{"message": "", "1_1": {"plan": "Plan 1: Call\nIf I call, I match my opponent's bet of 4 chips, bringing the total pot to 10 chips. \n\nThe winning/losing/draw rates when board_game_expert holds a King: \nIf board_game_expert holds a King, he is likely to 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, lose if it's a King, and draw if it's a Jack. The overall winning rate is 30%, losing rate is 60%, and draw rate is 10%.\n\nThe winning/losing/draw rates when board_game_expert holds a Queen: \nIf board_game_expert holds a Queen, he is likely to call (50% probability) or fold (50% probability). 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. If he folds, I win. The overall winning rate is 75%, losing rate is 12.5%, and draw rate is 12.5%.\n\nThe winning/losing/draw rates when board_game_expert holds a Jack: \nIf board_game_expert holds a Jack, he is likely to call (30% probability) or fold (70% probability). If he calls, I will win if the public card is a Queen or Jack, and lose if it's a King. If he folds, I win. The overall winning rate is 80%, losing rate is 10%, and draw rate is 10%.\n\nPlan1 overall GoodGuy's Winning/Lose/Draw rates: \nThe Winning rate for plan 1 is 61.67%, Lose rate for plan 1 is 27.5%, Draw Rate for plan 1 is 10.83%.\n\nPlan 2: Raise\nIf I raise, I increase the bet by 4 chips, bringing the total pot to 12 chips. \n\nThe winning/losing/draw rates when board_game_expert holds a King, Queen, or Jack would be similar to Plan 1, but with a higher risk due to the increased bet. \n\nPlan2 overall GoodGuy's Winning/Lose/Draw rates: \nThe Winning rate for plan 2 is 61.67%, Lose rate for plan 2 is 27.5%, Draw Rate for plan 2 is 10.83%.\n\nPlan 3: Fold\nIf I fold, I concede the round and lose my initial bet of 2 chips. \n\nPlan3 overall GoodGuy's Winning/Lose/Draw rates: \nThe Winning rate for plan 3 is 0%, Lose rate for plan 3 is 100%, Draw Rate for plan 3 is 0%.\n\nThe number of payoffs for each plan:\nPlan1: If win, the winning payoff would be 5 chips. If lose, the lose payoff would be 5 chips.\nPlan2: If win, the winning payoff would be 6 chips. If lose, the lose payoff would be 6 chips.\nPlan3: If win, the winning payoff would be 0 chips. If lose, the lose payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\nPlan1: Expected Chips Gain = 0.6167 * 5 - 0.275 * 5 = 1.7085 chips\nPlan2: Expected Chips Gain = 0.6167 * 6 - 0.275 * 6 = 2.05 chips\nPlan3: Expected Chips Gain = 0 * 0 - 1 * 2 = -2 chips\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows: Plan2 > Plan1 > Plan3. Therefore, the best strategy would be to raise (Plan2), as it has the highest estimated expected chips gain."}}
{"message": "", "1_3": {"plan": "Plan 1: Raise\nIf I raise, I would put 4 more chips into the pot, making the total pot 16 chips. \n\nThe winning/lose/draw rates when board_game_expert holds a King: \nIf board_game_expert holds a King, he would have a pair of Kings, which would beat my single Queen. The probability of this happening is 2/5. If he sees my raise, he might believe that I am holding a strong card and decide to call or raise. If he calls, the probability of me winning is 0, losing is 1, and drawing is 0. If he raises, the probability of me winning is 0, losing is 1, and drawing is 0. \n\nThe winning/lose/draw rates when board_game_expert holds a Queen: \nIf board_game_expert holds a Queen, he would have a single Queen, which is a lower rank than a King. The probability of this happening is 1/5. If he sees my raise, he might believe that I am holding a strong card and decide to fold, call, or raise. If he folds, the probability of me winning is 1, losing is 0, and drawing is 0. If he calls or raises, the probability of me winning is 1/2, losing is 1/2, and drawing is 0. \n\nThe winning/lose/draw rates when board_game_expert holds a Jack: \nIf board_game_expert holds a Jack, he would have a single Jack, which is a lower rank than both a King and a Queen. The probability of this happening is 2/5. If he sees my raise, he might believe that I am holding a strong card and decide to fold, call, or raise. If he folds, the probability of me winning is 1, losing is 0, and drawing is 0. If he calls or raises, the probability of me winning is 1, losing is 0, and drawing is 0. \n\nPlan1 overall GoodGuy's Winning/Lose/Draw rates : \nThe Winning rate for plan 1 is 0.6, Lose rate for plan 1 is 0.4, Draw Rate for plan 1 is 0. \n\nPlan 2: Fold\nIf I fold, I would forfeit the game, and the total pot would remain at 12 chips. \n\nThe winning/lose/draw rates when board_game_expert holds a King, Queen, or Jack: \nIf I fold, the probability of me winning is 0, losing is 1, and drawing is 0, regardless of what card board_game_expert holds. \n\nPlan2 overall GoodGuy's Winning/Lose/Draw rates : \nThe Winning rate for plan 2 is 0, Lose rate for plan 2 is 1, Draw Rate for plan 2 is 0. \n\nPlan 3: Check\nIf I check, I would not add any more chips to the pot, and the total pot would remain at 12 chips. \n\nThe winning/lose/draw rates when board_game_expert holds a King, Queen, or Jack: \nIf I check, the probability of me winning, losing, or drawing would be the same as in Plan 1, as my action does not affect the outcome of the game. \n\nPlan3 overall GoodGuy's Winning/Lose/Draw rates : \nThe Winning rate for plan 3 is 0.6, Lose rate for plan 3 is 0.4, Draw Rate for plan 3 is 0. \n\nThe number of payoffs for each plan: \nPlan1: If win, the winning payoff would be 8 chips. If lose, the lose payoff would be 8 chips. \nPlan2: If win, the winning payoff would be 0 chips. If lose, the lose payoff would be 6 chips. \nPlan3: If win, the winning payoff would be 6 chips. If lose, the lose payoff would be 6 chips. \n\nEstimate Expected Chips Gain for Each Plan: \nPlan1: The expected chips gain is 0.6 * 8 - 0.4 * 8 = 1.6 chips. \nPlan2: The expected chips gain is 0 * 0 - 1 * 6 = -6 chips. \nPlan3: The expected chips gain is 0.6 * 6 - 0.4 * 6 = 1.2 chips. \n\nPlan Selection: \nThe rank of estimated expected chips gains for every plan is: Plan1 > Plan3 > Plan2. Therefore, I should select Plan1, which is to raise."}}
{"message": "", "2_1": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (20% chance), he would likely call (80%) or raise (20%). If he calls, I would win as my card matches the public card. If he raises, I should call to keep the pot small and minimize risk. The winning rate is 80%, the losing rate is 20%, and the draw rate is 0%.\n- If board_game_expert holds a Queen (40% chance), he would likely call (70%) or fold (30%). If he calls, I would win as my card is higher. If he folds, I would also win. The winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n- If board_game_expert holds a Jack (40% chance), he would likely call (60%) or fold (40%). If he calls, I would win as my card is higher. If he folds, I would also win. The winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If board_game_expert holds a King (20% chance), he would likely call (80%) or raise (20%). If he calls, I would win as my card matches the public card. If he raises, I should call to keep the pot small and minimize risk. The winning rate is 80%, the losing rate is 20%, and the draw rate is 0%.\n- If board_game_expert holds a Queen (40% chance), he would likely call (70%) or fold (30%). If he calls, I would win as my card is higher. If he folds, I would also win. The winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n- If board_game_expert holds a Jack (40% chance), he would likely call (60%) or fold (40%). If he calls, I would win as my card is higher. If he folds, I would also win. The winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I would lose regardless of what card board_game_expert holds. The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPayoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 6 chips (half of the total pot of 12 chips). If I lose, the losing payoff would be 6 chips.\n- Plan 2: If I win, the winning payoff would be 8 chips (half of the total pot of 16 chips). If I lose, the losing payoff would be 8 chips.\n- Plan 3: If I fold, I would lose 2 chips.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.96 chips (winning rate * Winning Payoff - losing rate * Losing Payoff)\n- Plan 2: Expected Chips Gain = 1.28 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain and is therefore the best strategy to follow."}}
{"message": "", "2_3": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (40% chance), he would likely call (60%) or raise (40%). If he calls, I would lose as we both have a King but he has more chips. If he raises, I would also lose as we both have a King but he has more chips. Therefore, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If board_game_expert holds a Queen (20% chance), he would likely call (50%) or fold (50%). If he calls, I would win as my King beats his Queen. If he folds, I would also win as he forfeits the game. Therefore, the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n- If board_game_expert holds a Jack (40% chance), he would likely call (30%) or fold (70%). If he calls, I would lose as his pair of Jacks beats my King. If he folds, I would win as he forfeits the game. Therefore, the winning rate is 70%, the losing rate is 30%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I would lose regardless of what card board_game_expert holds. Therefore, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If board_game_expert holds a King (40% chance), he would likely call (60%) or raise (40%). If he calls, I would lose as we both have a King but he has more chips. If he raises, I would also lose as we both have a King but he has more chips. Therefore, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If board_game_expert holds a Queen (20% chance), he would likely call (50%) or fold (50%). If he calls, I would win as my King beats his Queen. If he folds, I would also win as he forfeits the game. Therefore, the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n- If board_game_expert holds a Jack (40% chance), he would likely call (30%) or fold (70%). If he calls, I would lose as his pair of Jacks beats my King. If he folds, I would win as he forfeits the game. Therefore, the winning rate is 70%, the losing rate is 30%, and the draw rate is 0%.\n\nThe number of 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 6 chips.\n- Plan 2: If I lose, the losing payoff would be 6 chips.\n- Plan 3: If I win, the winning payoff would be 6 chips. If I lose, the losing payoff would be 6 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.7 * 6 - 0.3 * 6 = 2.4 chips\n- Plan 2: Expected Chips Gain = 0 - 1 * 6 = -6 chips\n- Plan 3: Expected Chips Gain = 0.7 * 6 - 0.3 * 6 = 2.4 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 have the highest expected chips gain of 2.4 chips, while Plan 2 has the lowest expected chips gain of -6 chips. Therefore, I should either raise (Plan 1) or check (Plan 3). Considering the strategy improvement, I should choose to raise (Plan 1) to potentially confuse board_game_expert and make him believe I hold a Queen."}}
{"message": "", "3_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (40% probability), he would likely call (60%) or raise (40%). If he calls, I have a 20% chance of winning (if the public card is a Queen), 40% chance of losing (if the public card is a King or Jack), and 40% chance of a draw (if the public card is a Queen). If he raises, I have a 20% chance of winning, 40% chance of losing, and 40% chance of a draw.\n- If board_game_expert holds a Queen (20% probability), he would likely call (60%) or raise (40%). If he calls, I have a 20% chance of winning (if the public card is a King), 20% chance of losing (if the public card is a Queen), and 60% chance of a draw (if the public card is a King or Jack). If he raises, I have a 20% chance of winning, 20% chance of losing, and 60% chance of a draw.\n- If board_game_expert holds a Jack (40% probability), he would likely call (70%) or raise (30%). If he calls, I have a 40% chance of winning (if the public card is a King or Queen), 20% chance of losing (if the public card is a Jack), and 40% chance of a draw (if the public card is a King or Queen). If he raises, I have a 40% chance of winning, 20% chance of losing, and 40% chance of a draw.\n- Overall, the winning rate for Plan 1 is 28%, the losing rate is 28%, and the draw rate is 44%.\n\nPlan 2: Raise\n- If board_game_expert holds a King (40% probability), he would likely call (80%) or raise (20%). If he calls, I have a 20% chance of winning (if the public card is a Queen), 40% chance of losing (if the public card is a King or Jack), and 40% chance of a draw (if the public card is a Queen). If he raises, I have a 20% chance of winning, 40% chance of losing, and 40% chance of a draw.\n- If board_game_expert holds a Queen (20% probability), he would likely call (70%) or raise (30%). If he calls, I have a 20% chance of winning (if the public card is a King), 20% chance of losing (if the public card is a Queen), and 60% chance of a draw (if the public card is a King or Jack). If he raises, I have a 20% chance of winning, 20% chance of losing, and 60% chance of a draw.\n- If board_game_expert holds a Jack (40% probability), he would likely call (80%) or raise (20%). If he calls, I have a 40% chance of winning (if the public card is a King or Queen), 20% chance of losing (if the public card is a Jack), and 40% chance of a draw (if the public card is a King or Queen). If he raises, I have a 40% chance of winning, 20% chance of losing, and 40% chance of a draw.\n- Overall, the winning rate for Plan 2 is 28%, the losing rate is 28%, and the draw rate is 44%.\n\nPlan 3: Fold\n- If I fold, I automatically lose the game. Therefore, the winning rate for Plan 3 is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips (half of the total pot of 6 chips). If I lose, the losing payoff would be 3 chips.\n- Plan 2: If I win, the winning payoff would be 5 chips (half of the total pot of 10 chips). If I lose, the losing payoff would be 5 chips.\n- Plan 3: If I fold, there is no payoff.\n\nThe estimated expected chips gain for each plan:\n- Plan 1: 28% * 3 chips - 28% * 3 chips = 0 chips\n- Plan 2: 28% * 5 chips - 28% * 5 chips = 0 chips\n- Plan 3: 0% * 0 chips - 100% * 2 chips = -2 chips\n\nPlan Selection:\n- Plan 1 and Plan 2 both have an estimated expected chips gain of 0 chips, while Plan 3 has an estimated expected chips loss of 2 chips. Therefore, Plan 1 and Plan 2 are ranked higher than Plan 3. Considering the strategy improvement, I should select Plan 2 (raise) to maximize potential winnings when I hold a Queen and the public card is a Queen."}}
