Overall, the winning rate is 18%, the losing rate is 12%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot. The losing rate is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the call 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 raise 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 fold action, chips in the pot: 3. If lose, the lose payoff would be 1.5.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.77 * 2 - 0.09 * 2 = 1.36\n- Plan 2: Expected Chips Gain = 0.74 * 3 - 0.12 * 3 = 1.86\n- Plan 3: Expected Chips Gain = -1.5\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so it should be selected. Plan 1 (Call) is the second best option, and Plan 3 (Fold) is the worst option."}}
{"message": "", "30_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (50% probability), he will likely raise (80% probability) or call (20% probability). If he raises, we will both have a King and the game will be a draw. If he calls, I will win because I have a King and the public card is a Jack. So, the winning rate is 20%, the losing rate is 0%, and the draw rate is 80%.\n- If GoodGuy holds a Queen (50% probability), he will likely call (70% probability) or fold (30% probability). If he calls or folds, I will win because I have a King and the public card is a Jack. So, 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 regardless of GoodGuy's card. 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 King (50% probability), he will likely raise (80% probability) or call (20% probability). If he raises, we will both have a King and the game will be a draw. If he calls, I will win because I have a King and the public card is a Jack. So, the winning rate is 20%, the losing rate is 0%, and the draw rate is 80%.\n- If GoodGuy holds a Queen (50% probability), he will likely call (70% probability) or fold (30% probability). If he calls or folds, I will win because I have a King and the public card is a Jack. So, the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips (half of the pot). If I lose, the lose payoff would be 4 chips.\n- Plan 2: If I fold, I will lose 4 chips.\n- Plan 3: If I win, the winning payoff would be 4 chips. If I lose, the lose payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.6 * 4 - 0 * 4 = 2.4 chips\n- Plan 2: Expected Chips Gain = 0 * 4 - 1 * 4 = -4 chips\n- Plan 3: Expected Chips Gain = 0.6 * 4 - 0 * 4 = 2.4 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 both have the highest expected chips gain of 2.4 chips, while Plan 2 has the lowest expected chips gain of -4 chips. Therefore, I should either raise (Plan 1) or check (Plan 3). Considering the strategy improvement, I should raise to exploit GoodGuy's game pattern."}}
{"message": "", "32_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (30% probability), he is likely to raise (70%) or call (30%). If he raises, I will win as I also hold a King. If he calls, I will also win as I hold a higher card. So, the winning rate for this plan is 100%.\n- If GoodGuy holds a Queen (60% probability), he is likely to call (60%) or fold (40%). If he calls, I will win as I hold a higher card. If he folds, I will also win as he forfeits the game. So, the winning rate for this plan is 100%.\n- If GoodGuy holds a Jack (10% probability), he is likely to fold (80%). If he folds, I will win as he forfeits the game. So, 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. So, the losing rate for this plan is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (30% probability), he is likely to raise (70%) or call (30%). If he raises, I will win as I also hold a King. If he calls, I will also win as I hold a higher card. So, the winning rate for this plan is 100%.\n- If GoodGuy holds a Queen (60% probability), he is likely to check (70%) or raise (30%). If he checks, I will win as I hold a higher card. If he raises, I will also win as I hold a higher card. So, the winning rate for this plan is 100%.\n- If GoodGuy holds a Jack (10% probability), he is likely to check (60%) or raise (40%). If he checks, I will win as I hold a higher card. If he raises, I will also win as I hold a higher card. So, the winning rate for this plan is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, Chips in the pot: 6. If win, the winning payoff would be 3. If lose, the lose payoff would be 3.\n- Plan 2: After the action, Chips in the pot: 2. If win, the winning payoff would be 1. If lose, the lose payoff would be 1.\n- Plan 3: After the action, Chips in the pot: 2. If win, the winning payoff would be 1. If lose, the lose payoff would be 1.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 1 * 3 - 0 * 3 = 3\n- Plan 2: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 0 * 1 - 1 * 1 = -1\n- Plan 3: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 1 * 1 - 0 * 1 = 1\n\nPlan Selection:\n- Plan 1: Raise (Expected Chips Gain = 3)\n- Plan 3: Check (Expected Chips Gain = 1)\n- Plan 2: Fold (Expected Chips Gain = -1)\n\nBased on the estimated expected chips gains, I should choose Plan 1: Raise."}}
{"message": "", "33_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King, he is likely to raise (70%) or call (30%) in the 1st round. If he raises, I will lose (70%). If he calls, I have a chance to win if the public card is a Jack (30%).\n- If GoodGuy holds a Queen, he is likely to call (60%) or fold (40%) in the 1st round. If he calls, I have a chance to win if the public card is a Jack (60%). If he folds, I will win (40%).\n- If GoodGuy holds a Jack, he is likely to fold (70%) or call (30%) in the 1st round. If he folds, I will win (70%). If he calls, it will be a draw (30%).\n- Overall, the winning rate for plan 1 is 0.7*0.4 + 0.6*0.6 + 0.7*0.7 = 1.23, the lose rate is 0.7*0.7 = 0.49, and the draw rate is 0.3*0.3 = 0.09.\n\nPlan 2: Raise\n- If GoodGuy holds a King, he is likely to raise (70%) or call (30%) in the 1st round. If he raises, I will lose (70%). If he calls, I have a chance to win if the public card is a Jack (30%).\n- If GoodGuy holds a Queen, he is likely to call (60%) or fold (40%) in the 1st round. If he calls, I have a chance to win if the public card is a Jack (60%). If he folds, I will win (40%).\n- If GoodGuy holds a Jack, he is likely to fold (70%) or call (30%) in the 1st round. If he folds, I will win (70%). If he calls, it will be a draw (30%).\n- Overall, the winning rate for plan 2 is 0.7*0.4 + 0.6*0.6 + 0.7*0.7 = 1.23, the lose rate is 0.7*0.7 = 0.49, and the draw rate is 0.3*0.3 = 0.09.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of GoodGuy's card. The lose rate is 1.\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.\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.\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: 1.23 * 1.5 - 0.49 * 1 = 1.345\n- Plan 2: 1.23 * 2.5 - 0.49 * 2 = 2.075\n- Plan 3: -1 * 0.5 = -0.5\n\nPlan Selection:\n- Plan 2 has the highest estimated expected chips gain, so I will choose Plan 2: Raise."}}
{"message": "", "33_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (50% probability), he is likely to call (60%) or fold (40%). If he calls, I will win (as I have a pair of Jacks). If he folds, I will also win (as he forfeits the game). Therefore, the winning rate for this plan is 100%.\n- If GoodGuy holds a Queen (40% probability), he is likely to call (50%) or fold (50%). If he calls, I will win. If he folds, I will also win. Therefore, the winning rate for this plan is 100%.\n- If GoodGuy holds a Jack (10% probability), he is likely to raise (60%) or call (40%). If he raises or calls, the game will be a draw (as we both have a pair of Jacks). Therefore, the draw rate for this plan is 100%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of GoodGuy's hand or actions. Therefore, the losing rate for this plan is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (50% probability), he is likely to call (60%) or fold (40%). If he calls, I will win. If he folds, I will also win. Therefore, the winning rate for this plan is 100%.\n- If GoodGuy holds a Queen (40% probability), he is likely to call (50%) or fold (50%). If he calls, I will win. If he folds, I will also win. Therefore, the winning rate for this plan is 100%.\n- If GoodGuy holds a Jack (10% probability), he is likely to raise (60%) or call (40%). If he raises or calls, the game will be a draw. Therefore, the draw rate for this plan is 100%.\n\nWinning/Lose Payoffs:\n- Plan 1: If I win, the pot will be 8 chips (4 from me, 4 from GoodGuy), so the winning payoff would be 4 chips. If I lose, the pot will be 4 chips (all from me), so the losing payoff would be 2 chips.\n- Plan 2: If I fold, I will lose 4 chips.\n- Plan 3: If I win, the pot will be 8 chips, so the winning payoff would be 4 chips. If I lose, the pot will be 4 chips, so the losing payoff would be 2 chips.\n\nExpected Chips Gain:\n- Plan 1: Expected gain = winning rate * winning payoff - losing rate * losing payoff = 1.0 * 4 - 0 * 2 = 4 chips.\n- Plan 2: Expected gain = 0 - 1.0 * 4 = -4 chips.\n- Plan 3: Expected gain = 1.0 * 4 - 0 * 2 = 4 chips.\n\nPlan Selection:\n- Plan 1 and Plan 3 both have the highest expected chips gain (4 chips), so I should choose either of these plans. However, Plan 1 (raise) is more aggressive and may pressure GoodGuy into folding, so I will choose Plan 1."}}
{"message": "", "34_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (33.3% chance), he is likely to raise (40%) or call (60%) in the next round. 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 GoodGuy holds a Jack) or drawing (if GoodGuy holds a Queen). \n- If GoodGuy holds a Queen (33.3% chance), he is likely to raise (40%) or call (60%) in the next round. If the public card is a Queen, it will be a draw. If the public card is a King or Jack, I have a 50% chance of winning (if GoodGuy holds a Jack) or losing (if GoodGuy holds a King).\n- If GoodGuy holds a Jack (33.3% chance), he is likely to call (50%) or fold (50%) in the next round. If the public card is a Jack, I will lose. If the public card is a King or Queen, I will win.\n\nPlan 2: Raise\n- If GoodGuy holds a King (33.3% chance), he is likely to raise (30%) or call (70%) in the next round. 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 GoodGuy holds a Jack) or drawing (if GoodGuy holds a Queen). \n- If GoodGuy holds a Queen (33.3% chance), he is likely to raise (40%) or call (60%) in the next round. If the public card is a Queen, it will be a draw. If the public card is a King or Jack, I have a 50% chance of winning (if GoodGuy holds a Jack) or losing (if GoodGuy holds a King).\n- If GoodGuy holds a Jack (33.3% chance), he is likely to fold (50%) or call (50%) in the next round. If the public card is a Jack, I will lose. If the public card is a King or Queen, I will win.\n\nPlan 3: Fold\n- If I fold, I will lose the round and lose any chips I have already put into the pot.\n\nWinning 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 4 chips (half of the pot). If I lose, the losing payoff would be 3 chips (my current bet).\n- Plan 3: If I fold, the losing payoff would be 1 chip (my current bet).\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected gain = (33.3% * 50% * 3) - (33.3% * 50% * 2) = 0.167 chips\n- Plan 2: Expected gain = (33.3% * 50% * 4) - (33.3% * 50% * 3) = 0.167 chips\n- Plan 3: Expected gain = -1 chip (as I will lose my current bet)\n\nPlan Selection:\nBased on the expected chips gain, Plan 1 and Plan 2 are equally good, while Plan 3 is the worst. However, considering the strategy improvement, I should bluff more often when holding a Jack, especially in the 1st round. Therefore, I will choose Plan 2: Raise."}}
{"message": "", "34_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King, he is likely to call (70%) or raise (30%). If he calls, I will lose as his King is higher than my Queen. If he raises, I will also lose. The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a Queen, he is likely to call (50%) or raise (50%). If he calls or raises, it will be a draw as we both hold Queens. The winning rate is 0%, the losing rate is 0%, and the draw rate is 100%.\n- If GoodGuy holds a Jack, he is likely to fold (70%) or call (30%). If he folds, I will win. If he calls, I will also win as my Queen is higher than his Jack. 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 pot 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, he is likely to call (70%) or raise (30%). If he calls, I will lose as his King is higher than my Queen. If he raises, I will also lose. The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a Queen, he is likely to call (50%) or raise (50%). If he calls or raises, it will be a draw as we both hold Queens. The winning rate is 0%, the losing rate is 0%, and the draw rate is 100%.\n- If GoodGuy holds a Jack, he is likely to fold (70%) or call (30%). If he folds, I will win. If he calls, I will also win as my Queen is higher than his Jack. The winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nWinning/Lose Payoffs for Each Plan:\n- Plan 1: If I win, the pot will be 12 chips, so the winning payoff would be 6 chips. If I lose, the pot will be 12 chips, so the losing payoff would be 6 chips.\n- Plan 2: If I fold, I will lose the pot of 8 chips, so the losing payoff would be 4 chips.\n- Plan 3: If I win, the pot will be 8 chips, so the winning payoff would be 4 chips. If I lose, the pot will be 8 chips, so the losing payoff would be 4 chips.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0% * 6 chips - 100% * 6 chips = -6 chips\n- Plan 2: Expected Chips Gain = 0% * 0 chips - 100% * 4 chips = -4 chips\n- Plan 3: Expected Chips Gain = 100% * 4 chips - 0% * 4 chips = 4 chips\n\nPlan Selection:\n- Plan 1: -6 chips\n- Plan 2: -4 chips\n- Plan 3: 4 chips\n\nBased on the expected chips gain, Plan 3 (Check) is the best strategy to use in this situation."}}
{"message": "", "34_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a King: \n  - He might raise (40%) or call (60%). If he raises, I will lose (as King is higher than Queen). If he calls, I will win (as Queen is higher than Jack). So, the winning rate is 60%, and the losing rate is 40%.\n- If GoodGuy holds a Queen: \n  - He might raise (50%) or call (50%). If he raises or calls, it will be a draw (as we both hold Queens). So, the draw rate is 100%.\n- If GoodGuy holds a Jack: \n  - He might fold (70%) or call (30%). If he folds, I will win. If he calls, I will lose (as Jack matches the public card). So, the winning rate is 70%, and the losing rate is 30%.\n\nPlan 2: Raise\n- If GoodGuy holds a King: \n  - He might raise (40%) or call (60%). If he raises or calls, I will lose (as King is higher than Queen). So, the losing rate is 100%.\n- If GoodGuy holds a Queen: \n  - He might raise (50%) or call (50%). If he raises or calls, it will be a draw (as we both hold Queens). So, the draw rate is 100%.\n- If GoodGuy holds a Jack: \n  - He might fold (70%) or call (30%). If he folds, I will win. If he calls, I will lose (as Jack matches the public card). So, the winning rate is 70%, and the losing rate is 30%.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of what card GoodGuy holds. So, the losing rate is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, chips in the pot: 16. If win, the winning payoff would be 8. If lose, the lose payoff would be 8.\n- Plan 2: After the action, chips in the pot: 20. If win, the winning payoff would be 10. If lose, the lose payoff would be 10.\n- Plan 3: After the action, chips in the pot: 12. If lose, the lose payoff would be 6.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.6 * 8 - 0.4 * 8 = 1.6\n- Plan 2: Expected Chips Gain = 0.7 * 10 - 0.3 * 10 = 4\n- Plan 3: Expected Chips Gain = -6\n\nPlan Selection:\n- Plan 2 > Plan 1 > Plan 3\n- Therefore, I should choose Plan 2: Raise."}}
{"message": "", "35_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (40% probability), he will likely call or raise (80% probability). If the public card is a King, we will draw. If the public card is a Queen or Jack, I will win. So, the winning rate is 80%, draw rate is 20%, and lose rate is 0%.\n- If GoodGuy holds a Queen (60% probability), he will likely call (50% probability) or raise (25% probability). If the public card is a King, I will win. If the public card is a Queen, we will draw. If the public card is a Jack, I will win. So, the winning rate is 75%, draw rate is 25%, and lose rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (40% probability), he will likely call or raise (80% probability). If the public card is a King, we will draw. If the public card is a Queen or Jack, I will win. So, the winning rate is 80%, draw rate is 20%, and lose rate is 0%.\n- If GoodGuy holds a Queen (60% probability), he will likely call (50% probability) or raise (25% probability). If the public card is a King, I will win. If the public card is a Queen, we will draw. If the public card is a Jack, I will win. So, the winning rate is 75%, draw rate is 25%, and lose rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the round and lose any chips I have already put in the pot. So, the 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 I win, the winning payoff would be 3 chips (half of the 6 chips in the pot). If I lose, the lose payoff would be 1 chip (the chip I have already put in the pot).\n- Plan 2: If I win, the winning payoff would be 5 chips (half of the 10 chips in the pot). If I lose, the lose payoff would be 5 chips (the 1 chip I have already put in the pot plus the 4 chips I put in to raise).\n- Plan 3: If I fold, I will lose 1 chip (the chip I have already put in the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.8 * 3 - 0 * 1 = 2.4 chips\n- Plan 2: Expected Chips Gain = 0.8 * 5 - 0 * 5 = 4 chips\n- Plan 3: Expected Chips Gain = 0 * 0 - 1 * 1 = -1 chip\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I will choose this plan."}}
{"message": "", "35_2": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (80% probability), he will likely call or raise (90% probability). If the public card is a King, it will be a draw. If the public card is a Queen or a Jack, I will win unless GoodGuy holds a card of the same rank as the public card. The overall winning rate for this plan is 0.8*0.9 = 0.72, the losing rate is 0.2*0.1 = 0.02, and the draw rate is 0.2*0.9 = 0.18.\n- If GoodGuy holds a Queen (15% probability), he will likely call (70% probability) or raise (20% probability). If the public card is a Queen, I will lose unless I hold a King. If the public card is a King or a Jack, I will win. The overall winning rate for this plan is 0.15*0.8 = 0.12, the losing rate is 0.15*0.2 = 0.03, and the draw rate is 0.15*0.7 = 0.105.\n- If GoodGuy holds a Jack (5% probability), he will likely fold (80% probability). If the public card is a Jack, I will lose unless I hold a King. If the public card is a King or a Queen, I will win. The overall winning rate for this plan is 0.05*0.2 = 0.01, the losing rate is 0.05*0.8 = 0.04, and the draw rate is 0.05*0.2 = 0.01.\n\nPlan 2: Fold\n- If I fold, I will lose the round regardless of what card GoodGuy holds or what the public card is. The overall winning rate for this plan 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: If I win, the winning payoff would be half of the pot, which is (4+6)/2 = 5 chips. If I lose, the losing payoff would be half of the pot, which is (4+6)/2 = 5 chips.