{"message": "", "3_2": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (69.23% chance), he will likely call (70%) or raise (30%). If he calls, I will likely lose (2/5 chance the public card is a King). If he raises, I will likely lose (2/5 chance the public card is a King).\n- If board_game_expert holds a Queen (30.77% chance), he will likely call (60%) or raise (40%). If he calls, I will likely win (1/5 chance the public card is a Queen) or draw (1/5 chance the public card is a Queen). If he raises, I will likely win (1/5 chance the public card is a Queen) or draw (1/5 chance the public card is a Queen).\n- Overall, my winning rate for Plan 1 is (0.3077 * 0.2) = 6.15%, my losing rate is (0.6923 * 0.4) = 27.69%, and my draw rate is (0.3077 * 0.2) = 6.15%.\n\nPlan 2: Fold\n- If I fold, I will lose the round and forfeit any chips I have already put into the pot. Therefore, my losing rate for Plan 2 is 100%.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (currently 10 chips, so 5 chips). If I lose, the losing payoff would be half of the total pot (currently 10 chips, so 5 chips).\n- Plan 2: If I lose (which is certain if I fold), the losing payoff would be the number of chips I have already put into the pot (currently 6 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = winning rate * Winning Payoff - losing rate * Losing Payoff = 6.15% * 5 chips - 27.69% * 5 chips = -1.077 chips\n- Plan 2: Expected Chips Gain = -100% * 6 chips = -6 chips\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain (-1.077 chips) than Plan 2 (-6 chips). Therefore, I should choose Plan 1: Call."}}
{"message": "", "3_4": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (25% probability), he would likely call (70%) or raise (30%). If he calls, I would lose (probability = 25% * 70% = 17.5%). If he raises, I would also lose (probability = 25% * 30% = 7.5%).\n- If board_game_expert holds a Queen (55% probability), he would likely raise (80%) or call (20%). If he raises or calls, it would be a draw (probability = 55% * 100% = 55%).\n- If board_game_expert holds a Jack (20% probability), he would likely call (80%) or raise (20%). If he calls or raises, I would win (probability = 20% * 100% = 20%).\n\nPlan 2: Check\n- If board_game_expert holds a King (25% probability), he would likely call (70%) or raise (30%). If he calls, I would lose (probability = 25% * 70% = 17.5%). If he raises, I would also lose (probability = 25% * 30% = 7.5%).\n- If board_game_expert holds a Queen (55% probability), he would likely raise (80%) or call (20%). If he raises or calls, it would be a draw (probability = 55% * 100% = 55%).\n- If board_game_expert holds a Jack (20% probability), he would likely call (80%) or raise (20%). If he calls or raises, I would win (probability = 20% * 100% = 20%).\n\nPlan 3: Fold\n- If I fold, I would lose regardless of what card board_game_expert holds.\n\nThe number of payoffs for each plan:\n- Plan 1: After the action, all chips in the pot would be 16. If I win, the winning payoff would be 8. If I lose, the losing payoff would be 8.\n- Plan 2: After the action, all chips in the pot would be 12. If I win, the winning payoff would be 6. If I lose, the losing payoff would be 6.\n- Plan 3: After the action, all chips in the pot would be 12. If I lose, the losing payoff would be 6.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 20% * 8 - 25% * 8 = 1.6 - 2 = -0.4\n- Plan 2: Expected Chips Gain = 20% * 6 - 25% * 6 = 1.2 - 1.5 = -0.3\n- Plan 3: Expected Chips Gain = -25% * 6 = -1.5\n\nPlan Selection:\n- Plan 1: -0.4\n- Plan 2: -0.3\n- Plan 3: -1.5\n\nBased on the estimated expected chips gains, Plan 2 (Check) would be the best strategy to follow in this situation."}}
{"message": "", "4_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, he will likely raise (80% probability) or call (20% probability). If he raises, I will likely lose (80% probability) or draw (20% probability). If he calls, I will likely lose (60% probability) or draw (40% probability). Overall, my winning rate is 0%, losing rate is 70%, and drawing rate is 30%.\n- If board_game_expert holds a Queen, he will likely call (60% probability) or raise (40% probability). If he raises, I will likely lose (60% probability) or draw (40% probability). If he calls, I will likely lose (50% probability) or draw (50% probability). Overall, my winning rate is 0%, losing rate is 55%, and drawing rate is 45%.\n- If board_game_expert holds a Jack, he will likely call (70% probability) or fold (30% probability). If he folds, I will win (100% probability). If he calls, I will likely draw (100% probability). Overall, my winning rate is 30%, losing rate is 0%, and drawing rate is 70%.\n\nPlan 2: Raise\n- If board_game_expert holds a King, he will likely raise (70% probability) or call (30% probability). If he raises, I will likely lose (80% probability) or draw (20% probability). If he calls, I will likely lose (60% probability) or draw (40% probability). Overall, my winning rate is 0%, losing rate is 75%, and drawing rate is 25%.\n- If board_game_expert holds a Queen, he will likely call (70% probability) or fold (30% probability). If he folds, I will win (100% probability). If he calls, I will likely lose (50% probability) or draw (50% probability). Overall, my winning rate is 30%, losing rate is 35%, and drawing rate is 35%.\n- If board_game_expert holds a Jack, he will likely fold (60% probability) or call (40% probability). If he folds, I will win (100% probability). If he calls, I will likely draw (100% probability). Overall, my winning rate is 60%, losing rate is 0%, and drawing rate is 40%.\n\nPlan 3: Fold\n- If I fold, I will lose all the chips I have put in the pot. My winning rate is 0%, losing rate is 100%, and drawing rate is 0%.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips. If I lose, the losing payoff would be 2 chips.\n- Plan 2: If I win, the winning payoff would be 7 chips. If I lose, the losing payoff would be 6 chips.\n- Plan 3: If I lose, the losing payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0% * 3 - 70% * 2 = -1.4 chips\n- Plan 2: Expected Chips Gain = 30% * 7 - 35% * 6 = -0.3 chips\n- Plan 3: Expected Chips Gain = 0% * 0 - 100% * 2 = -2 chips\n\nPlan Selection:\n- Plan 1: -1.4 chips\n- Plan 2: -0.3 chips\n- Plan 3: -2 chips\n\nThe rank of estimated expected chips gains for every plan is Plan 2 > Plan 1 > Plan 3. Therefore, I should choose Plan 2: Raise."}}
{"message": "", "4_2": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (63.6% probability), he will likely raise (70% probability) or call (30% probability) 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 it's a Jack) or losing (if it's a Queen).\n- If board_game_expert holds a Queen (36.4% probability), he will likely raise (40% probability) or call (60% probability) 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 it's a Jack) or losing (if it's a King).\n- Overall, the winning rate for Plan 1 is (0.636 * 0.5 * 0.5) + (0.364 * 0.5 * 0.5) = 0.25, the losing rate is (0.636 * 0.5 * 0.5) + (0.364 * 0.5 * 0.5) = 0.25, and the draw rate is 0.5.\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of what card board_game_expert holds or what the public card is. Therefore, the winning rate for Plan 2 is 0, the losing rate is 1, and the draw rate is 0.\n\nPayoffs for Each Plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot, which is (6+4)/2 = 5 chips. If I lose, the losing payoff would be half of the total pot, which is (6+4)/2 = 5 chips.\n- Plan 2: If I fold, I will lose the game and the losing payoff would be half of the total pot, which is (6+4)/2 = 5 chips.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is winning rate * winning payoff - losing rate * losing payoff = 0.25 * 5 - 0.25 * 5 = 0 chips.\n- Plan 2: The expected chips gain is winning rate * winning payoff - losing rate * losing payoff = 0 * 5 - 1 * 5 = -5 chips.\n\nPlan Selection:\n- Plan 1 has an expected chips gain of 0, while Plan 2 has an expected chips gain of -5. Therefore, Plan 1 is the better strategy."}}
{"message": "", "4_4": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (30% probability), he would likely call (60% probability) or fold (40% probability). If he calls, I would lose (100% probability). If he folds, I would win (100% probability).\n- If board_game_expert holds a Queen (70% probability), he would likely call (50% probability) or fold (50% probability). If he calls, I would lose (100% probability). If he folds, I would win (100% probability).\n- Overall, the winning rate for plan 1 is 45% (30% * 100% + 70% * 50%), the losing rate is 55% (30% * 100% + 70% * 50%), and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I would lose (100% probability) regardless of what card board_game_expert holds.\n- Overall, the winning rate for plan 2 is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If board_game_expert holds a King (30% probability), he would likely raise (90% probability) or check (10% probability). If he raises, I would lose (100% probability). If he checks, I would lose (100% probability).\n- If board_game_expert holds a Queen (70% probability), he would likely raise (80% probability) or check (20% probability). If he raises, I would lose (100% probability). If he checks, I would lose (100% probability).\n- Overall, the winning rate for plan 3 is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 6 chips (half of the total pot). If I lose, the losing payoff would be 6 chips.\n- Plan 2: If I lose, the losing payoff would be 6 chips.\n- Plan 3: If I lose, the losing payoff would be 6 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is 45% * 6 chips - 55% * 6 chips = -0.6 chips.\n- Plan 2: The expected chips loss is 100% * 6 chips = -6 chips.\n- Plan 3: The expected chips loss is 100% * 6 chips = -6 chips.\n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 1 > Plan 2 = Plan 3.\n- Therefore, I should select Plan 1 (Raise) as it has the highest estimated expected chips gain."}}
{"message": "", "5_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (33.33% chance), he will likely raise (100% chance). If the public card is a King, I will win (100% chance). If the public card is not a King, I will win (50% chance) or draw (50% chance).\n- If board_game_expert holds a Queen (33.33% chance), he will likely raise (100% chance). If the public card is a Queen, I will lose (100% chance). If the public card is not a Queen, I will win (100% chance).\n- If board_game_expert holds a Jack (33.33% chance), he will likely raise (100% chance). If the public card is a Jack, I will lose (100% chance). If the public card is not a Jack, I will win (100% chance).\n- Overall, the winning rate for Plan 1 is 66.67%, the losing rate is 33.33%, and the drawing rate is 0%.\n\nPlan 2: Raise\n- If board_game_expert holds a King (33.33% chance), he will likely call (100% chance). If the public card is a King, I will win (100% chance). If the public card is not a King, I will win (50% chance) or draw (50% chance).\n- If board_game_expert holds a Queen (33.33% chance), he will likely call (100% chance). If the public card is a Queen, I will lose (100% chance). If the public card is not a Queen, I will win (100% chance).\n- If board_game_expert holds a Jack (33.33% chance), he will likely call (100% chance). If the public card is a Jack, I will lose (100% chance). If the public card is not a Jack, I will win (100% chance).\n- Overall, the winning rate for Plan 2 is 66.67%, the losing rate is 33.33%, and the drawing rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose 100% of the time.\n\nPayoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips (half of the total pot of 6 chips). If I lose, the losing payoff would be 2 chips (half of the total pot of 4 chips).\n- Plan 2: If I win, the winning payoff would be 4 chips (half of the total pot of 8 chips). If I lose, the losing payoff would be 3 chips (half of the total pot of 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 = 66.67% * 3 chips - 33.33% * 2 chips = 1.33 chips\n- Plan 2: Expected Chips Gain = 66.67% * 4 chips - 33.33% * 3 chips = 1.67 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain, so I should choose Plan 2: Raise."}}
{"message": "", "5_2": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (33% probability), he will call (100% probability). Since we both hold a King and the public card is a King, it will be a draw. \n- If board_game_expert holds a Queen (33% probability), he will call (100% probability). Since I hold a King and the public card is a King, I will win. \n- If board_game_expert holds a Jack (33% probability), he will call (100% probability). Since I hold a King and the public card is a King, I will win. \n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card board_game_expert holds. \n\nPlan 3: Check\n- If board_game_expert holds a King (33% probability), he will raise (100% probability). Since we both hold a King and the public card is a King, it will be a draw. \n- If board_game_expert holds a Queen (33% probability), he will raise (100% probability). Since I hold a King and the public card is a King, I will win. \n- If board_game_expert holds a Jack (33% probability), he will raise (100% probability). Since I hold a King and the public card is a King, I will win. \n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (8 chips). If I lose, the losing payoff would be half of the total pot (8 chips).\n- Plan 2: If I lose, the losing payoff would be half of the total pot (4 chips).\n- Plan 3: If I win, the winning payoff would be half of the total pot (8 chips). If I lose, the losing payoff would be half of the total pot (8 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.66 * 8 - 0 * 8 = 5.28 chips\n- Plan 2: Expected Chips Gain = 0 * 4 - 1 * 4 = -4 chips\n- Plan 3: Expected Chips Gain = 0.66 * 8 - 0 * 8 = 5.28 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 have the highest expected chips gain (5.28 chips), while Plan 2 has the lowest expected chips gain (-4 chips). Therefore, I should either raise (Plan 1) or check (Plan 3). Since raising can potentially lead to a higher total pot, I will choose Plan 1: Raise."}}