\n- Plan 2: If I fold, I will lose the round and the losing payoff would be the chips I have put into the pot, which is 4 chips.\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 = 0.85*5 - 0.09*5 = 3.8 chips.\n- Plan 2: The expected chips gain is the winning rate * winning payoff - losing rate * losing payoff = 0*5 - 1*4 = -4 chips.\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": "", "35_4": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (60% probability), he will likely call (70% probability) or raise (20% probability), and fold (10% probability). If he calls or raises, I will win (probability = 60% * 90% = 54%). If he folds, it's a draw (probability = 60% * 10% = 6%).\n- If GoodGuy holds a Jack (40% probability), he will likely fold (80% probability) or call/raise (20% probability). If he folds, it's a draw (probability = 40% * 80% = 32%). If he calls or raises, I will win (probability = 40% * 20% = 8%).\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what GoodGuy holds. Therefore, the lose rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a Queen (60% probability), he will likely call (70% probability) or raise (20% probability), and fold (10% probability). If he calls or raises, I will win (probability = 60% * 90% = 54%). If he folds, it's a draw (probability = 60% * 10% = 6%).\n- If GoodGuy holds a Jack (40% probability), he will likely fold (80% probability) or call/raise (20% probability). If he folds, it's a draw (probability = 40% * 80% = 32%). If he calls or raises, I will win (probability = 40% * 20% = 8%).\n\nWinning/Lose Payoffs for Each Plan:\n- Plan 1: If I win, the pot will be 14 chips, so the winning payoff would be 7 chips. If I lose, the pot will be 14 chips, so the lose payoff would be 7 chips.\n- Plan 2: If I fold, I will lose 6 chips.\n- Plan 3: If I win, the pot will be 12 chips, so the winning payoff would be 6 chips. If I lose, the pot will be 12 chips, so the lose payoff would be 6 chips.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected gain = winning rate * winning payoff - lose rate * lose payoff = 54% * 7 - 0% * 7 = 3.78 chips\n- Plan 2: Expected gain = 0% * 0 - 100% * 6 = -6 chips\n- Plan 3: Expected gain = 54% * 6 - 0% * 6 = 3.24 chips\n\nPlan Selection:\n- Plan 1: 3.78 chips\n- Plan 2: -6 chips\n- Plan 3: 3.24 chips\n\nTherefore, I should choose Plan 1 (raise) as it has the highest expected chips gain."}}
{"message": "", "36_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (30% chance), he will likely raise (70% chance). If the public card is a King, I will win (70% * 30% = 21%). If the public card is not a King, I will lose (70% * 70% = 49%).\n- If GoodGuy holds a Queen (60% chance), he will likely check (50% chance). If the public card is a Queen, I will lose (50% * 60% = 30%). If the public card is not a Queen, I will win (50% * 40% = 20%).\n- If GoodGuy holds a Jack (10% chance), he will likely fold (60% chance). I will win (60% * 10% = 6%).\n\nPlan 1 overall Winning/Lose/Draw rates: Winning rate = 21% + 20% + 6% = 47%. Lose rate = 49% + 30% = 79%. Draw rate = 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (30% chance), he will likely call (30% chance). If the public card is a King, I will win (30% * 30% = 9%). If the public card is not a King, I will lose (70% * 30% = 21%).\n- If GoodGuy holds a Queen (60% chance), he will likely raise (40% chance). If the public card is a Queen, I will lose (40% * 60% = 24%). If the public card is not a Queen, I will win (60% * 40% = 24%).\n- If GoodGuy holds a Jack (10% chance), he will likely fold (60% chance). I will win (60% * 10% = 6%).\n\nPlan 2 overall Winning/Lose/Draw rates: Winning rate = 9% + 24% + 6% = 39%. Lose rate = 21% + 24% = 45%. Draw rate = 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 3 chips. If lose, the lose payoff would be 1 chip.\n- Plan 2: If win, the winning payoff would be 5 chips. If lose, the lose payoff would be 3 chips.\n- Plan 3: If I fold, I will lose 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 47% * 3 - 79% * 1 = 0.14 chips\n- Plan 2: Expected Chips Gain = 39% * 5 - 45% * 3 = 0.45 chips\n- Plan 3: Expected Chips Gain = -1 chip\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I should choose this plan."}}
{"message": "", "36_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (30% chance), he will likely raise (70% chance) or call (30% chance). If he raises, I will lose (0% chance), draw (0% chance), or win (100% chance). If he calls, I will lose (0% chance), draw (0% chance), or win (100% chance). Overall, my winning rate is 30%.\n- If GoodGuy holds a Queen (60% chance), he will likely check (50% chance) or raise (50% chance). If he checks, I will lose (0% chance), draw (0% chance), or win (100% chance). If he raises, I will lose (0% chance), draw (0% chance), or win (100% chance). Overall, my winning rate is 60%.\n- If GoodGuy holds a Jack (40% chance), he will likely fold (60% chance) or check (40% chance). If he folds, I will win (100% chance). If he checks, I will lose (0% chance), draw (0% chance), or win (100% chance). Overall, my winning rate is 40%.\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card. My losing rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (30% chance), he will likely raise (70% chance) or call (30% chance). If he raises, I will lose (0% chance), draw (0% chance), or win (100% chance). If he calls, I will lose (0% chance), draw (0% chance), or win (100% chance). Overall, my winning rate is 30%.\n- If GoodGuy holds a Queen (60% chance), he will likely check (50% chance) or raise (50% chance). If he checks, I will lose (0% chance), draw (0% chance), or win (100% chance). If he raises, I will lose (0% chance), draw (0% chance), or win (100% chance). Overall, my winning rate is 60%.\n- If GoodGuy holds a Jack (40% chance), he will likely fold (60% chance) or check (40% chance). If he folds, I will win (100% chance). If he checks, I will lose (0% chance), draw (0% chance), or win (100% chance). Overall, my winning rate is 40%.\n\nWinning/Lose Payoffs for Each Plan:\n- Plan 1: If I win, the winning payoff would be half of the pot (8 chips). If I lose, the losing payoff would be half of the pot (8 chips).\n- Plan 2: If I fold, I will lose the game and the losing payoff would be half of the pot (8 chips).\n- Plan 3: If I win, the winning payoff would be half of the pot (8 chips). If I lose, the losing payoff would be half of the pot (8 chips).\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected chips gain = winning rate * winning payoff - losing rate * losing payoff = (30% + 60% + 40%) * 8 - 0% * 8 = 10.4 chips\n- Plan 2: Expected chips gain = 0% * 8 - 100% * 8 = -8 chips\n- Plan 3: Expected chips gain = (30% + 60% + 40%) * 8 - 0% * 8 = 10.4 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 have the highest expected chips gain (10.4 chips), while Plan 2 has the lowest expected chips gain (-8 chips). Therefore, I should either raise (Plan 1) or check (Plan 3). Considering my strategy improvement, I should choose to raise (Plan 1) to put pressure on GoodGuy and potentially force him to make a mistake."}}
{"message": "", "37_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (20% chance), he will likely raise (70%) or call (30%). If he raises, we will have a draw as we both hold Kings. If he calls, I will win as I hold the higher card. So, the winning rate is 30%, draw rate is 70%, and lose rate is 0%.\n- If GoodGuy holds a Queen (40% chance), he will likely call (60%) or raise (40%). In either case, I will win as I hold the higher card. So, the winning rate is 100%, draw rate is 0%, and lose rate is 0%.\n- If GoodGuy holds a Jack (40% chance), he will likely call (50%) or fold (50%). If he calls, I will win as I hold the higher card. If he folds, I will also win as he forfeits the game. So, the winning rate is 100%, draw rate is 0%, and lose rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will automatically lose the game regardless of GoodGuy's card. So, the winning rate is 0%, draw rate is 0%, and lose rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (20% chance), he will likely raise (70%) or check (30%). If he raises, we will have a draw as we both hold Kings. If he checks, I will win as I hold the higher card. So, the winning rate is 30%, draw rate is 70%, and lose rate is 0%.\n- If GoodGuy holds a Queen (40% chance), he will likely check (60%) or raise (40%). In either case, I will win as I hold the higher card. So, the winning rate is 100%, draw rate is 0%, and lose rate is 0%.\n- If GoodGuy holds a Jack (40% chance), he will likely check (50%) or fold (50%). If he checks, I will win as I hold the higher card. If he folds, I will also win as he forfeits the game. So, the winning rate is 100%, draw rate is 0%, and lose 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 2 chips (half of the pot).\n- Plan 2: If I fold, I will lose 2 chips (my initial bet).\n- Plan 3: If I win, the winning payoff would be 2 chips (half of the pot). If I lose, the lose payoff would be 2 chips (my initial bet).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: (0.7 * 4) - (0 * 2) = 2.8 chips\n- Plan 2: 0 - (1 * 2) = -2 chips\n- Plan 3: (0.7 * 2) - (0 * 2) = 1.4 chips\n\nPlan Selection:\n- Plan 1: Raise (Expected gain: 2.8 chips)\n- Plan 3: Check (Expected gain: 1.4 chips)\n- Plan 2: Fold (Expected gain: -2 chips)\n\nBased on the expected chips gain, I should choose Plan 1: Raise."}}