{"message": "", "5_4": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (33.3% chance), he will call (100% chance). This will result in a draw as we both have a pair of Kings. \n- If board_game_expert holds a Queen (33.3% chance), he will call (100% chance). This will result in a win for me as my pair of Kings beats his high card Queen.\n- If board_game_expert holds a Jack (33.3% chance), he will call (100% chance). This will result in a win for me as my pair of Kings beats his high card Jack.\n\nPlan 2: Fold\n- If I fold, I will automatically lose the game regardless of what card board_game_expert holds. \n\nPayoffs for each plan:\nPlan 1: After the action, all chips in the pot would be 24. If I win, the winning payoff would be 12. If I lose, the lose payoff would be 12.\nPlan 2: After the action, all chips in the pot would be 20. If I lose, the lose payoff would be 10.\n\nExpected Chips Gain for Each Plan:\nPlan 1: Expected Chips Gain = (66.6% * 12) - (0% * 12) = 8\nPlan 2: Expected Chips Gain = (0% * 0) - (100% * 10) = -10\n\nPlan Selection:\nPlan 1 has the highest expected chips gain, so I should choose to call."}}
{"message": "", "6_1": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, he will likely raise (100% probability). If the public card is a King, I will win (100% probability). If the public card is not a King, I will lose (66.67% probability) or draw (33.33% probability).\n- If board_game_expert holds a Queen or Jack, he will likely raise (100% probability). If the public card is a King, I will win (100% probability). If the public card is not a King, I will lose (66.67% probability).\n- Overall, the winning rate for Plan 1 is 33.33%, the losing rate is 66.67%, and the drawing rate is 0%.\n\nPlan 2: Raise\n- If board_game_expert holds a King, he will likely call (100% probability). If the public card is a King, I will win (100% probability). If the public card is not a King, I will lose (66.67% probability) or draw (33.33% probability).\n- If board_game_expert holds a Queen or Jack, he will likely call (100% probability). If the public card is a King, I will win (100% probability). If the public card is not a King, I will lose (66.67% probability).\n- Overall, the winning rate for Plan 2 is 33.33%, the losing rate is 66.67%, and the drawing rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose 100% of the time.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips. If I lose, the loss would be 2 chips.\n- Plan 2: If I win, the winning payoff would be 7 chips. If I lose, the loss would be 6 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 = 33.33% * 3 - 66.67% * 2 = -0.67 chips\n- Plan 2: Expected gain = 33.33% * 7 - 66.67% * 6 = -1.67 chips\n- Plan 3: Expected gain = -2 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I will choose Plan 1: Call."}}
{"message": "", "6_3": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (50% probability), he will call (100% probability). In this case, it will be a draw. \n- If board_game_expert holds a Jack (50% probability), he will call (100% probability). In this case, I will win. \nOverall, the winning rate for this plan is 50%, the losing rate is 0%, and the draw rate is 50%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card board_game_expert holds. \nOverall, 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 board_game_expert holds a King (50% probability), he will check (100% probability). In this case, it will be a draw. \n- If board_game_expert holds a Jack (50% probability), he will check (100% probability). In this case, I will win. \nOverall, the winning rate for this plan is 50%, the losing rate is 0%, and the draw rate is 50%.\n\nThe number of payoffs for each plan:\n- Plan 1: After the action, all chips in the pot would be 12. If win, the winning payoff would be 6. If lose, the lose payoff would be 6.\n- Plan 2: After the action, all chips in the pot would be 8. If lose, the lose payoff would be 4.\n- Plan 3: After the action, all chips in the pot would be 8. If win, the winning payoff would be 4. If lose, the lose payoff would be 4.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 50% * 6 - 0% * 6 = 3\n- Plan 2: Expected Chips Gain = 0% * 4 - 100% * 4 = -4\n- Plan 3: Expected Chips Gain = 50% * 4 - 0% * 4 = 2\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows:\n1. Plan 1: Raise\n2. Plan 3: Check\n3. Plan 2: Fold\n\nTherefore, the plan with the highest estimated expected chips gain is Plan 1: Raise."}}
{"message": "", "6_5": {"plan": "Plan 1: Call\n- If board_game_expert holds a Queen (80% probability), he will call (100% probability). I will lose as his Queen matches the public card. \n- If board_game_expert holds a King (10% probability), he will call (100% probability). I will win as my King is higher than the public card.\n- If board_game_expert holds a Jack (10% probability), he will call (100% probability). I will win as my King is higher than the public card and Jack.\n\nPlan 2: Fold\n- If I fold, I will lose the chips I have already put in the pot, but I will not lose any more chips. \n\nThe number of payoffs for each plan:\nPlan 1: After the action, all chips in the pot: If win, the winning payoff would be 12 chips (half of the total pot). If lose, the lose payoff would be 12 chips (half of the total pot).\nPlan 2: After the action, all chips in the pot: If fold, I will lose the 12 chips I have already put in the pot.\n\nEstimate Expected Chips Gain for Each Plan:\nPlan 1: Expected Chips Gain = 0.2 * 12 - 0.8 * 12 = -7.2 chips\nPlan 2: Expected Chips Gain = -12 chips\n\nPlan Selection:\nPlan 1 has a higher expected chips gain (-7.2 chips) than Plan 2 (-12 chips). Therefore, I should choose Plan 1: Call."}}
{"message": "", "7_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, he will raise with 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. The winning rate is 0%, the losing rate is 66.67%, and the draw rate is 33.33%.\n- If board_game_expert holds a Queen, he will raise with 70% probability and call with 30% probability. If the public card is a King, I will win. If the public card is a Queen or Jack, it will be a draw. The winning rate is 33.33%, the losing rate is 0%, and the draw rate is 66.67%.\n- If board_game_expert holds a Jack, he will raise with 50% probability and call with 50% probability. If the public card is a King or Queen, I will win. If the public card is a Jack, it will be a draw. The winning rate is 66.67%, the losing rate is 0%, and the draw rate is 33.33%.\n\nPlan 2: Raise\n- If board_game_expert holds a King, he will call with 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. The winning rate is 0%, the losing rate is 66.67%, and the draw rate is 33.33%.\n- If board_game_expert holds a Queen, he will call with 100% probability. If the public card is a King, I will win. If the public card is a Queen or Jack, it will be a draw. The winning rate is 33.33%, the losing rate is 0%, and the draw rate is 66.67%.\n- If board_game_expert holds a Jack, he will call with 100% probability. If the public card is a King or Queen, I will win. If the public card is a Jack, it will be a draw. The winning rate is 66.67%, the losing rate is 0%, and the draw rate is 33.33%.\n\nPlan 3: Fold\n- If I fold, I will lose 1 chip regardless of what card board_game_expert holds or what the public card is. The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips. If I lose, the losing payoff would be 1 chip.\n- Plan 2: If I win, the winning payoff would be 7 chips. If I lose, the losing payoff would be 3 chips.\n- Plan 3: If I fold, the losing payoff would be 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 33.33% * 3 - 66.67% * 1 = 0 chips\n- Plan 2: Expected Chips Gain = 33.33% * 7 - 66.67% * 3 = -6.67 chips\n- Plan 3: Expected Chips Gain = -1 chip\n\nPlan Selection:\n- Plan 1: 0 chips\n- Plan 2: -6.67 chips\n- Plan 3: -1 chip\n\nBased on the estimated expected chips gain, Plan 1 (Call) is the best strategy to use in this situation."}}
{"message": "", "7_2": {"plan": "Plan 1: Raise\n- If board_game_expert holds a Jack (70% probability), he will call (100% probability). I will lose (0% probability), win (0% probability), or draw (100% probability). \n- If board_game_expert holds a Queen (15% probability), he will call (100% probability). I will lose (0% probability), win (100% probability), or draw (0% probability).\n- If board_game_expert holds a King (15% probability), he will call (100% probability). I will lose (100% probability), win (0% probability), or draw (0% probability).\n- Overall winning rate for Plan 1: 0.15, overall losing rate for Plan 1: 0.15, overall draw rate for Plan 1: 0.7.\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of what card board_game_expert holds. \n- Overall winning rate for Plan 2: 0, overall losing rate for Plan 2: 1, overall draw rate for Plan 2: 0.\n\nPlan 3: Check\n- If board_game_expert holds a Jack (70% probability), he will check (100% probability). I will lose (0% probability), win (0% probability), or draw (100% probability). \n- If board_game_expert holds a Queen (15% probability), he will check (100% probability). I will lose (0% probability), win (100% probability), or draw (0% probability).\n- If board_game_expert holds a King (15% probability), he will check (100% probability). I will lose (100% probability), win (0% probability), or draw (0% probability).\n- Overall winning rate for Plan 3: 0.15, overall losing rate for Plan 3: 0.15, overall draw rate for Plan 3: 0.7.\n\nThe number of payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 6 chips. If lose, the losing payoff would be 6 chips.\n- Plan 2: If lose, the losing payoff would be 2 chips.\n- Plan 3: If win, the winning payoff would be 4 chips. If lose, the losing payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0.15 * 6 - 0.15 * 6 = 0 chips\n- Plan 2: 0 * 0 - 1 * 2 = -2 chips\n- Plan 3: 0.15 * 4 - 0.15 * 4 = 0 chips\n\nPlan Selection:\n- Plan 1: 0 chips\n- Plan 2: -2 chips\n- Plan 3: 0 chips\n\nBased on the estimated expected chips gain, Plan 1 and Plan 3 are the best strategies to follow. However, considering the strategy improvement, Plan 1 (Raise) would be the best strategy to follow as it could potentially confuse board_game_expert and make him believe that I hold a King."}}
{"message": "", "8_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a Queen (50% probability), he will likely call (60%) or raise (40%). If he calls, the pot will be 4 chips and if he raises, the pot will be 8 chips. If the public card is a King, I will win (probability 1). If the public card is a Queen or Jack, I will win (probability 0.5) or draw (probability 0.5).\n- If board_game_expert holds a Jack (50% probability), he will likely call (70%) or raise (30%). If he calls, the pot will be 4 chips and if he raises, the pot will be 8 chips. If the public card is a King, I will win (probability 1). If the public card is a Queen, I will win (probability 0.5) or lose (probability 0.5). If the public card is a Jack, I will win (probability 0.5) or draw (probability 0.5).\n\nPlan 2: Raise\n- If board_game_expert holds a Queen (50% probability), he will likely call (70%) or fold (30%). If he calls, the pot will be 10 chips and if he folds, the pot will be 6 chips. If the public card is a King, I will win (probability 1). If the public card is a Queen or Jack, I will win (probability 0.5) or draw (probability 0.5).\n- If board_game_expert holds a Jack (50% probability), he will likely fold (60%) or call (40%). If he folds, the pot will be 6 chips and if he calls, the pot will be 10 chips. If the public card is a King, I will win (probability 1). If the public card is a Queen, I will win (probability 0.5) or lose (probability 0.5). If the public card is a Jack, I will win (probability 0.5) or draw (probability 0.5).\n\nPlan 3: Fold\n- If I fold, I will lose the 2 chips I have already put in the pot.\n\nThe number of payoffs for each plan:\n- Plan 1: If win, the winning payoff would be half of the pot (2 or 4 chips). If lose, the lose payoff would be half of the pot (2 or 4 chips).\n- Plan 2: If win, the winning payoff would be half of the pot (3 or 5 chips). If lose, the lose payoff would be half of the pot (3 or 5 chips).\n- Plan 3: If lose, the lose payoff would be 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.5 * (2 or 4 chips) - 0.5 * (2 or 4 chips) = 0 or 0 chips\n- Plan 2: Expected Chips Gain = 0.5 * (3 or 5 chips) - 0.5 * (3 or 5 chips) = 0 or 0 chips\n- Plan 3: Expected Chips Gain = -1 chip\n\nPlan Selection:\n- Plan 1 and Plan 2 both have an expected chips gain of 0, while Plan 3 has a negative expected chips gain. Therefore, Plan 1 and Plan 2 are ranked higher than Plan 3. Considering the strategy improvement, Plan 2 (Raise) is selected as it applies more pressure on board_game_expert and has a higher potential payoff."}}
{"message": "", "8_2": {"plan": "Make Reasonable Plans:\n\nPlan 1: Raise\n- This is a strong move as I have a pair of Kings, which is the highest possible combination in Leduc Hold'em. This could potentially pressure board_game_expert into folding if he has a weaker hand.\n\nPlan 2: Check\n- This is a more conservative move, which could potentially lead board_game_expert to believe that I have a weaker hand than I actually do. This could potentially lead him to raise, allowing me to win more chips.\n\nPlan 3: Fold\n- This is the least favorable move as I have a strong hand. However, it could potentially confuse board_game_expert and make him less certain about my game pattern.\n\nPotential board_game_expert's actions (if release) and Estimate Winning/Lose/Draw Rate for Each Plan:\n\nPlan 1: Raise\n- If board_game_expert holds a King, he would likely raise (70% probability), leading to a draw.\n- If he holds a Queen or a Jack, he would likely fold (60% probability for Queen, 80% probability for Jack), leading to a win for me.\n\nPlan 2: Check\n- If board_game_expert holds a King, he would likely raise (70% probability), leading to a draw.\n- If he holds a Queen or a Jack, he would likely call (40% probability for Queen, 20% probability for Jack), leading to a win for me.\n\nPlan 3: Fold\n- If board_game_expert holds a King, Queen, or Jack, he would likely call (100% probability), leading to a loss for me.\n\nThe number of payoffs for each plan:\n\nPlan 1: Raise\n- If win, the winning payoff would be half of the total pot, which would be 8 chips.\n- If lose, the lose payoff would be half of the total pot, which would be 8 chips.\n\nPlan 2: Check\n- If win, the winning payoff would be half of the total pot, which would be 4 chips.\n- If lose, the lose payoff would be half of the total pot, which would be 4 chips.\n\nPlan 3: Fold\n- If win, the winning payoff would be half of the total pot, which would be 0 chips.\n- If lose, the lose payoff would be half of the total pot, which would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n\nPlan 1: Raise\n- Expected Chips Gain = Winning rate * Winning Payoff - Lose rate * Lose Payoff = (0.7 * 8) - (0.3 * 8) = 5.6 - 2.4 = 3.2 chips\n\nPlan 2: Check\n- Expected Chips Gain = Winning rate * Winning Payoff - Lose rate * Lose Payoff = (0.6 * 4) - (0.4 * 4) = 2.4 - 1.6 = 0.8 chips\n\nPlan 3: Fold\n- Expected Chips Gain = Winning rate * Winning Payoff - Lose rate * Lose Payoff = (0 * 0) - (1 * 4) = -4 chips\n\nPlan Selection:\n\nBased on the estimated expected chips gains, the ranking of the plans is as follows:\n1. Plan 1: Raise\n2. Plan 2: Check\n3. Plan 3: Fold\n\nTherefore, the best plan to execute would be Plan 1: Raise."}}
{"message": "", "8_4": {"plan": "Plan 1: Call\n- If board_game_expert holds a Queen (70% probability), he will likely fold (60% probability). I will win the game (probability = 0.7 * 0.6 = 0.42).\n- If board_game_expert holds a Jack (30% probability), he will likely fold (80% probability). I will win the game (probability = 0.3 * 0.8 = 0.24).\n- Overall, the winning rate for Plan 1 is 0.42 + 0.24 = 0.66 (66%), the losing rate is 0, and the draw rate is 0.\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of what card board_game_expert holds. The losing rate for Plan 2 is 100%, and the winning and draw rates are both 0.\n\nPayoffs for Each Plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (12 + 8) / 2 = 10 chips. If I lose, the losing payoff would be 0 chips.\n- Plan 2: If I fold, I will lose the 12 chips I have already put into the pot.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = winning rate * Winning Payoff - losing rate * Losing Payoff = 0.66 * 10 - 0 * 0 = 6.6 chips.\n- Plan 2: Expected Chips Gain = winning rate * Winning Payoff - losing rate * Losing Payoff = 0 * 10 - 1 * 12 = -12 chips.\n\nPlan Selection:\n- The estimated expected chips gains for Plan 1 and Plan 2 are 6.6 chips and -12 chips respectively. Therefore, Plan 1 (Call) is the better strategy as it has the highest estimated expected chips gain."}}
{"message": "", "9_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, he will likely raise (80%) or call (20%). If he raises, I will lose as my Jack is lower than his King. If he calls, it's a draw as we both have the same amount of chips in the pot. The overall winning rate for this plan is 0%, the losing rate is 80%, and the draw rate is 20%.\n- If board_game_expert holds a Queen, he will likely raise (60%) or call (40%). If he raises, I will lose as my Jack is lower than his Queen. If he calls, it's a draw as we both have the same amount of chips in the pot. The overall winning rate for this plan is 0%, the losing rate is 60%, and the draw rate is 40%.\n- If board_game_expert holds a Jack, he will likely call (70%) or raise (30%). If he raises, it's a draw as we both have the same amount of chips in the pot. If he calls, it's a draw as we both have the same amount of chips in the pot. The overall winning rate for this plan is 0%, the losing rate is 0%, and the draw rate is 100%.\n\nPlan 2: Raise\n- If board_game_expert holds a King, 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, I will win as I have more chips in the pot. The overall winning rate for this plan is 30%, the losing rate is 70%, and the draw rate is 0%.\n- If board_game_expert holds a Queen, he will likely call (70%) or raise (30%). If he raises, I will lose as my Jack is lower than his Queen. If he calls, I will win as I have more chips in the pot. The overall winning rate for this plan is 70%, the losing rate is 30%, and the draw rate is 0%.\n- If board_game_expert holds a Jack, he will likely call (80%) or fold (20%). If he folds, I will win as he has no chips in the pot. If he calls, it's a draw as we both have the same amount of chips in the pot. The overall winning rate for this plan is 20%, the losing rate is 0%, and the draw rate is 80%.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of what card board_game_expert holds. The overall winning rate for this plan is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 0 chips. If I lose, the losing payoff would be 1 chip.\n- Plan 2: If I win, the winning payoff would be 2 chips. If I lose, the losing payoff would be 2 chips.\n- Plan 3: If I win, the winning payoff would be 0 chips. If I lose, the losing payoff would be 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0% * 0 chips - 70% * 1 chip = -0.7 chips\n- Plan 2: Expected Chips Gain = 40% * 2 chips - 33.3% * 2 chips = 0.13 chips\n- Plan 3: Expected Chips Gain = 0% * 0 chips - 100% * 1 chip = -1 chip\n\nPlan Selection:\nBased on the estimated expected chips gain, the ranking of the plans from best to worst is Plan 2, Plan 1, Plan 3. Therefore, the best plan to execute in this situation is Plan 2: Raise."}}
{"message": "", "9_2": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (20% probability), he would likely raise (60%) or call (40%). If he raises, I would lose as his King is higher than my Jack. If he calls, the game would proceed to the next round and the outcome would depend on the next public card. The overall winning rate for this plan is 0%, the losing rate is 60%, and the draw rate is 40%.\n- If board_game_expert holds a Queen (47% probability), he would likely call (80%) or fold (20%). If he calls, the game would proceed to the next round and the outcome would depend on the next public card. If he folds, I would win. The overall winning rate for this plan is 20%, the losing rate is 0%, and the draw rate is 80%.\n- If board_game_expert holds a Jack (33% probability), he would likely fold (60%) or call (40%). If he folds, I would win. If he calls, the game would proceed to the next round and the outcome would depend on the next public card. The overall winning rate for this plan is 60%, the losing rate is 0%, and the draw rate is 40%.\n\nPlan 2: Fold\n- If I fold, I would lose the game immediately. 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 I check, the game would proceed to the next round and the outcome would depend on the next public card and board_game_expert's action. The overall winning rate for this plan is uncertain, the losing rate is uncertain, and the draw rate is uncertain.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips (half of the total pot). If I lose, the losing payoff would be 4 chips.\n- Plan 2: If I lose, the losing payoff would be 4 chips.\n- Plan 3: The payoff would depend on the next public card and board_game_expert's action.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.2 * 4 - 0.6 * 4 = -1.6 chips\n- Plan 2: Expected Chips Gain = 0 * 4 - 1 * 4 = -4 chips\n- Plan 3: Expected Chips Gain is uncertain.\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain (-1.6 chips), followed by Plan 3 (uncertain), and Plan 2 (-4 chips). Therefore, I should select Plan 1: Raise."}}
{"message": "", "9_4": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (15% probability), he will likely raise (60%) or call (40%). If he raises, I will lose as his King pairs with the public card. If he calls, I will also lose as his King is higher than my Jack. So, the winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n- If board_game_expert holds a Queen (31% probability), he will likely fold (60%) or call (40%). If he folds, I will win. If he calls, I will lose as his Queen is higher than my Jack. So, the winning rate is 60%, losing rate is 40%, and draw rate is 0%.\n- If board_game_expert holds a Jack (54% probability), he will likely fold (60%) or call (40%). If he folds, I will win. If he calls, it will be a draw as we both hold a Jack. So, the winning rate is 60%, losing rate is 0%, and draw rate is 40%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card board_game_expert holds. So, the winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n\nThe number of payoffs for each plan:\n- Plan 1: After the action, all chips in the pot would be 20. If win, the winning payoff would be 10. If lose, the lose payoff would be 10.\n- Plan 2: After the action, all chips in the pot would be 12. If lose, the lose payoff would be 6.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.15 * 0 - 1 * 0.15 * 10 + 0.31 * 0.6 * 10 - 0.4 * 0.31 * 10 + 0.54 * 0.6 * 10 - 0 * 0.54 * 10 = -1.5 + 1.86 + 3.24 = 3.6\n- Plan 2: Expected Chips Gain = -1 * 6 = -6\n\nPlan Selection:\n- Plan 1 has an expected chips gain of 3.6, and Plan 2 has an expected chips gain of -6. Therefore, Plan 1 (Call) is the better strategy."}}
{"message": "", "10_1": {"plan": "Plan 1: Raise\n- If board_game_expert holds a Jack (probability 63.64%), he will likely fold (probability 40%) or call (probability 60%). If he folds, I win and the payoff would be half of the total pot (3 chips). If he calls, I still win unless the public card is a Jack. The winning rate is 80%, the losing rate is 20%, and the draw rate is 0%.\n- If board_game_expert holds a Queen (probability 36.36%), he will likely call (probability 80%) or fold (probability 20%). If he folds, I win and the payoff would be half of the total pot (3 chips). If he calls, I win unless the public card is a Queen. The winning rate is 70%, the losing rate is 30%, and the draw rate is 0%.\n- Overall, the winning rate for Plan 1 is (0.6364 * 0.8) + (0.3636 * 0.7) = 0.7455, the losing rate is (0.6364 * 0.2) + (0.3636 * 0.3) = 0.2545, and the draw rate is 0.\n\nPlan 2: Fold\n- If I fold, I lose regardless of what card board_game_expert holds. The losing rate is 100%, and the payoff would be half of the total pot (3 chips).\n\nPlan 3: Check\n- If board_game_expert holds a Jack (probability 63.64%), he will likely call (probability 60%) or raise (probability 40%). If he raises, I can call and win unless the public card is a Jack. The winning rate is 80%, the losing rate is 20%, and the draw rate is 0%.\n- If board_game_expert holds a Queen (probability 36.36%), he will likely call (probability 70%) or raise (probability 30%). If he raises, I can call and win unless the public card is a Queen. The winning rate is 70%, the losing rate is 30%, and the draw rate is 0%.\n- Overall, the winning rate for Plan 3 is (0.6364 * 0.8) + (0.3636 * 0.7) = 0.7455, the losing rate is (0.6364 * 0.2) + (0.3636 * 0.3) = 0.2545, and the draw rate is 0.\n\nPayoffs for Each Plan:\n- Plan 1: If win, the winning payoff would be 3 chips. If lose, the losing payoff would be 3 chips.\n- Plan 2: If lose, the losing payoff would be 3 chips.\n- Plan 3: If win, the winning payoff would be 3 chips. If lose, the losing payoff would be 3 chips.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: 0.7455 * 3 - 0.2545 * 3 = 1.47 chips\n- Plan 2: -3 chips\n- Plan 3: 0.7455 * 3 - 0.2545 * 3 = 1.47 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 have the highest expected chips gain (1.47 chips), while Plan 2 has the lowest expected chips gain (-3 chips). Therefore, I should either raise (Plan 1) or check (Plan 3). Considering the strategy improvement, I should choose to raise (Plan 1) to put pressure on board_game_expert."}}