{"message": "", "38_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a Jack (40% probability), he will likely fold (70% probability) or call (30% probability). If he folds, I win and the winning rate is 28% (40% * 70%). If he calls, the outcome depends on the public card. If the public card is a King or Queen, I win (80% probability), so the winning rate is 9.6% (40% * 30% * 80%). If the public card is a Jack, it's a draw (20% probability), so the draw rate is 2.4% (40% * 30% * 20%).\n- If GoodGuy holds a Queen (40% probability), he will likely call (60% probability) or raise (40% probability). If he calls, the outcome depends on the public card. If the public card is a King, I win (33.33% probability), so the winning rate is 8% (40% * 60% * 33.33%). If the public card is a Queen, it's a draw (33.33% probability), so the draw rate is 8% (40% * 60% * 33.33%). If the public card is a Jack, I win (33.33% probability), so the winning rate is 8% (40% * 60% * 33.33%).\n- If GoodGuy holds a King (20% probability), he will likely call (50% probability) or raise (50% probability). If he calls, it's a draw regardless of the public card, so the draw rate is 10% (20% * 50%). If he raises, I can choose to call or fold in the next turn.\n\nPlan 1 overall board_game_expert's Winning/Lose/Draw rates: Winning rate = 28% + 9.6% + 8% + 8% = 53.6%. Draw rate = 2.4% + 8% + 10% = 20.4%. Lose rate = 100% - 53.6% - 20.4% = 26%.\n\nPlan 2: Raise\n- The analysis is similar to Plan 1, but GoodGuy's actions may change due to my raise. \n\nPlan 3: Fold\n- If I fold, I lose regardless of GoodGuy's card. So the 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 half of the pot (3 chips). If lose, the lose payoff would be 1 chip (my bet).\n- Plan 2: If win, the winning payoff would be half of the pot (5 chips). If lose, the lose payoff would be 2 chips (my bet).\n- Plan 3: If lose, the lose payoff would be 1 chip (my bet).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 53.6% * 3 - 26% * 1 = 1.08 chips.\n- Plan 2: Expected Chips Gain = (Winning rate for Plan 2) * 5 - (Lose rate for Plan 2) * 2.\n- Plan 3: Expected Chips Gain = -1 chip.\n\nPlan Selection:\n- If the Expected Chips Gain for Plan 2 is higher than 1.08 chips, I will choose Plan 2 (raise). Otherwise, I will choose Plan 1 (call). I will not choose Plan 3 (fold) as it guarantees a loss."}}
{"message": "", "38_2": {"plan": "Plan 1: Call\n- If GoodGuy holds a Queen (50% probability), he will likely raise (50% probability) or call (50% probability). If the public card is a Queen, I will lose. If the public card is a King or Jack, I will win unless GoodGuy raises and I fold. The overall winning rate is 50%, losing rate is 50%, and draw rate is 0%.\n- If GoodGuy holds a King (50% probability), he will likely raise (40% probability) or call (60% probability). 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 GoodGuy raises and I fold. The overall winning rate is 60%, losing rate is 0%, and draw rate is 40%.\n\nPlan 2: Raise\n- If GoodGuy holds a Queen (50% 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 a King or Jack, I will win unless GoodGuy raises and I fold. The overall winning rate is 60%, losing rate is 40%, and draw rate is 0%.\n- If GoodGuy holds a King (50% probability), he will likely call (50% probability) or raise (50% probability). 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 GoodGuy raises and I fold. The overall winning rate is 50%, losing rate is 0%, and draw rate is 50%.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot. The overall winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n\nWinning/Lose Payoffs:\n- Plan 1: If I win, the winning payoff would be 6 chips. If I lose, the losing payoff would be 2 chips.\n- Plan 2: If I win, the winning payoff would be 10 chips. If I lose, the losing payoff would be 4 chips.\n- Plan 3: If I fold, the losing payoff would be 2 chips.\n\nExpected Chips Gain:\n- Plan 1: Expected Chips Gain = 0.55 * 6 - 0.45 * 2 = 2.1 chips\n- Plan 2: Expected Chips Gain = 0.55 * 10 - 0.45 * 4 = 4.1 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I will choose this plan."}}
{"message": "", "38_4": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Jack, he will likely fold (60% probability) or call (40% probability). If he folds, I win and the winning rate is 60%. If he calls, I win because my King beats his Jack, so the winning rate is 40%. The overall winning rate for this plan is 100%.\n- If GoodGuy holds a Queen, he will likely raise (80% probability) or call (20% probability). If he raises, I lose because his pair of Queens beats my King, so the losing rate is 80%. If he calls, I lose because his Queen beats my King, so the losing rate is 20%. The overall losing rate for this plan is 100%.\n- If GoodGuy holds a King, he will likely call (60% probability) or raise (40% probability). If he calls, it's a draw because we both have Kings, so the draw rate is 60%. If he raises, it's a draw because we both have Kings, so the draw rate is 40%. The overall draw rate for this plan is 100%.\n\nPlan 2: Fold\n- If I fold, I lose regardless of what card GoodGuy holds. The overall losing rate for this plan is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a Jack, he will likely fold (60% probability) or call (40% probability). If he folds, I win and the winning rate is 60%. If he calls, I win because my King beats his Jack, so the winning rate is 40%. The overall winning rate for this plan is 100%.\n- If GoodGuy holds a Queen, he will likely raise (80% probability) or call (20% probability). If he raises, I lose because his pair of Queens beats my King, so the losing rate is 80%. If he calls, I lose because his Queen beats my King, so the losing rate is 20%. The overall losing rate for this plan is 100%.\n- If GoodGuy holds a King, he will likely call (60% probability) or raise (40% probability). If he calls, it's a draw because we both have Kings, so the draw rate is 60%. If he raises, it's a draw because we both have Kings, so the draw rate is 40%. The overall draw rate for this plan is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, Chips in the pot: 14. If win, the winning payoff would be 7. After the action, Chips in the pot: 14. 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: 12. If win, the winning payoff would be 6. After the action, Chips in the pot: 12. If lose, the lose payoff would be 6.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 100% * 7 - 100% * 7 = 0\n- Plan 2: Expected Chips Gain = 0 - 100% * 3 = -3\n- Plan 3: Expected Chips Gain = 100% * 6 - 100% * 6 = 0\n\nPlan Selection:\n- Plan 1 and Plan 3 have the same expected chips gain, but Plan 1 is more aggressive and may put more pressure on GoodGuy, so I choose Plan 1: Raise."}}
{"message": "", "40_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (50% probability), he will likely raise (80% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I have a chance to win. The overall winning rate is 10% (50% * 20%), the losing rate is 40% (50% * 80%), and the draw rate is 0%.\n- If GoodGuy holds a Queen (30% probability), he will likely call (60% probability) or raise (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 lose. The overall winning rate is 0%, the losing rate is 30% (30% * 100%), and the draw rate is 0%.\n- If GoodGuy holds a Jack (20% probability), he will likely call (60% probability) or raise (40% probability). If the public card is a Jack, I will lose. If the public card is a Queen or King, I will win. The overall winning rate is 20% (20% * 100%), the losing rate is 0%, and the draw rate is 0%.\n\nPlan 1 overall Winning/Lose/Draw rates: Winning rate is 30%, Lose rate is 70%, Draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (50% probability), he will likely raise (80% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I have a chance to win. The overall winning rate is 10% (50% * 20%), the losing rate is 40% (50% * 80%), and the draw rate is 0%.\n- If GoodGuy holds a Queen (30% probability), he will likely call (60% probability) or fold (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. The overall winning rate is 30% (30% * 100%), the losing rate is 0%, 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 the public card is a Jack, I will lose. If the public card is a Queen or King, I will win. The overall winning rate is 20% (20% * 100%), the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2 overall Winning/Lose/Draw rates: Winning rate is 60%, Lose rate is 40%, Draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot. The overall winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 3 chips. If lose, the lose payoff would be 2 chips.\n- Plan 2: If win, the winning payoff would be 5 chips. If lose, the lose payoff would be 4 chips.\n- Plan 3: If lose, the lose payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 30% * 3 - 70% * 2 = -0.1 chips\n- Plan 2: Expected Chips Gain = 60% * 5 - 40% * 4 = 1 chip\n- Plan 3: Expected Chips Gain = -100% * 2 = -2 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I should choose this plan."}}
{"message": "", "40_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (45% probability), he will likely raise (80% probability). If he raises, I will win as my Queen matches the public card. Therefore, the winning rate for this plan if GoodGuy holds a King is 45% * 80% = 36%. \n- If GoodGuy holds a Queen (40% probability), it will be a draw as our hands match the public card. Therefore, the draw rate for this plan if GoodGuy holds a Queen is 40%.\n- If GoodGuy holds a Jack (15% probability), he will likely fold (70% probability). If he folds, I will win. Therefore, the winning rate for this plan if GoodGuy holds a Jack is 15% * 70% = 10.5%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of GoodGuy's hand. Therefore, the losing rate for this plan is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (45% probability), he will likely raise (80% probability). If he raises, I will win as my Queen matches the public card. Therefore, the winning rate for this plan if GoodGuy holds a King is 45% * 80% = 36%. \n- If GoodGuy holds a Queen (40% probability), it will be a draw as our hands match the public card. Therefore, the draw rate for this plan if GoodGuy holds a Queen is 40%.\n- If GoodGuy holds a Jack (15% probability), he will likely fold (70% probability). If he folds, I will win. Therefore, the winning rate for this plan if GoodGuy holds a Jack is 15% * 70% = 10.5%.\n\nWinning/Lose Payoffs for Each Plan:\n- Plan 1: If I win, the pot will be 14 chips (6 chips already in the pot + 8 chips from my raise), and the winning payoff would be 7 chips. If I lose, the pot will be 14 chips, and the lose payoff would be 7 chips.\n- Plan 2: If I fold, I will lose the 6 chips already in the pot.\n- Plan 3: If I win, the pot will be 6 chips, and the winning payoff would be 3 chips. If I lose, the pot will be 6 chips, and the lose payoff would be 3 chips.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning Rate * Winning Payoff - Losing Rate * Losing Payoff = (46.5% * 7 chips) - (0% * 7 chips) = 3.255 chips\n- Plan 2: Expected Chips Gain = Winning Rate * Winning Payoff - Losing Rate * Losing Payoff = (0% * 0 chips) - (100% * 6 chips) = -6 chips\n- Plan 3: Expected Chips Gain = Winning Rate * Winning Payoff - Losing Rate * Losing Payoff = (46.5% * 3 chips) - (0% * 3 chips) = 1.395 chips\n\nPlan Selection:\n- Plan 1: Expected Chips Gain = 3.255 chips\n- Plan 2: Expected Chips Gain = -6 chips\n- Plan 3: Expected Chips Gain = 1.395 chips\n\nTherefore, I should choose Plan 1 (Raise) as it has the highest expected chips gain."}}
{"message": "", "41_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he is likely to raise (70%) or call (30%). If he raises, I will lose unless the public card is a Jack. If he calls, the outcome will depend on the public card. The estimated winning rate is 30%, losing rate is 70%, and draw rate is 0%.\n- If GoodGuy holds a Queen (30% probability), he is likely to raise (40%) or call (60%). If he raises, I will lose unless the public card is a Jack. If he calls, the outcome will depend on the public card. The estimated winning rate is 60%, losing rate is 40%, and draw rate is 0%.\n- Overall, the winning rate for Plan 1 is 45%, the losing rate is 55%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (70% probability), he is likely to raise (70%) or call (30%). If he raises, I will lose unless the public card is a Jack. If he calls, the outcome will depend on the public card. The estimated winning rate is 30%, losing rate is 70%, and draw rate is 0%.\n- If GoodGuy holds a Queen (30% probability), he is likely to raise (40%) or call (60%). If he raises, I will lose unless the public card is a Jack. If he calls, the outcome will depend on the public card. The estimated winning rate is 60%, losing rate is 40%, and draw rate is 0%.\n- Overall, the winning rate for Plan 2 is 45%, the losing rate is 55%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot. The 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 6 chips. If I lose, the lose payoff would be 2 chips.\n- Plan 2: If I win, the winning payoff would be 10 chips. If I lose, the lose payoff would be 6 chips.\n- Plan 3: If I fold, the lose payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is 45% * 6 - 55% * 2 = 1.7 chips.\n- Plan 2: The expected chips gain is 45% * 10 - 55% * 6 = 0.5 chips.\n- Plan 3: The expected chips gain is -2 chips.\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I will choose to call."}}
{"message": "", "41_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (14% probability), he is likely to call (20%) or fold (80%). If he calls, I will lose (King is higher than Jack). If he folds, I will win. So, the winning rate is 11.2% (14% * 80%), and the losing rate is 2.8% (14% * 20%).\n- If GoodGuy holds a Queen (8% probability), he is likely to raise (70%) or call (30%). In both cases, I will lose (Queen matches the public card). So, the losing rate is 8%.\n- If GoodGuy holds a Jack (10% probability), he is likely to fold (80%) or call (20%). If he folds, I will win. If he calls, it will be a draw. So, the winning rate is 8% (10% * 80%), and the draw rate is 2% (10% * 20%).\n\nPlan 2: Fold\n- If I fold, I will lose regardless of GoodGuy's card. So, the losing rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (14% probability), he is likely to call (20%) or fold (80%). If he calls, I will lose (King is higher than Jack). If he folds, I will win. So, the winning rate is 11.2% (14% * 80%), and the losing rate is 2.8% (14% * 20%).\n- If GoodGuy holds a Queen (8% probability), he is likely to raise (70%) or call (30%). In both cases, I will lose (Queen matches the public card). So, the losing rate is 8%.\n- If GoodGuy holds a Jack (10% probability), he is likely to fold (80%) or call (20%). If he folds, I will win. If he calls, it will be a draw. So, the winning rate is 8% (10% * 80%), and the draw rate is 2% (10% * 20%).\n\nWinning/Lose Payoffs:\n- Plan 1: If I win, the pot will be 12 chips (4 chips from me, 4 chips from GoodGuy, and 4 chips from my raise), and the winning payoff will be 6 chips. If I lose, the pot will be 12 chips, and the lose payoff will be 6 chips.\n- Plan 2: If I fold, I will lose 4 chips.\n- Plan 3: If I win, the pot will be 8 chips (4 chips from me, 4 chips from GoodGuy), and the winning payoff will be 4 chips. If I lose, the pot will be 8 chips, and the lose payoff will be 4 chips.\n\nExpected Chips Gain:\n- Plan 1: (11.2% * 6 chips) - (10.8% * 6 chips) = 0.024 chips\n- Plan 2: -4 chips\n- Plan 3: (19.2% * 4 chips) - (10.8% * 4 chips) = 0.034 chips\n\nPlan Selection:\n- Plan 3 (Check) has the highest expected chips gain, followed by Plan 1 (Raise), and Plan 2 (Fold). Therefore, I should choose Plan 3 (Check)."}}
{"message": "", "42_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (50% probability), he will likely raise (70% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. The overall winning rate is 0.5*0.7*1/3=11.67%, the losing rate is 0.5*0.7*2/3=23.33%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (30% probability), he will likely call (60% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I will win. The overall winning rate is 0.3*0.6*2/3=12%, the losing rate is 0.3*0.6*1/3=6%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (20% probability), he will likely fold (60% probability). If he folds, I will win regardless of the public card. The overall winning rate is 0.2*0.6=12%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (50% probability), he will likely raise (70% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. The overall winning rate is 0.5*0.7*1/3=11.67%, the losing rate is 0.5*0.7*2/3=23.33%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (30% probability), he will likely raise (40% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I will win. The overall winning rate is 0.3*0.4*2/3=8%, the losing rate is 0.3*0.4*1/3=4%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (20% probability), he will likely fold (60% probability). If he folds, I will win regardless of the public card. The overall winning rate is 0.2*0.6=12%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of GoodGuy's card or the public card. The overall 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: 4. If win, the winning payoff would be 2. If lose, the lose payoff would be 2.\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: 3. If lose, the lose payoff would be 1.5.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.1167*2 - 0.2333*2 = -0.2332\n- Plan 2: Expected Chips Gain = 0.1167*3 - 0.2333*3 = -0.3498\n- Plan 3: Expected Chips Gain = 0 - 1*1.5 = -1.5\n\nPlan Selection:\n- Plan 1: -0.2332\n- Plan 2: -0.3498\n- Plan 3: -1.5\n\nBased on the estimated expected chips gain, Plan 1 (Call) is the best strategy to use in this round."}}
{"message": "", "42_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (0% probability), he will likely raise (70% probability) or call (30% probability). However, since I hold a Jack and the public card is a King, I will lose this round (100% probability).\n- If GoodGuy holds a Queen (40% probability), he will likely call (60% probability) or raise (40% probability). Since I hold a Jack and the public card is a King, I will lose this round (100% probability).\n- If GoodGuy holds a Jack (60% probability), he will likely fold (60% probability) or call (40% probability). Since we both hold a Jack and the public card is a King, this round will be a draw (100% probability).\nOverall, the winning rate for Plan 1 is 0%, the losing rate is 40%, and the draw rate is 60%.\n\nPlan 2: Fold\n- If I fold, I will lose this round regardless of what card GoodGuy holds. Therefore, 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 (0% probability), he will likely raise (70% probability) or call (30% probability). However, since I hold a Jack and the public card is a King, I will lose this round (100% probability).\n- If GoodGuy holds a Queen (40% probability), he will likely call (60% probability) or raise (40% probability). Since I hold a Jack and the public card is a King, I will lose this round (100% probability).\n- If GoodGuy holds a Jack (60% probability), he will likely fold (60% probability) or call (40% probability). Since we both hold a Jack and the public card is a King, this round will be a draw (100% probability).