{"message": "", "11_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a Jack (54% probability), he will likely fold (60% probability) or call (40% probability). If he folds, I win. If he calls, the outcome will depend on the public card. If the public card is a Queen, I win. If the public card is a Jack, I lose. If the public card is a King, I win. \n- If board_game_expert holds a Queen (46% probability), he will likely call (50% probability) or fold (50% probability). If he folds, I win. If he calls, the outcome will depend on the public card. If the public card is a Queen, it's a draw. If the public card is a Jack or a King, I win. \n- Winning rate for Plan 1: 54% * 60% (he holds a Jack and folds) + 54% * 40% * 1/3 (he holds a Jack, calls, and the public card is a Queen or King) + 46% * 50% (he holds a Queen and folds) + 46% * 50% * 2/3 (he holds a Queen, calls, and the public card is a Jack or King) = 32.2% + 7.2% + 23% + 15.3% = 77.7%\n- Lose rate for Plan 1: 54% * 40% * 1/3 (he holds a Jack, calls, and the public card is a Jack) = 7.2%\n- Draw rate for Plan 1: 46% * 50% * 1/3 (he holds a Queen, calls, and the public card is a Queen) = 7.7%\n- Payoff for Plan 1: If win, the winning payoff would be 3 chips (half of the total pot). If lose, the lose payoff would be 2 chips (half of the total pot).\n- Expected chips gain for Plan 1: 77.7% * 3 - 7.2% * 2 = 2.32 - 0.14 = 2.18 chips\n\nPlan 2: Raise\n- If board_game_expert holds a Jack (54% probability), he will likely fold (60% probability) or call (40% probability). If he folds, I win. If he calls, the outcome will depend on the public card. If the public card is a Queen, I win. If the public card is a Jack, I lose. If the public card is a King, I win. \n- If board_game_expert holds a Queen (46% probability), he will likely fold (50% probability) or call (50% probability). If he folds, I win. If he calls, the outcome will depend on the public card. If the public card is a Queen, it's a draw. If the public card is a Jack or a King, I win. \n- Winning rate for Plan 2: 54% * 60% (he holds a Jack and folds) + 54% * 40% * 1/3 (he holds a Jack, calls, and the public card is a Queen or King) + 46% * 50% (he holds a Queen and folds) + 46% * 50% * 2/3 (he holds a Queen, calls, and the public card is a Jack or King) = 32.2% + 7.2% + 23% + 15.3% = 77.7%\n- Lose rate for Plan 2: 54% * 40% * 1/3 (he holds a Jack, calls, and the public card is a Jack) = 7.2%\n- Draw rate for Plan 2: 46% * 50% * 1/3 (he holds a Queen, calls, and the public card is a Queen) = 7.7%\n- Payoff for Plan 2: If win, the winning payoff would be 4 chips (half of the total pot). If lose, the lose payoff would be 3 chips (half of the total pot).\n- Expected chips gain for Plan 2: 77.7% * 4 - 7.2% * 3 = 3.1 - 0.22 = 2.88 chips\n\nPlan 3: Fold\n- If I fold, I automatically lose the game. \n- Winning rate for Plan 3: 0%\n- Lose rate for Plan 3: 100%\n- Draw rate for Plan 3: 0%\n- Payoff for Plan 3: If lose, the lose payoff would be 2 chips (half of the total pot).\n- Expected chips gain for Plan 3: -2 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain (2.88 chips), followed by Plan 1 (Call) with 2.18 chips, and Plan 3 (Fold) with -2 chips. Therefore, I should choose Plan 2 (Raise)."}}
{"message": "", "11_2": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (60% probability), he will likely call (70% probability) or raise (30% probability). If he calls, I will lose (as King is higher than Queen). If he raises, I will also lose. So, the overall losing rate for this plan is 60%.\n- If board_game_expert holds a Queen (30% probability), it will be a draw as we both hold the same card. So, the overall draw rate for this plan is 30%.\n- If board_game_expert holds a Jack (10% probability), he will likely fold (60% probability) or call (40% probability). If he folds, I will win. If he calls, I will also win (as Queen is higher than Jack). So, the overall winning rate for this plan is 10%.\n\nPlan 2: Fold\n- If I fold, regardless of what card board_game_expert holds, I will lose. So, the overall losing rate for this plan is 100%.\n\nThe number of payoffs for each plan:\n- Plan 1: After the action, all chips in the pot would be 10. If I win, the winning payoff would be 5 chips. If I lose, the losing payoff would be 5 chips.\n- Plan 2: After the action, all chips in the pot would be 10. If I lose, the losing payoff would be 5 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 10% * 5 - 60% * 5 = -2.5 chips\n- Plan 2: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 0% * 5 - 100% * 5 = -5 chips\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain (-2.5 chips) than Plan 2 (-5 chips). Therefore, I should choose Plan 1: Call."}}
{"message": "", "11_4": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (40% probability), he would likely call (60% probability) or fold (40% probability). If he calls, I would lose (probability = 40% * 60% = 24%). If he folds, I would win (probability = 40% * 40% = 16%).\n- If board_game_expert holds a Queen (30% probability), he would likely call (50% probability) or fold (50% probability). If he calls, it would be a draw (probability = 30% * 50% = 15%). If he folds, I would win (probability = 30% * 50% = 15%).\n- If board_game_expert holds a Jack (30% probability), he would likely fold (60% probability) or call (40% probability). If he folds, I would win (probability = 30% * 60% = 18%). If he calls, I would win (probability = 30% * 40% = 12%).\n- Overall, the winning rate for Plan 1 is 16% + 15% + 18% + 12% = 61%, the losing rate is 24%, and the draw rate is 15%.\n\nPlan 2: Fold\n- If I fold, I would lose regardless of what card board_game_expert holds. The losing rate for Plan 2 is 100%.\n\nPlan 3: Check\n- If board_game_expert holds a King (40% probability), he would likely raise (90% probability) or check (10% probability). If he raises, I would lose (probability = 40% * 90% = 36%). If he checks, I would lose (probability = 40% * 10% = 4%).\n- If board_game_expert holds a Queen (30% probability), he would likely raise (80% probability) or check (20% probability). If he raises, it would be a draw (probability = 30% * 80% = 24%). If he checks, it would be a draw (probability = 30% * 20% = 6%).\n- If board_game_expert holds a Jack (30% probability), he would likely raise (70% probability) or check (30% probability). If he raises, I would win (probability = 30% * 70% = 21%). If he checks, I would win (probability = 30% * 30% = 9%).\n- Overall, the winning rate for Plan 3 is 21% + 9% = 30%, the losing rate is 36% + 4% = 40%, and the draw rate is 24% + 6% = 30%.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (14 chips). If I lose, the losing payoff would be half of the total pot (14 chips).\n- Plan 2: If I lose, the losing payoff would be half of the total pot (12 chips).\n- Plan 3: If I win, the winning payoff would be half of the total pot (12 chips). If I lose, the losing payoff would be half of the total pot (12 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 61% * 14 - 24% * 14 = 5.18 chips\n- Plan 2: Expected Chips Gain = -100% * 12 = -12 chips\n- Plan 3: Expected Chips Gain = 30% * 12 - 40% * 12 = -1.2 chips\n\nPlan Selection:\n- Plan 1: 5.18 chips\n- Plan 2: -12 chips\n- Plan 3: -1.2 chips\n\nBased on the estimated expected chips gain, I should select Plan 1 (Raise) as it has the highest expected chips gain."}}
{"message": "", "12_1": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (12.5% probability), he will likely raise (70% probability) or call (30% probability). If he raises, I will likely lose unless the public card is a Jack. If he calls, I will likely win if the public card is a Jack, and lose if it's a King or Queen. \n- If board_game_expert holds a Queen (37.5% probability), he will likely call (70% probability) or fold (30% probability). If he calls, I will likely win if the public card is a Jack, and lose if it's a King or Queen. If he folds, I will win.\n- If board_game_expert holds a Jack (50% probability), he will likely fold (80% probability) or call (20% probability). If he folds, I will win. If he calls, it will be a draw unless the public card is a King or Queen, in which case I will lose.\n\nPlan 2: Fold\n- If I fold, I will lose the current pot, but I will not lose any additional chips. This is a safe strategy, but it does not give me a chance to win the current game.\n\nPlan 3: Check\n- If board_game_expert holds a King (12.5% probability), he will likely raise (80% probability) or call (20% probability). If he raises, I will likely lose unless the public card is a Jack. If he calls, I will likely win if the public card is a Jack, and lose if it's a King or Queen. \n- If board_game_expert holds a Queen (37.5% probability), he will likely call (60% probability) or raise (40% probability). If he calls, I will likely win if the public card is a Jack, and lose if it's a King or Queen. If he raises, I will likely lose unless the public card is a Jack.\n- If board_game_expert holds a Jack (50% probability), he will likely call (70% probability) or fold (30% probability). If he calls, it will be a draw unless the public card is a King or Queen, in which case I will lose. If he folds, I will win.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Raise: (0.125 * 0.7 * -4) + (0.125 * 0.3 * 4) + (0.375 * 0.7 * 4) + (0.375 * 0.3 * 4) + (0.5 * 0.8 * 4) + (0.5 * 0.2 * 0) = 1.5 chips\n- Plan 2: Fold: -2 chips\n- Plan 3: Check: (0.125 * 0.8 * -4) + (0.125 * 0.2 * 4) + (0.375 * 0.6 * 4) + (0.375 * 0.4 * -4) + (0.5 * 0.7 * 0) + (0.5 * 0.3 * 4) = 0.5 chips\n\nPlan Selection:\n- Plan 1: Raise has the highest expected chips gain, so I should choose this plan."}}
{"message": "", "14_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, he will likely raise (60% probability) or call (40% probability). If he raises, I will lose unless the public card is a Jack. If he calls, the game will be a draw unless the public card is a King. The winning rate is 0%, the losing rate is 60%, and the draw rate is 40%.\n- If board_game_expert holds a Queen, he will likely call (80% probability) or raise (20% probability). If he raises, I will lose unless the public card is a Jack. If he calls, the game will be a draw unless the public card is a Queen. The winning rate is 0%, the losing rate is 20%, and the draw rate is 80%.\n- If board_game_expert holds a Jack, he will likely call (60% probability) or fold (40% probability). If he calls, the game will be a draw unless the public card is a King or Queen. If he folds, I will win. The winning rate is 40%, the losing rate is 0%, and the draw rate is 60%.\nThe overall winning rate for Plan 1 is 13.33%, the losing rate is 26.67%, and the draw rate is 60%.\n\nPlan 2: Raise\n- If board_game_expert holds a King, he will likely raise (70% probability) or call (30% probability). If he raises or calls, I will 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- If board_game_expert holds a Queen, he will likely fold (30% probability) or call (70% probability). If he folds, I will win. If he calls, I will lose unless the public card is a Jack. The winning rate is 30%, the losing rate is 70%, and the draw rate is 0%.\n- If board_game_expert holds a Jack, he will likely fold (80% probability) or call (20% probability). If he folds, I will win. If he calls, the game will be a draw unless the public card is a King or Queen. The winning rate is 80%, the losing rate is 0%, and the draw rate is 20%.\nThe overall winning rate for Plan 2 is 36.67%, the losing rate is 56.67%, and the draw rate is 6.67%.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of what card board_game_expert holds. The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips. If I lose, the losing payoff would be 2 chips.\n- Plan 2: If I win, the winning payoff would be 5 chips. If I lose, the losing payoff would be 4 chips.\n- Plan 3: If I lose, the losing payoff would be 2 chips.\n\nThe estimated expected chips gain for each plan:\n- Plan 1: 0 * 3 - 26.67% * 2 = -0.5334 chips\n- Plan 2: 36.67% * 5 - 56.67% * 4 = -0.6668 chips\n- Plan 3: 0 * 0 - 100% * 2 = -2 chips\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows: Plan 1 > Plan 2 > Plan 3. Therefore, I should choose Plan 1: Call."}}
{"message": "", "14_2": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (20% probability), he will likely raise (70% probability) or call (30% probability). If he raises, I will lose (70% * 20% = 14%). If he calls, I have a chance to win if the public card changes to a Jack in the next round (30% * 20% = 6%).\n- If board_game_expert holds a Queen (40% probability), he will likely call (70% probability) or fold (30% probability). If he calls, I will lose (70% * 40% = 28%). If he folds, I will win (30% * 40% = 12%).\n- If board_game_expert holds a Jack (40% probability), he will likely fold (80% probability) or call (20% probability). If he folds, I will win (80% * 40% = 32%). If he calls, it will be a draw (20% * 40% = 8%).\n\nPlan 2: Fold\n- If I fold, I will lose the 2 chips in the pot. \n\nPlan 3: Check\n- If board_game_expert holds a King (20% probability), he will likely raise (80% probability) or call (20% probability). If he raises, I will lose (80% * 20% = 16%). If he calls, I have a chance to win if the public card changes to a Jack in the next round (20% * 20% = 4%).\n- If board_game_expert holds a Queen (40% probability), he will likely raise (40% probability) or call (60% probability). If he raises, I will lose (40% * 40% = 16%). If he calls, I will lose (60% * 40% = 24%).\n- If board_game_expert holds a Jack (40% probability), he will likely fold (30% probability) or call (70% probability). If he folds, I will win (30% * 40% = 12%). If he calls, it will be a draw (70% * 40% = 28%).\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips (half of the total pot of 8 chips). If I lose, the losing 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 winning payoff would be 2 chips (half of the total pot of 4 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 * (Winning Rate * Winning Payoff - Losing Rate * Losing Payoff) = 0.5 * ((50% * 4 chips) - (42% * 4 chips)) = 0.5 * (2 chips - 1.68 chips) = 0.16 chips\n- Plan 2: Expected Chips Gain = -2 chips (since I will lose the 2 chips in the pot)\n- Plan 3: Expected Chips Gain = 0.5 * ((44% * 2 chips) - (56% * 2 chips)) = 0.5 * (0.88 chips - 1.12 chips) = -0.12 chips\n\nPlan Selection:\n- Plan 1: Expected Chips Gain = 0.16 chips\n- Plan 2: Expected Chips Gain = -2 chips\n- Plan 3: Expected Chips Gain = -0.12 chips\n\nTherefore, the best plan is Plan 1 (Raise), followed by Plan 3 (Check), and the worst plan is Plan 2 (Fold)."}}