\nOverall, the winning rate for Plan 3 is 0%, the losing rate is 40%, and the draw rate is 60%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 2 chips. If I lose, the losing payoff would be 2 chips.\n- Plan 2: If I win, the winning payoff would be 0 chips. If I lose, the losing payoff would be 2 chips.\n- Plan 3: If I win, the winning payoff would be 2 chips. If I lose, the losing payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0% * 2 chips - 40% * 2 chips = -0.8 chips\n- Plan 2: 0% * 0 chips - 100% * 2 chips = -2 chips\n- Plan 3: 0% * 2 chips - 40% * 2 chips = -0.8 chips\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": "", "43_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (33.3% probability), he may raise (70% probability) or call (30% probability). If he raises, I will lose unless the public card is a Queen. If he calls, I will win if the public card is a Queen, and lose if it is a King or Jack. \n- If GoodGuy holds a Queen (33.3% probability), he may call (50% probability) or fold (50% probability). If he calls, it will be a draw unless the public card is a King or Jack. If he folds, I will win.\n- If GoodGuy holds a Jack (33.3% probability), he may call (70% probability) or raise (30% probability). If he calls, I will win unless the public card is a Jack. If he raises, I will lose unless the public card is a Queen.\n\nPlan 2: Raise\n- If GoodGuy holds a King (33.3% probability), he may raise (70% probability) or call (30% probability). If he raises, I will lose unless the public card is a Queen. If he calls, I will win if the public card is a Queen, and lose if it is a King or Jack. \n- If GoodGuy holds a Queen (33.3% probability), he may call (40% probability) or fold (60% probability). If he calls, it will be a draw unless the public card is a King or Jack. If he folds, I will win.\n- If GoodGuy holds a Jack (33.3% probability), he may call (40% probability) or fold (60% probability). If he calls, I will win unless the public card is a Jack. If he folds, I will win.\n\nPlan 3: Fold\n- If I fold, I will lose the game.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 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, I will lose 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 33.3% * (70% * -2 + 30% * 3) + 33.3% * (50% * 3 + 50% * 3) + 33.3% * (70% * 3 + 30% * -2) = 1.5 chips\n- Plan 2: Expected Chips Gain = 33.3% * (70% * -3 + 30% * 4) + 33.3% * (40% * 4 + 60% * 4) + 33.3% * (40% * 4 + 60% * 4) = 2.2 chips\n- Plan 3: Expected Chips Gain = -1 chip\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain, so I should choose to raise."}}
{"message": "", "43_2": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he will likely raise (70% probability). If the public card is a Queen, I will win (probability = 0.7*0.7 = 0.49). If the public card is a King or Jack, I will lose (probability = 0.7*0.3 = 0.21).\n- If GoodGuy holds a Queen (30% probability), he will likely call (60% probability). If the public card is a Queen, it will be a draw (probability = 0.3*0.6 = 0.18). If the public card is a King or Jack, I will lose (probability = 0.3*0.4 = 0.12).\n- Overall, the winning rate for Plan 1 is 0.49, the losing rate is 0.33, and the draw rate is 0.18.\n- After the call action, 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\nPlan 2: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card or the public card. The losing rate for Plan 2 is 1.\n- After the fold action, there will be 6 chips in the pot. If I lose, the losing payoff would be 3 chips.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning Rate * Winning Payoff - Losing Rate * Losing Payoff = 0.49 * 4 - 0.33 * 4 = 0.64 chips.\n- Plan 2: Expected Chips Gain = Winning Rate * Winning Payoff - Losing Rate * Losing Payoff = 0 * 0 - 1 * 3 = -3 chips.\n\nPlan Selection:\n- The rank of estimated expected chips gains for each plan is: Plan 1 > Plan 2.\n- Therefore, I should select Plan 1 (Call) as it has the highest estimated expected chips gain. This plan also aligns with my strategy improvement to be more aggressive when I have a high-ranking card."}}
{"message": "", "43_4": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (70% probability), he may call (60% probability) or fold (40% probability). If he calls, I will lose (as his Queen matches my Queen, it's a draw, but he has more chips so he wins). If he folds, I will win. So the winning rate is 40%, the losing rate is 60%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (30% probability), he may call (60% probability) or fold (40% probability). If he calls, I will win (as my Queen is higher than his Jack). If he folds, 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 I fold, I will lose regardless of GoodGuy's card. 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 (70% probability), he may check (70% probability) or call (30% probability). If he checks, I will lose (as his Queen matches my Queen, it's a draw, but he has more chips so he wins). If he calls, 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 (30% probability), he may check (70% probability) or call (30% probability). If he checks, I will win (as my Queen is higher than his Jack). If he calls, I will also win. So the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 6 chips (half of the pot). If I lose, the losing payoff would be 6 chips.\n- Plan 2: If I fold, I will lose 6 chips.\n- Plan 3: If I win, the winning payoff would be 6 chips. If I lose, the losing payoff would be 6 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.4 * 6 - 0.6 * 6 = -1.2 chips\n- Plan 2: Expected Chips Gain = 0 - 1 * 6 = -6 chips\n- Plan 3: Expected Chips Gain = 0.3 * 6 - 0.7 * 6 = -2.4 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain (-1.2 chips), followed by Plan 3 (-2.4 chips) and Plan 2 (-6 chips). Therefore, I should choose Plan 1: Raise."}}
{"message": "", "44_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (20% probability), he will likely call (60%) or fold (40%). If he calls, I will likely lose unless the public card is a Jack. If he folds, I will win. The overall winning rate is 40%, losing rate is 12%, and draw rate is 0%.\n- If GoodGuy holds a Queen (35% probability), he will likely call (50%) or fold (50%). If he calls, I will likely lose unless the public card is a Jack. If he folds, I will win. The overall winning rate is 50%, losing rate is 17.5%, and draw rate is 0%.\n- If GoodGuy holds a Jack (45% probability), he will likely call (30%) or fold (70%). If he calls, it will be a draw unless the public card is a Queen or King. If he folds, I will win. The overall winning rate is 70%, losing rate is 0%, and draw rate is 13.5%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of GoodGuy's card. The overall winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King (20% probability), he will likely raise (80%) or check (20%). If he raises, I will likely lose unless the public card is a Jack. If he checks, it will be a draw unless the public card is a Queen or King. The overall winning rate is 0%, losing rate is 16%, and draw rate is 4%.\n- If GoodGuy holds a Queen (35% probability), he will likely raise (30%) or check (70%). If he raises, I will likely lose unless the public card is a Jack. If he checks, it will be a draw unless the public card is a Queen or King. The overall winning rate is 0%, losing rate is 10.5%, and draw rate is 24.5%.\n- If GoodGuy holds a Jack (45% probability), he will likely raise (50%) or check (50%). If he raises, it will be a draw unless the public card is a Queen or King. If he checks, it will be a draw. The overall winning rate is 0%, losing rate is 0%, and draw rate is 45%.\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: 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: (40%+50%+70%) * 3 - (12%+17.5%) * 3 = 1.605\n- Plan 2: 0 * 2 - 100% * 2 = -2\n- Plan 3: 0 * 2 - (16%+10.5%) * 2 = -0.53\n\nPlan Selection:\n- Plan 1: 1.605\n- Plan 2: -2\n- Plan 3: -0.53\n\nThe rank of estimated expected chips gains for every plan is Plan 1 > Plan 3 > Plan 2. Therefore, I should choose Plan 1: Raise."}}
{"message": "", "45_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% 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 (20% chance), he will likely call (60% chance) or raise (40% chance). If the public card is a King, I will lose. If the public card is a Queen or Jack, it will be a draw. Overall, the winning rate is 0%, the losing rate is 20%, and the draw rate is 80%.\n- If GoodGuy holds a Jack (10% chance), he will likely call (60% chance) or raise (40% chance). If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. Overall, the winning rate is 10%, the losing rate is 0%, and the draw rate is 90%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (70% chance), he will likely call (30% chance) or 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 (20% chance), he will likely fold (60% chance) or call (40% chance). If the public card is a King, I will lose. If the public card is a Queen or Jack, it will be a draw. Overall, the winning rate is 0%, the losing rate is 20%, and the draw rate is 80%.\n- If GoodGuy holds a Jack (10% chance), he will likely fold (70% chance) or call (30% chance). If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. Overall, the winning rate is 10%, the losing rate is 0%, and the draw rate is 90%.\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 4 chips. If I lose, the losing payoff would be 2 chips.\n- Plan 2: If I win, the winning payoff would be 6 chips. If I lose, the losing payoff would be 4 chips.\n- Plan 3: If I lose, the losing payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0% * 4 - 70% * 2 = -1.4 chips\n- Plan 2: Expected Chips Gain = 10% * 6 - 70% * 4 = -2.4 chips\n- Plan 3: Expected Chips Gain = 0% * 0 - 100% * 2 = -2 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain (-1.4 chips), followed by Plan 3 (-2 chips), and Plan 2 (-2.4 chips). Therefore, I should choose Plan 1: Call."}}
{"message": "", "45_3": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he will likely call (70% probability). If he calls, we will have a draw as we both have a pair of Jacks. The winning rate is 0%, the losing rate is 0%, and the draw rate is 70%.\n- If GoodGuy holds a Queen (40% probability), he will likely fold (40% probability). If he folds, I will win. The winning rate is 40%, the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (30% probability), he will likely call (70% probability). If he calls, we will have a draw as we both have a pair of Jacks. The winning rate is 0%, the losing rate is 0%, and the draw rate is 30%.\n\nPlan 1 overall Winning/Lose/Draw rates: Winning rate is 40%, Losing rate is 0%, Draw rate is 100%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (70% probability), he will likely call (70% probability). If he calls, we will have a draw as we both have a pair of Jacks. The winning rate is 0%, the losing rate is 0%, and the draw rate is 70%.\n- If GoodGuy holds a Queen (40% probability), he will likely fold (40% probability). If he folds, I will win. The winning rate is 40%, the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (30% probability), he will likely call (70% probability). If he calls, we will have a draw as we both have a pair of Jacks. The winning rate is 0%, the losing rate is 0%, and the draw rate is 30%.\n\nPlan 2 overall Winning/Lose/Draw rates: Winning rate is 40%, Losing rate is 0%, Draw rate is 100%.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. 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 6 chips. If I lose, the losing payoff would be 4 chips.\n- Plan 2: If I win, the winning payoff would be 10 chips. If I lose, the losing payoff would be 8 chips.\n- Plan 3: If I fold, I will lose 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 40% * 6 - 0% * 4 = 2.4 chips\n- Plan 2: Expected Chips Gain = 40% * 10 - 0% * 8 = 4 chips\n- Plan 3: Expected Chips Gain = 0% * 0 - 100% * 4 = -4 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I will choose this plan."}}
{"message": "", "46_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King, he will likely raise (80% chance) or call (20% chance). If he raises, I will lose unless the public card is a Queen. If he calls, I will win if the public card is a Queen or a Jack. The overall winning rate is 20%, losing rate is 80%, and drawing rate is 0%.\n- If GoodGuy holds a Queen, he will likely call (70% chance) or raise (30% chance). If he calls, I will win if the public card is a Queen or a Jack. If he raises, I will lose unless the public card is a Queen. The overall winning rate is 70%, losing rate is 30%, and drawing rate is 0%.\n- If GoodGuy holds a Jack, he will likely call (60% chance) or check (40% chance). If he calls, I will win if the public card is a Queen or a King. If he checks, I will win if the public card is a Queen or a King. The overall winning rate is 100%, losing rate is 0%, and drawing rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King, he will likely call (80% chance) or fold (20% chance). If he calls, I will lose unless the public card is a Queen. If he folds, I will win. The overall winning rate is 20%, losing rate is 80%, and drawing rate is 0%.\n- If GoodGuy holds a Queen, he will likely call (70% chance) or fold (30% chance). If he calls, I will win if the public card is a Queen or a Jack. If he folds, I will win. The overall winning rate is 100%, losing rate is 0%, and drawing rate is 0%.\n- If GoodGuy holds a Jack, he will likely fold (60% chance) or call (40% chance). If he folds, I will win. If he calls, I will win if the public card is a Queen or a King. The overall winning rate is 100%, losing rate is 0%, and drawing rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card. The overall winning rate is 0%, losing rate is 100%, and 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. If I lose, the losing payoff would be 1 chip.\n- Plan 2: If I win, the winning payoff would be 5 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: Expected Chips Gain = 20% * 3 - 80% * 1 = -0.4 chips\n- Plan 2: Expected Chips Gain = 100% * 5 - 0% * 2 = 5 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 will choose this plan."}}
{"message": "", "46_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King, he will likely raise (70%) or call (30%). If he raises, I will lose as his King beats my Queen. If he calls, I will also lose unless the public card is a Queen. The overall winning rate is 10% (1/3 * 30%), losing rate is 90% (70% + 20% * 2/3), and draw rate is 0%.\n- If GoodGuy holds a Queen, he will likely check (70%) or call (30%). If he checks, I will win unless the public card is a Jack. If he calls, I will win unless the public card is a Jack. The overall winning rate is 70% (70% + 30% * 1/3), losing rate is 20% (30% * 2/3), and draw rate is 10% (30% * 1/3).\n- If GoodGuy holds a Jack, he will likely check (80%) or fold (20%). If he checks, I will win unless the public card is a Jack. If he folds, I will win. The overall winning rate is 100%, losing rate is 0%, and draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card. The overall winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King, he will likely raise (70%) or call (30%). If he raises, I will lose as his King beats my Queen. If he calls, I will also lose unless the public card is a Queen. The overall winning rate is 10% (1/3 * 30%), losing rate is 90% (70% + 20% * 2/3), and draw rate is 0%.\n- If GoodGuy holds a Queen, he will likely check (70%) or call (30%). If he checks, I will win unless the public card is a Jack. If he calls, I will win unless the public card is a Jack. The overall winning rate is 70% (70% + 30% * 1/3), losing rate is 20% (30% * 2/3), and draw rate is 10% (30% * 1/3).\n- If GoodGuy holds a Jack, he will likely check (80%) or fold (20%). If he checks, I will win unless the public card is a Jack. If he folds, I will win. The overall winning rate is 100%, losing rate is 0%, and draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips (half of the pot). If I lose, the lose payoff would be 4 chips.\n- Plan 2: If I fold, I will lose 4 chips.\n- Plan 3: If I win, the winning payoff would be 4 chips. If I lose, the lose payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.8 * 4 - 0.2 * 4 = 2.4 chips\n- Plan 2: Expected Chips Gain = -4 chips\n- Plan 3: Expected Chips Gain = 0.9 * 4 - 0.1 * 4 = 3.2 chips\n\nPlan Selection:\n- Plan 1: 2nd\n- Plan 2: 3rd\n- Plan 3: 1st\n\nBased on the above analysis, I should choose Plan 3 (Check) as it has the highest expected chips gain."}}
{"message": "", "47_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (30% chance), he will likely raise (70%) or call (30%). If he raises, I will lose (as King is higher than Jack). If he calls, the outcome will depend on the public card. \n- If GoodGuy holds a Queen (60% chance), he will likely fold (60%) or call (40%). If he folds, I will win. If he calls, the outcome will depend on the public card. \n- If GoodGuy holds a Jack (30% chance), he will likely fold (70%) or call (30%). If he folds, I will win. If he calls, it will be a draw as we both hold Jacks. \n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card. \n\nPlan 3: Check\n- If GoodGuy holds a King (30% chance), he will likely raise (70%) or call (30%). If he raises, I will lose (as King is higher than Jack). If he calls, the outcome will depend on the public card. \n- If GoodGuy holds a Queen (60% chance), he will likely check (40%) or call (60%). If he checks, the outcome will depend on the public card. If he calls, the outcome will also depend on the public card. \n- If GoodGuy holds a Jack (30% chance), he will likely check (40%) or call (60%). If he checks, it will be a draw as we both hold Jacks. If he calls, it will also be a draw as we both hold Jacks. \n\nWinning/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 fold, I will lose the game and the losing payoff would be 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\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning Rate * Winning Payoff - Losing Rate * Losing Payoff = (0.3*0.7 + 0.6*0.6 + 0.3*0.7) * 6 - (0.3*0.3 + 0.6*0.4 + 0.3*0.3) * 6 = 1.8 chips\n- Plan 2: Expected Chips Gain = 0 - 1 * 2 = -2 chips\n- Plan 3: Expected Chips Gain = (0.3*0.3 + 0.6*0.4 + 0.3*0.4) * 4 - (0.3*0.7 + 0.6*0.6 + 0.3*0.6) * 4 = -0.8 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain (1.8 chips), followed by Plan 3 (-0.8 chips), and Plan 2 (-2 chips). Therefore, I should choose Plan 1: Raise."}}