{"message": "", "14_4": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (50% probability), he would likely raise (70% probability) or call (30% probability). If he raises, I would lose this round as King is higher than my Jack. If he calls, it would be a draw as neither of our cards match the public card. Therefore, the winning rate for this plan is 0%, the losing rate is 35% (50% * 70%), and the draw rate is 15% (50% * 30%).\n- If board_game_expert holds a Queen (50% probability), he would likely call (80% probability) or fold (20% probability). If he calls, I would lose this round as his Queen matches the public card. If he folds, I would win this round. Therefore, the winning rate for this plan is 10% (50% * 20%), the losing rate is 40% (50% * 80%), and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I would lose this round regardless of what card board_game_expert holds. Therefore, the winning rate for this plan is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of payoffs for each plan:\n- Plan 1: After the action, all chips in the pot would be 16 (my 6 chips + board_game_expert's 10 chips). If I win, the winning payoff would be 8 chips (half of the total pot). If I lose, the losing payoff would be 8 chips.\n- Plan 2: After the action, all chips in the pot would be 10 (my 6 chips + board_game_expert's 4 chips). If I lose, the losing payoff would be 5 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain for this plan is winning rate * winning payoff - losing rate * losing payoff = 10% * 8 chips - 75% * 8 chips = -5.6 chips.\n- Plan 2: The expected chips gain for this plan is winning rate * winning payoff - losing rate * losing payoff = 0% * 0 chips - 100% * 5 chips = -5 chips.\n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 2 > Plan 1.\n- Therefore, I should select Plan 2: Fold, as it has the highest estimated expected chips gain."}}
{"message": "", "15_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, he will likely raise (70% probability) or call (30% probability). If he raises, I will likely lose unless the public card is a Queen. If he calls, I will likely win unless the public card is a King. The winning rate is 30%, the losing rate is 70%, and the draw rate is 0%.\n- If board_game_expert holds a Queen, he will likely call (80% probability) or raise (20% probability). If he raises, I will likely lose unless the public card is a Queen. If he calls, it will be a draw unless the public card is a King or Jack. The winning rate is 20%, the losing rate is 20%, and the draw rate is 60%.\n- If board_game_expert holds a Jack, he will likely call (60% probability) or fold (40% probability). If he calls, I will likely win unless the public card is a King. If he folds, I will win. The winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If board_game_expert holds a King, he will likely raise (70% probability) or call (30% probability). If he raises, I will likely lose unless the public card is a Queen. If he calls, I will likely win unless the public card is a King. The winning rate is 30%, the losing rate is 70%, and the draw rate is 0%.\n- If board_game_expert holds a Queen, he will likely fold (30% probability) or call (70% probability). If he folds, I will win. If he calls, it will be a draw unless the public card is a King or Jack. The winning rate is 30%, the losing rate is 0%, and the draw rate is 70%.\n- If board_game_expert holds a Jack, he will likely fold (80% probability) or call (20% probability). If he folds, I will win. If he calls, I will likely win unless the public card is a King. The winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of what card board_game_expert holds. The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of 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 4 chips. If I lose, the losing payoff would be 2 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: The expected chips gain is 30% * 3 - 70% * 2 = -0.1 chips.\n- Plan 2: The expected chips gain is 60% * 4 - 40% * 2 = 1.6 chips.\n- Plan 3: The expected chips gain is -2 chips.\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I should choose this plan."}}
{"message": "", "15_2": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (70% probability), he would likely raise (60% probability) or call (40% probability). If he raises, I would lose (probability = 0.7 * 0.6 = 0.42). If he calls, I would win if the public card is a Queen (probability = 0.7 * 0.4 * 1/3 = 0.093), draw if the public card is a King (probability = 0.7 * 0.4 * 1/3 = 0.093), and lose if the public card is a Jack (probability = 0.7 * 0.4 * 1/3 = 0.093).\n- If board_game_expert holds a Queen (30% probability), he would likely call (80% probability) or raise (20% probability). If he calls, I would win if the public card is a Queen (probability = 0.3 * 0.8 * 1/3 = 0.08), draw if the public card is a King (probability = 0.3 * 0.8 * 1/3 = 0.08), and lose if the public card is a Jack (probability = 0.3 * 0.8 * 1/3 = 0.08). If he raises, I would lose (probability = 0.3 * 0.2 = 0.06).\n- Overall, the winning rate for Plan 1 is 0.093 + 0.08 = 0.173, the losing rate is 0.42 + 0.093 + 0.08 + 0.06 = 0.653, and the draw rate is 0.093 + 0.08 = 0.173.\n\nPlan 2: Fold\n- If I fold, I would lose all the chips I have already put into the pot. The losing rate for Plan 2 is 1.\n\nThe number of payoffs for each plan:\n- Plan 1: After the action, all chips in the pot would be 10. If win, the winning payoff would be 5. If lose, the lose payoff would be 5.\n- Plan 2: After the action, all chips in the pot would be 6. If lose, the lose payoff would be 3.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = winning rate * Winning Payoff - lose rate * Lose Payoff = 0.173 * 5 - 0.653 * 5 = -2.4\n- Plan 2: Expected Chips Gain = -1 * Lose Payoff = -3\n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 1 > Plan 2.\n- Therefore, I should select Plan 1: Call."}}
{"message": "", "15_4": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King, he will likely raise (70% probability) or call (30% probability). If he raises, I will win because my pair of Queens beats his single King. If he calls, I will also win. Therefore, the winning rate for this plan is 100%.\n- If board_game_expert holds a Jack, he will likely fold (80% probability) or call (20% probability). If he folds, I will win. If he calls, I will also win because my pair of Queens beats his single Jack. Therefore, the winning rate for this plan is also 100%.\n\nPlan 2: Check\n- If board_game_expert holds a King, he will likely raise (70% probability) or call (30% probability). If he raises, I will call and win. If he calls, I will also win. Therefore, the winning rate for this plan is 100%.\n- If board_game_expert holds a Jack, he will likely fold (80% probability) or call (20% probability). If he folds, I will win. If he calls, I will also win because my pair of Queens beats his single Jack. Therefore, the winning rate for this plan is also 100%.\n\nPlan 3: Fold\n- This plan guarantees a loss, as I will forfeit the game. Therefore, the losing rate for this plan is 100%.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot, which is currently 6 chips. If I lose, the losing payoff would be half of the total pot, which is currently 6 chips.\n- Plan 2: If I win, the winning payoff would be half of the total pot, which is currently 6 chips. If I lose, the losing payoff would be half of the total pot, which is currently 6 chips.\n- Plan 3: If I fold, I will lose all the chips I have put in the pot, which is currently 6 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is 100% * 6 chips - 0% * 6 chips = 6 chips.\n- Plan 2: The expected chips gain is 100% * 6 chips - 0% * 6 chips = 6 chips.\n- Plan 3: The expected chips gain is 0% * 6 chips - 100% * 6 chips = -6 chips.\n\nPlan Selection:\n- Plan 1 and Plan 2 both have the highest expected chips gain of 6 chips, while Plan 3 has the lowest expected chips gain of -6 chips. Therefore, I should either raise (Plan 1) or check (Plan 2). Considering the strategy improvement, raising (Plan 1) would be the best choice as it could potentially lead to a larger pot and thus a larger payoff."}}
{"message": "", "17_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (30% probability), he will likely raise (40%) or call (60%). If he raises, I will lose as King outranks Queen. If he calls, it will be a draw as we both hold Queen. \n- If board_game_expert holds a Queen (30% probability), he will likely call (60%) or raise (40%). If he calls, it will be a draw as we both hold Queen. If he raises, I will lose as King outranks Queen. \n- If board_game_expert holds a Jack (40% probability), he will likely call (40%) or fold (60%). If he calls, I will win as Queen outranks Jack. If he folds, I will win as he forfeits the game. \n\nPlan 2: Raise\n- If board_game_expert holds a King (30% probability), he will likely call (70%) or raise (30%). If he calls, I will lose as King outranks Queen. If he raises, I will lose as King outranks Queen. \n- If board_game_expert holds a Queen (30% probability), he will likely fold (30%) or call (70%). If he folds, I will win as he forfeits the game. If he calls, it will be a draw as we both hold Queen. \n- If board_game_expert holds a Jack (40% probability), he will likely fold (60%) or call (40%). If he folds, I will win as he forfeits the game. If he calls, I will win as Queen outranks Jack. \n\nPlan 3: Fold\n- If I fold, I will lose regardless of what card board_game_expert holds. \n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips (half of the total pot of 6 chips). If I lose, the losing payoff would be 3 chips. \n- Plan 2: If I win, the winning payoff would be 4 chips (half of the total pot of 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: Expected Chips Gain = 0.4 * 3 - 0.6 * 3 = -0.6 chips\n- Plan 2: Expected Chips Gain = 0.7 * 4 - 0.3 * 4 = 1.6 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I should choose this plan."}}
{"message": "", "17_2": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King, he would likely call (60%) or raise (40%). If he calls, I would win as my Queen is higher than the public Jack. If he raises, I would still win as my Queen is higher than his King. \n- If board_game_expert holds a Queen, he would likely call (50%) or fold (50%). If he calls, it would be a draw as we both hold Queens. If he folds, I would win. \n- If board_game_expert holds a Jack, he would likely fold (60%) or call (40%). If he folds, I would win. If he calls, he would win as his Jack matches the public card. \n\nPlan 2: Fold\n- If I fold, I would lose regardless of what card board_game_expert holds. \n\nPlan 3: Check\n- If board_game_expert holds a King, he would likely raise (40%) or check (60%). If he raises, I would lose as his King is higher than my Queen. If he checks, I would win as my Queen is higher than the public Jack. \n- If board_game_expert holds a Queen, he would likely raise (20%) or check (80%). If he raises, it would be a draw as we both hold Queens. If he checks, it would be a draw as we both hold Queens. \n- If board_game_expert holds a Jack, he would likely raise (30%) or check (70%). If he raises, he would win as his Jack matches the public card. If he checks, he would win as his Jack matches the public card. \n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 8 chips (half of the total pot of 16 chips). If I lose, the losing payoff would be 8 chips. \n- Plan 2: If I fold, I would lose 4 chips (the amount I have already put in the pot). \n- Plan 3: If I win, the winning payoff would be 8 chips (half of the total pot of 16 chips). If I lose, the losing payoff would be 8 chips. \n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: (0.7 * 8) - (0.3 * 8) = 2.8 chips\n- Plan 2: -4 chips\n- Plan 3: (0.5 * 8) - (0.5 * 8) = 0 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I would choose Plan 1: Raise."}}
{"message": "", "19_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, he will likely call (60%) or raise (40%). If he raises, I will lose unless the public card is a Jack. If he calls, the game will be decided by the public card. \n- If board_game_expert holds a Queen, he will likely call (70%) or raise (30%). If he raises, I will lose unless the public card is a Jack. If he calls, the game will be decided by the public card. \n- If board_game_expert holds a Jack, he will likely call (60%) or fold (40%). If he folds, I will win. If he calls, the game will be a draw unless the public card is a King or Queen. \n\nPlan 2: Raise\n- If board_game_expert holds a King, he will likely call (50%) or raise (50%). If he raises, I will lose unless the public card is a Jack. If he calls, the game will be decided by the public card. \n- If board_game_expert holds a Queen, he will likely call (50%) or fold (50%). If he folds, I will win. If he calls, the game will be decided by the public card. \n- If board_game_expert holds a Jack, he will likely fold (70%) or call (30%). If he folds, I will win. If he calls, the game will be a draw unless the public card is a King or Queen. \n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of board_game_expert's card. \n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips (half of the total pot). If I lose, the losing payoff would be 1 chip (half of the total pot). \n- Plan 2: If I win, the winning payoff would be 5 chips (half of the total pot). If I lose, the losing payoff would be 3 chips (half of the total 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 = 0.33*(0.6*3 - 0.4*1) + 0.33*(0.7*3 - 0.3*1) + 0.33*(0.6*3 - 0.4*1) = 1.98 chips\n- Plan 2: Expected Chips Gain = 0.33*(0.5*5 - 0.5*3) + 0.33*(0.5*5 - 0.5*3) + 0.33*(0.7*5 - 0.3*3) = 2.64 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 Plan 2: Raise."}}
{"message": "", "19_2": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (50% probability), he will likely call (60%) or raise (40%). If he calls, we will go to the second round with equal chips in the pot. If he raises, I will lose 4 chips. The overall winning rate for this plan is 0% (since I hold a Jack and he holds a King), the losing rate is 100%, and the draw rate is 0%.\n- If board_game_expert holds a Queen (50% probability), he will likely call (70%) or raise (30%). If he calls, we will go to the second round with equal chips in the pot. If he raises, I will lose 4 chips. The overall winning rate for this plan is 0% (since I hold a Jack and he holds a Queen), the losing rate is 100%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose the 6 chips I have already put in the pot. The overall winning rate for this plan is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (currently 10 chips, so 5 chips). If I lose, the losing payoff would be half of the total pot (currently 10 chips, so 5 chips).\n- Plan 2: If I fold, I will lose the 6 chips I have already put in the pot. There is no winning payoff for this plan.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is 0% * 5 chips - 100% * 5 chips = -5 chips.\n- Plan 2: The expected chips gain is 0% * 0 chips - 100% * 6 chips = -6 chips.\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain (-5 chips) than Plan 2 (-6 chips). Therefore, I should choose Plan 1: Call."}}