{"message": "", "48_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he will likely raise (70% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I have a chance to win if GoodGuy doesn't fold. The overall winning rate for this scenario is 0.7*0.7*0.33 = 16.17%.\n- If GoodGuy holds a Queen (60% probability), he will likely raise (60% probability) if I call. If the public card is a Queen, I will lose. If the public card is a King or Jack, I have a chance to win if GoodGuy doesn't fold. The overall winning rate for this scenario is 0.6*0.6*0.33 = 11.88%.\n- If GoodGuy holds a Jack (30% probability), he will likely call (60% probability) if I call. If the public card is a Jack, I will win. If the public card is a King or Queen, I have a chance to win if GoodGuy doesn't fold. The overall winning rate for this scenario is 0.3*0.6*0.33 = 5.94%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (70% probability), he will likely raise (70% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I have a chance to win if GoodGuy doesn't fold. The overall winning rate for this scenario is 0.7*0.7*0.33 = 16.17%.\n- If GoodGuy holds a Queen (60% probability), he will likely fold (40% probability) if I raise. If the public card is a Queen, I will lose. If the public card is a King or Jack, I have a chance to win if GoodGuy doesn't fold. The overall winning rate for this scenario is 0.6*0.4*0.33 = 7.92%.\n- If GoodGuy holds a Jack (30% probability), he will likely fold (70% probability) if I raise. If the public card is a Jack, I will win. If the public card is a King or Queen, I have a chance to win if GoodGuy doesn't fold. The overall winning rate for this scenario is 0.3*0.7*0.33 = 6.93%.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot. The overall winning rate for this scenario 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 (3 chips). If I lose, the lose payoff would be 1 chip.\n- Plan 2: If I win, the winning payoff would be half of the pot (4 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: 0.1617*3 - 0.8383*1 = 0.1461 chips\n- Plan 2: 0.1617*4 - 0.8383*2 = -0.3386 chips\n- Plan 3: -1 chip\n\nPlan Selection:\n- Plan 1 has the highest estimated expected chips gain, so I will choose to call."}}
{"message": "", "48_2": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he will likely raise (70% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. Overall, the winning rate is 30%, the losing rate is 70%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (30% probability), he will likely raise (60% probability) or call (40% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I will win. Overall, the winning rate is 60%, the losing rate is 40%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (70% probability), he will likely call (30% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. Overall, the winning rate is 30%, the losing rate is 70%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (30% probability), he will likely fold (40% probability) or call (60% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I will win. Overall, the winning rate is 60%, the losing rate is 40%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot. The 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 6 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 8 chips (half of the pot). If I lose, the losing payoff would be 4 chips (half of the pot).\n- Plan 3: If I fold, I will lose the 2 chips I have already put in the pot.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.6 * 6 - 0.4 * 2 = 2.8 chips\n- Plan 2: Expected Chips Gain = 0.6 * 8 - 0.4 * 4 = 3.2 chips\n- Plan 3: Expected Chips Gain = 0 - 1 * 2 = -2 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I will choose this plan."}}
{"message": "", "48_4": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (40% probability), he will likely call (60% probability) or fold (40% probability). If he calls, I will lose unless the next public card is a Jack. If he folds, I will win. The overall winning rate is 40% * 40% = 16%, and the losing rate is 40% * 60% = 24%.\n- If GoodGuy holds a Queen (60% probability), he will likely raise (80% probability) or call (20% probability). In both cases, I will lose unless the next public card is a Jack. The overall winning rate is 0%, and the losing rate is 60%.\n\nPlan 2: Fold\n- If I fold, I will lose the current pot but avoid further losses. The overall winning rate is 0%, and the losing rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (40% probability), he will likely raise (50% probability) or call (50% probability). If he raises, I will lose unless the next public card is a Jack. If he calls, I will win if the next public card is a Jack. The overall winning rate is 40% * 50% * 33.33% = 6.67%, and the losing rate is 40% * 50% * 66.67% = 13.33%.\n- If GoodGuy holds a Queen (60% probability), he will likely raise (80% probability) or call (20% probability). In both cases, I will lose unless the next public card is a Jack. The overall winning rate is 0%, and the losing rate is 60%.\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 (8 chips), which is 7 chips. If I lose, the losing payoff would be my raise (8 chips).\n- Plan 2: If I fold, there is no winning payoff, and the losing payoff would be the chips I have already put in the pot (6 chips).\n- Plan 3: If I win, the winning payoff would be half of the pot (6 chips). If I lose, the losing payoff would be the chips I have already put in the pot (6 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 16% * 7 chips - 24% * 8 chips = -0.92 chips\n- Plan 2: Expected Chips Gain = 0% * 0 chips - 100% * 6 chips = -6 chips\n- Plan 3: Expected Chips Gain = 6.67% * 6 chips - 13.33% * 6 chips = -0.4 chips\n\nPlan Selection:\n- Plan 1: -0.92 chips\n- Plan 2: -6 chips\n- Plan 3: -0.4 chips\n\nBased on the estimated expected chips gain, Plan 3 (Check) is the best strategy to use in this situation."}}
{"message": "", "48_6": {"plan": "Plan 1: Call\n- If GoodGuy holds a Queen (80% probability), he will likely raise (80% probability). I will lose as his card matches the public card. \n- If GoodGuy holds a King (20% probability), he will likely raise (50% probability) or call (50% probability). I will lose as his card is of a higher rank than mine.\n- If GoodGuy holds a Jack (0% probability), it's impossible in this round as I'm holding the Jack.\n\nPlan 2: Raise\n- If GoodGuy holds a Queen (80% probability), he will likely raise (80% probability). I will lose as his card matches the public card. \n- If GoodGuy holds a King (20% probability), he will likely raise (50% probability) or call (50% probability). I will lose as his card is of a higher rank than mine.\n- If GoodGuy holds a Jack (0% probability), it's impossible in this round as I'm holding the Jack.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot, but I will not lose any more chips in this round.\n\nWinning/Lose/Draw Rate for Each Plan:\n- Plan 1: Winning rate: 0%, Lose rate: 100%, Draw rate: 0%\n- Plan 2: Winning rate: 0%, Lose rate: 100%, Draw rate: 0%\n- Plan 3: Winning rate: 0%, Lose rate: 100%, Draw rate: 0%\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 0. If lose, the lose payoff would be 10.\n- Plan 2: If win, the winning payoff would be 0. If lose, the lose payoff would be 18.\n- Plan 3: If win, the winning payoff would be 0. If lose, the lose payoff would be 6.\n\nEstimated Expected Chips Gain for Each Plan:\n- Plan 1: Expected chips gain = 0% * 0 - 100% * 10 = -10\n- Plan 2: Expected chips gain = 0% * 0 - 100% * 18 = -18\n- Plan 3: Expected chips gain = 0% * 0 - 100% * 6 = -6\n\nPlan Selection:\n- Plan 1: Rank 2\n- Plan 2: Rank 3\n- Plan 3: Rank 1\n\nBased on the analysis, I should choose Plan 3 (Fold) as it has the highest estimated expected chips gain. This is because I have a low probability of winning this round and folding will minimize my losses."}}
{"message": "", "50_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King, he is likely to call (70%) or raise (30%). If he calls, I will have a 50% chance of winning if the public card is a Queen, and a 50% chance of losing if the public card is a King or Jack. If he raises, I will have a 50% chance of winning if the public card is a Queen, and a 50% chance of losing if the public card is a King or Jack. Overall, my winning rate is 50%, my losing rate is 50%, and my draw rate is 0%.\n- If GoodGuy holds a Queen, he is likely to call (60%) or fold (40%). If he calls, I will have a 100% chance of winning if the public card is a Queen, and a 0% chance of losing. If he folds, I will win the pot. Overall, my winning rate is 100%, my losing rate is 0%, and my draw rate is 0%.\n- If GoodGuy holds a Jack, he is likely to fold (80%) or call (20%). If he folds, I will win the pot. If he calls, I will have a 100% chance of winning if the public card is a Queen or King, and a 0% chance of losing. Overall, my winning rate is 100%, my losing rate is 0%, and my draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose the pot regardless of what card GoodGuy holds. My winning rate is 0%, my losing rate is 100%, and my draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King, he is likely to raise (80%) or check (20%). If he raises, I will have a 50% chance of winning if the public card is a Queen, and a 50% chance of losing if the public card is a King or Jack. If he checks, I will have a 50% chance of winning if the public card is a Queen, and a 50% chance of losing if the public card is a King or Jack. Overall, my winning rate is 50%, my losing rate is 50%, and my draw rate is 0%.\n- If GoodGuy holds a Queen, he is likely to check (50%) or fold (50%). If he checks, I will have a 100% chance of winning if the public card is a Queen, and a 0% chance of losing. If he folds, I will win the pot. Overall, my winning rate is 100%, my losing rate is 0%, and my draw rate is 0%.\n- If GoodGuy holds a Jack, he is likely to check (30%) or fold (70%). If he checks, I will have a 100% chance of winning if the public card is a Queen or King, and a 0% chance of losing. If he folds, I will win the pot. Overall, my winning rate is 100%, my losing rate is 0%, and my 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: 4. If win, the winning payoff would be 0. 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 = 0.75 * 4 - 0.25 * 4 = 2\n- Plan 2: Expected Chips Gain = 0 * 0 - 1 * 2 = -2\n- Plan 3: Expected Chips Gain = 0.75 * 2 - 0.25 * 2 = 1\n\nPlan Selection:\n- Plan 1: Raise\n- Plan 3: Check\n- Plan 2: Fold\n\nThe best plan is to raise."}}