{"message": "", "19_4": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (70% chance), he will likely call (50%) or raise (50%). If he calls, I will lose unless the next public card is a Jack. If he raises, I will also lose unless the next public card is a Jack. The winning rate for this plan is 25% (50% chance he calls * 50% chance the next card is a Jack), the losing rate is 75% (50% chance he calls * 50% chance the next card is not a Jack + 50% chance he raises), and the draw rate is 0%.\n- If board_game_expert holds a Queen (30% chance), he will likely call (50%) or fold (50%). If he calls, I will lose unless the next public card is a Jack. If he folds, I will win. The winning rate for this plan is 65% (50% chance he calls * 30% chance the next card is a Jack + 50% chance he folds), the losing rate is 35% (50% chance he calls * 70% chance the next card is not a Jack), and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose the current pot but avoid further losses. 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 board_game_expert holds a King (70% chance), he will likely call (50%) or raise (50%). If he calls, I will lose unless the next public card is a Jack. If he raises, I will also lose unless the next public card is a Jack. The winning rate for this plan is 25% (50% chance he calls * 50% chance the next card is a Jack), the losing rate is 75% (50% chance he calls * 50% chance the next card is not a Jack + 50% chance he raises), and the draw rate is 0%.\n- If board_game_expert holds a Queen (30% chance), he will likely call (50%) or fold (50%). If he calls, I will lose unless the next public card is a Jack. If he folds, I will win. The winning rate for this plan is 65% (50% chance he calls * 30% chance the next card is a Jack + 50% chance he folds), the losing rate is 35% (50% chance he calls * 70% chance the next card is not a Jack), and the draw rate is 0%.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 12 chips (half of the total pot of 24 chips). If I lose, the losing payoff would be 12 chips.\n- Plan 2: If I fold, there is no winning payoff. The losing payoff would be 6 chips (half of the current pot).\n- Plan 3: If I win, the winning payoff would be 12 chips (half of the total pot of 24 chips). If I lose, the losing payoff would be 12 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 25% * 12 chips - 75% * 12 chips = -6 chips\n- Plan 2: Expected Chips Gain = 0% * 0 chips - 100% * 6 chips = -6 chips\n- Plan 3: Expected Chips Gain = 25% * 12 chips - 75% * 12 chips = -6 chips\n\nPlan Selection:\nAll three plans have the same expected chips loss of -6 chips. However, considering the strategy improvement, Plan 1 (Raise) might be the best choice as it could potentially pressure board_game_expert into folding, especially if he holds a Queen."}}
{"message": "", "20_1": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (70% probability), he will likely call (80%) or raise (20%). If he calls, I will likely lose (as King is higher than Queen). If he raises, I will likely lose as well. So, the winning rate is 0%, lose rate is 100%, and draw rate is 0%.\n- If board_game_expert holds a Queen (20% probability), he will likely call (70%) or fold (30%). If he calls, it will be a draw (as we both have Queens). If he folds, I will win. So, the winning rate is 30%, lose rate is 0%, and draw rate is 70%.\n- If board_game_expert holds a Jack (10% probability), he will likely fold (70%) or call (30%). If he folds, I will win. If he calls, I will likely win (as Queen is higher than Jack). So, the winning rate is 100%, lose rate is 0%, and draw rate is 0%.\n\nPlan 2: Raise\n- If board_game_expert holds a King (70% probability), he will likely call (80%) or raise (20%). If he calls, I will likely lose (as King is higher than Queen). If he raises, I will likely lose as well. So, the winning rate is 0%, lose rate is 100%, and draw rate is 0%.\n- If board_game_expert holds a Queen (20% probability), he will likely call (70%) or fold (30%). If he calls, it will be a draw (as we both have Queens). If he folds, I will win. So, the winning rate is 30%, lose rate is 0%, and draw rate is 70%.\n- If board_game_expert holds a Jack (10% probability), he will likely fold (70%) or call (30%). If he folds, I will win. If he calls, I will likely win (as Queen is higher than Jack). So, the winning rate is 100%, lose rate is 0%, and draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of what card board_game_expert holds. So, the winning rate is 0%, lose rate is 100%, and draw rate is 0%.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips (half of the total pot of 8 chips). If I lose, the losing payoff would be 2 chips (half of the total pot of 4 chips).\n- Plan 2: If I win, the winning payoff would be 6 chips (half of the total pot of 12 chips). If I lose, the losing payoff would be 4 chips (half of the total pot of 8 chips).\n- Plan 3: If I fold, I will lose 2 chips (the chips I have already put in the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.7 * 0 - 0.3 * 2 = -0.6 chips\n- Plan 2: Expected Chips Gain = 0.7 * 0 - 0.3 * 4 = -1.2 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\nBased on the estimated expected chips gains, Plan 1 (Call) is the best strategy as it has the highest expected chips gain."}}
{"message": "", "20_3": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (58.33% probability), he would likely call (60%) or raise (40%). If he calls, I would lose (as King is higher than Queen). If he raises, I would also lose. So, the overall losing rate for this plan is 100%.\n- If board_game_expert holds a Jack (41.67% probability), he would likely fold (80%) or call (20%). If he folds, I would win. If he calls, I would lose (as a pair of Jacks is higher than a single Queen). So, the overall winning rate for this plan is 33.34% and the losing rate is 66.66%.\n\nPlan 2: Raise\n- If board_game_expert holds a King (58.33% probability), he would likely call (80%) or raise (20%). If he calls, I would lose. If he raises, I would also lose. So, the overall losing rate for this plan is 100%.\n- If board_game_expert holds a Jack (41.67% probability), he would likely fold (70%) or call (30%). If he folds, I would win. If he calls, I would lose. So, the overall winning rate for this plan is 29.17% and the losing rate is 70.83%.\n\nPlan 3: Fold\n- If I fold, I would lose the chips I have already put in the pot. The losing rate for this plan is 100%.\n\nThe number of payoffs for each plan:\n- Plan 1: After the action, all chips in the pot would be 12. If win, the winning payoff would be 6. If lose, the lose payoff would be 6.\n- Plan 2: After the action, all chips in the pot would be 16. If win, the winning payoff would be 8. If lose, the lose payoff would be 8.\n- Plan 3: After the action, all chips in the pot would be 8. If lose, the lose payoff would be 4.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 33.34% * 6 - 100% * 6 = -4\n- Plan 2: Expected Chips Gain = 29.17% * 8 - 100% * 8 = -5.66\n- Plan 3: Expected Chips Gain = 0% * 0 - 100% * 4 = -4\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows: Plan 1 > Plan 3 > Plan 2. Therefore, I should choose Plan 1: Call."}}
{"message": "", "21_1": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (20% chance), he would likely call (80%) or raise (20%). If the public card is a Queen, I would win. If the public card is a King or Jack, I would lose. The winning rate is 20% * 80% = 16%, and the losing rate is 20% * 20% = 4%.\n- If board_game_expert holds a Queen (40% chance), he would likely call (70%) or fold (30%). If the public card is a Queen, it would be a draw. If the public card is a King or Jack, I would lose. The drawing rate is 40% * 70% = 28%, and the losing rate is 40% * 30% = 12%.\n- If board_game_expert holds a Jack (40% chance), he would likely fold (80%) or call (20%). If the public card is a Queen or King, I would win. If the public card is a Jack, I would lose. The winning rate is 40% * 80% = 32%, and the losing rate is 40% * 20% = 8%.\n\nPlan 2: Fold\n- If I fold, I would lose the current pot. The losing rate is 100%.\n\nPlan 3: Check\n- If board_game_expert holds a King (20% chance), he would likely raise (70%) or check (30%). If the public card is a Queen, I would win. If the public card is a King or Jack, I would lose. The winning rate is 20% * 30% = 6%, and the losing rate is 20% * 70% = 14%.\n- If board_game_expert holds a Queen (40% chance), he would likely raise (40%) or check (60%). If the public card is a Queen, it would be a draw. If the public card is a King or Jack, I would lose. The drawing rate is 40% * 60% = 24%, and the losing rate is 40% * 40% = 16%.\n- If board_game_expert holds a Jack (40% chance), he would likely fold (50%) or check (50%). If the public card is a Queen or King, I would win. If the public card is a Jack, I would lose. The winning rate is 40% * 50% = 20%, and the losing rate is 40% * 50% = 20%.\n\nThe number of payoffs for each plan:\n- Plan 1: If win, the winning payoff would be half of the total pot (4 chips). If lose, the losing payoff would be half of the total pot (4 chips).\n- Plan 2: If lose, the losing payoff would be half of the total pot (2 chips).\n- Plan 3: If win, the winning payoff would be half of the total pot (2 chips). If lose, the losing payoff would be half of the total pot (2 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 16% * 4 - 4% * 4 = 0.48 chips\n- Plan 2: Expected Chips Gain = -100% * 2 = -2 chips\n- Plan 3: Expected Chips Gain = 6% * 2 - 14% * 2 = -0.16 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I should choose to raise."}}
{"message": "", "22_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, he will likely raise (70% probability) or call (30% probability). 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/losing/draw rates are 30% win (if public card is a Jack), 70% lose (if public card is not a Jack), 0% draw.\n- If board_game_expert holds a Queen, he will likely raise (40% probability) or call (60% probability). 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/losing/draw rates are 60% win (if public card is a Jack), 40% lose (if public card is not a Jack), 0% draw.\n- If board_game_expert holds a Jack, he will likely call (70% probability) or fold (30% probability). If he calls, it will be a draw regardless of the public card. If he folds, I will win. The winning/losing/draw rates are 30% win (if he folds), 0% lose, 70% draw (if he calls).\n- The overall winning/losing/draw rates for Plan 1 are 40% win, 37% lose, 23% draw.\n\nPlan 2: Raise\n- If board_game_expert holds a King, he will likely call (60% probability) or raise (40% probability). If he calls or raises, I will lose unless the public card is a Jack. The winning/losing/draw rates are 0% win, 100% lose, 0% draw.\n- If board_game_expert holds a Queen, he will likely call (50% probability) or fold (50% probability). If he calls, I will lose unless the public card is a Jack. If he folds, I will win. The winning/losing/draw rates are 50% win (if he folds), 50% lose (if he calls), 0% draw.\n- If board_game_expert holds a Jack, he will likely fold (80% probability) or call (20% probability). If he folds, I will win. If he calls, it will be a draw regardless of the public card. The winning/losing/draw rates are 80% win (if he folds), 0% lose, 20% draw (if he calls).\n- The overall winning/losing/draw rates for Plan 2 are 43% win, 50% lose, 7% draw.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of board_game_expert's cards. The winning/losing/draw rates are 0% win, 100% lose, 0% draw.\n\nThe number of payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 3 chips. If lose, the losing payoff would be 2 chips.\n- Plan 2: If win, the winning payoff would be 4 chips. If lose, the losing payoff would be 2 chips.\n- Plan 3: If lose, the losing payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 40% * 3 - 37% * 2 = 0.2 chips\n- Plan 2: Expected Chips Gain = 43% * 4 - 50% * 2 = 0.72 chips\n- Plan 3: Expected Chips Gain = -100% * 2 = -2 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, followed by Plan 1 (Call), and Plan 3 (Fold). Therefore, I should choose Plan 2 (Raise)."}}
{"message": "", "22_2": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King, he will likely call (60% probability) or fold (40% probability). If he calls, I will lose (as King is higher than Jack), if he folds, I will win. So, the winning rate is 40%, losing rate is 60%, and draw rate is 0%.\n- If board_game_expert holds a Queen, he will likely call (50% probability) or fold (50% probability). If he calls, I will lose (as Queen is higher than Jack), if he folds, I will win. So, the winning rate is 50%, losing rate is 50%, and draw rate is 0%.\n- If board_game_expert holds a Jack, he will likely call (30% probability) or fold (70% probability). If he calls, it will be a draw (as both have Jack), if he folds, I will win. So, the winning rate is 70%, losing rate is 0%, and draw rate is 30%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card board_game_expert holds. So, the winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n\nPlan 3: Check\n- If board_game_expert holds a King, he will likely raise (80% probability) or call (20% probability). If he raises, I will lose (as King is higher than Jack), if he calls, I will lose. So, the winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n- If board_game_expert holds a Queen, he will likely raise (70% probability) or call (30% probability). If he raises, I will lose (as Queen is higher than Jack), if he calls, I will lose. So, the winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n- If board_game_expert holds a Jack, he will likely raise (60% probability) or call (40% probability). If he raises, it will be a draw (as both have Jack), if he calls, it will be a draw. So, the winning rate is 0%, losing rate is 0%, and draw rate is 100%.\n\nThe number of payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 8 chips (half of the total pot of 16 chips). If lose, the lose payoff would be 8 chips.\n- Plan 2: If lose, the lose payoff would be 4 chips (half of the total pot of 8 chips).\n- Plan 3: If draw, the draw payoff would be 4 chips (half of the total pot of 8 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.4 * 8 - 0.6 * 8 = -1.6 chips\n- Plan 2: Expected Chips Gain = -1 * 4 = -4 chips\n- Plan 3: Expected Chips Gain = 0\n\nPlan Selection:\n- Plan 1: -1.6 chips\n- Plan 2: -4 chips\n- Plan 3: 0 chips\n\nTherefore, the best plan to select would be Plan 3 (Check), as it has the highest expected chips gain."}}
{"message": "", "23_1": {"plan": "Plan 1: Raise\n- If board_game_expert holds a Queen (60% chance), he would likely call (70%) or fold (30%). If he calls, the pot would increase to 10 chips (4 from me, 4 from him, and the initial 2). If he folds, I would win the current pot of 4 chips. \n- If board_game_expert holds a Jack (40% chance), he would likely fold (70%) or call (30%). If he folds, I would win the current pot of 4 chips. If he calls, the pot would increase to 10 chips.\n\nPlan 2: Fold\n- If I fold, I would lose the current pot of 4 chips regardless of what card board_game_expert holds.\n\nPlan 3: Check\n- If board_game_expert holds a Queen (60% chance), he would likely call (60%) or raise (40%). If he calls, the pot would remain at 4 chips. If he raises, the pot would increase to 10 chips.\n- If board_game_expert holds a Jack (40% chance), he would likely call (50%) or fold (50%). If he calls, the pot would remain at 4 chips. If he folds, I would win the current pot of 4 chips.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: (0.6 * 0.7 * 10 + 0.6 * 0.3 * 4 + 0.4 * 0.7 * 4 + 0.4 * 0.3 * 10) / 4 = 6.8 chips\n- Plan 2: -4 chips (as I would lose the current pot)\n- Plan 3: (0.6 * 0.6 * 4 + 0.6 * 0.4 * 10 + 0.4 * 0.5 * 4 + 0.4 * 0.5 * 4) / 4 = 5.2 chips\n\nPlan Selection:\nBased on the expected chips gain, the ranking of the plans is as follows: Plan 1 > Plan 3 > Plan 2. Therefore, I should choose to raise as my strategy in this turn."}}
{"message": "", "24_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a Jack, he will likely fold (80%) or call (20%). If he folds, I win. If he calls, I have a 33.33% chance of winning (if the public card is a King), a 33.33% chance of drawing (if the public card is a Jack), and a 33.33% chance of losing (if the public card is a Queen).\n- If board_game_expert holds a Queen, he will likely call (70%) or raise (30%). If he raises, I have a 33.33% chance of winning (if the public card is a King), a 33.33% chance of drawing (if the public card is a Queen), and a 33.33% chance of losing (if the public card is a Jack).\n- If board_game_expert holds a King, he will likely raise (60%) or call (40%). If he raises, I have a 33.33% chance of winning (if the public card is a King), a 33.33% chance of drawing (if the public card is a Queen), and a 33.33% chance of losing (if the public card is a Jack).\n\nPlan 2: Raise\n- If board_game_expert holds a Jack, he will likely fold (80%) or call (20%). If he folds, I win. If he calls, I have a 33.33% chance of winning (if the public card is a King), a 33.33% chance of drawing (if the public card is a Jack), and a 33.33% chance of losing (if the public card is a Queen).\n- If board_game_expert holds a Queen, he will likely call (70%) or raise (30%). If he raises, I have a 33.33% chance of winning (if the public card is a King), a 33.33% chance of drawing (if the public card is a Queen), and a 33.33% chance of losing (if the public card is a Jack).\n- If board_game_expert holds a King, he will likely raise (60%) or call (40%). If he raises, I have a 33.33% chance of winning (if the public card is a King), a 33.33% chance of drawing (if the public card is a Queen), and a 33.33% chance of losing (if the public card is a Jack).\n\nPlan 3: Fold\n- If I fold, I lose the chips I have already put in the pot.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot. If I lose, the losing payoff would be half of the total pot.\n- Plan 2: If I win, the winning payoff would be half of the total pot. If I lose, the losing payoff would be half of the total pot.\n- Plan 3: If I fold, I lose the chips I have already put in the pot.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff\n- Plan 2: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff\n- Plan 3: Expected Chips Gain = -1 * Chips in the pot\n\nPlan Selection:\n- Based on the estimated expected chips gains, Plan 1 and Plan 2 have the same expected chips gain, and both are higher than Plan 3. Therefore, I should either call or raise. Considering the strategy improvement, I should raise to maximize potential gains."}}
{"message": "", "24_2": {"plan": "Plan 1: Raise\n- If board_game_expert holds a Queen (67% chance), he will likely call (60%) or raise (40%). If he calls, I will win as my King beats his Queen. If he raises, it means the public card is a Queen and he has a pair of Queens, in which case I will lose. So, the winning rate is 60%, and the losing rate is 40%.\n- If board_game_expert holds a King (33% chance), he will likely raise (70%) or call (30%). If he raises, it means the public card is a King and we both have a pair of Kings, resulting in a draw. If he calls, I will win as my King beats his single card. So, the winning rate is 30%, the losing rate is 0%, and the draw rate is 70%.\n\nPlan 2: Check\n- If board_game_expert holds a Queen (67% chance), he will likely call (60%) or raise (40%). If he calls, I will win as my King beats his Queen. If he raises, it means the public card is a Queen and he has a pair of Queens, in which case I will lose. So, the winning rate is 60%, and the losing rate is 40%.\n- If board_game_expert holds a King (33% chance), he will likely raise (70%) or call (30%). If he raises, it means the public card is a King and we both have a pair of Kings, resulting in a draw. If he calls, I will win as my King beats his single card. So, the winning rate is 30%, the losing rate is 0%, and the draw rate is 70%.\n\nPlan 3: Fold\n- If I fold, I will automatically lose the game, so the losing rate is 100%.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (8 chips). If I lose, the losing payoff would be half of the total pot (8 chips).\n- Plan 2: If I win, the winning payoff would be half of the total pot (4 chips). If I lose, the losing payoff would be half of the total pot (4 chips).\n- Plan 3: If I lose, the losing payoff would be half of the total pot (4 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.67*(0.6*8 - 0.4*8) + 0.33*(0.3*8 - 0*8) = 0.64 chips\n- Plan 2: Expected Chips Gain = 0.67*(0.6*4 - 0.4*4) + 0.33*(0.3*4 - 0*4) = 0.32 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I will choose Plan 1: Raise."}}
{"message": "", "24_4": {"plan": "Plan 1: Call\n- If board_game_expert holds a Jack (5% chance), he will likely fold (90% chance). I will win the game (probability = 0.05 * 0.9 = 0.045).\n- If board_game_expert holds a Queen (65% chance), he will likely call (60% chance) or raise (40% chance). I will win the game if he calls (probability = 0.65 * 0.6 = 0.39) and lose if he raises (probability = 0.65 * 0.4 = 0.26).\n- If board_game_expert holds a King (30% chance), he will likely raise (70% chance) or call (30% chance). I will draw the game if he raises (probability = 0.3 * 0.7 = 0.21) and win if he calls (probability = 0.3 * 0.3 = 0.09).\n- Overall, the winning rate for plan 1 is 0.045 + 0.39 + 0.09 = 0.525, the losing rate is 0.26, and the draw rate is 0.21.\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of what card board_game_expert holds. The losing rate for plan 2 is 1.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (20 chips). If I lose, the losing payoff would be half of the total pot (20 chips).\n- Plan 2: If I lose, the losing payoff would be the number of chips I have already put into the pot (12 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = winning rate * Winning Payoff - losing rate * Losing Payoff = 0.525 * 20 - 0.26 * 20 = 5.3 chips.\n- Plan 2: Expected Chips Gain = -1 * 12 = -12 chips.\n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 1 > Plan 2.\n- Therefore, I should choose Plan 1: Call."}}
{"message": "", "25_1": {"plan": "Plan 1: Raise\n- If board_game_expert holds a Jack, he will likely fold (80% probability) or call (20% probability). If he folds, I win the pot. If he calls, I have a 2/3 chance of winning (if the public card is a Queen or King) and a 1/3 chance of drawing (if the public card is a Jack).\n- If board_game_expert holds a Queen, he will likely call (70% probability) or raise (30% probability). If he calls, I have a 2/3 chance of winning (if the public card is a Jack or King) and a 1/3 chance of losing (if the public card is a Queen).\n- If board_game_expert holds a King, he will likely raise (80% probability) or call (20% probability). If he raises or calls, I have a 1/3 chance of winning (if the public card is a King) and a 2/3 chance of drawing (if the public card is a Queen or Jack).\n\nPlan 2: Fold\n- If I fold, I lose the pot regardless of what card board_game_expert holds.\n\nPlan 3: Check\n- If board_game_expert holds a Jack, he will likely fold (70% probability) or call (30% probability). If he folds, I win the pot. If he calls, I have a 2/3 chance of winning (if the public card is a Queen or King) and a 1/3 chance of drawing (if the public card is a Jack).\n- If board_game_expert holds a Queen, he will likely call (60% probability) or raise (40% probability). If he calls, I have a 2/3 chance of winning (if the public card is a Jack or King) and a 1/3 chance of losing (if the public card is a Queen).\n- If board_game_expert holds a King, he will likely raise (70% probability) or call (30% probability). If he raises or calls, I have a 1/3 chance of winning (if the public card is a King) and a 2/3 chance of drawing (if the public card is a Queen or Jack).\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (6 chips). If I lose, the losing payoff would be half of the total pot (6 chips).\n- Plan 2: If I fold, I lose the pot (4 chips).\n- Plan 3: If I win, the winning payoff would be half of the total pot (6 chips). If I lose, the losing payoff would be half of the total pot (6 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected gain = (winning rate * winning payoff) - (losing rate * losing payoff) = (0.7 * 6) - (0.3 * 6) = 2.4 chips\n- Plan 2: Expected gain = -4 chips\n- Plan 3: Expected gain = (0.7 * 6) - (0.3 * 6) = 2.4 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 have the highest expected gains, so I should choose one of these two plans. Since Plan 1 (raise) is more aggressive and can potentially lead to larger pots in the future, I will choose Plan 1."}}
{"message": "", "26_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a Jack, he will likely fold (80%) or call (20%). If he folds, I win and the pot is 3 chips. If he calls, the pot is 4 chips and I have a 80% chance of winning (if the public card is not a Jack) and 20% chance of drawing (if the public card is a Jack). \n- If board_game_expert holds a Queen, he will likely call (70%) or raise (30%). If he calls, the pot is 4 chips and I have a 60% chance of winning (if the public card is not a Queen) and 40% chance of drawing (if the public card is a Queen). If he raises, the pot is 6 chips and I have the same winning and drawing chances.\n\nPlan 2: Raise\n- If board_game_expert holds a Jack, he will likely fold (80%) or call (20%). If he folds, I win and the pot is 5 chips. If he calls, the pot is 6 chips and I have a 80% chance of winning (if the public card is not a Jack) and 20% chance of drawing (if the public card is a Jack). \n- If board_game_expert holds a Queen, he will likely call (70%) or raise (30%). If he calls, the pot is 6 chips and I have a 60% chance of winning (if the public card is not a Queen) and 40% chance of drawing (if the public card is a Queen). If he raises, the pot is 8 chips and I have the same winning and drawing chances.\n\nPlan 3: Fold\n- This is not a reasonable plan as I hold a King, which is the highest rank card.\n\nThe number of payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 1.5 chips (half of the total pot of 3 chips) if board_game_expert folds, or 2 chips (half of the total pot of 4 chips) if board_game_expert calls. If lose, the lose payoff would be 1.5 chips (half of the total pot of 3 chips).\n- Plan 2: If win, the winning payoff would be 2.5 chips (half of the total pot of 5 chips) if board_game_expert folds, or 3 chips (half of the total pot of 6 chips) if board_game_expert calls. If lose, the lose payoff would be 2.5 chips (half of the total pot of 5 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.8 * 1.5 + 0.2 * 2 - 0.2 * 1.5 = 1.3 chips\n- Plan 2: Expected Chips Gain = 0.8 * 2.5 + 0.2 * 3 - 0.2 * 2.5 = 2.1 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest estimated expected chips gain, so I should choose this plan."}}
{"message": "", "26_2": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (50% probability), he will likely raise (70%) or call (30%). If he raises, I will win if the public card is a King (33.33% probability) or lose if the public card is a Queen or Jack (66.67% probability). If he calls, the outcome will be the same. Overall, the winning rate is 16.67% (50% * 33.33%), the losing rate is 33.33% (50% * 66.67%), and the draw rate is 0%.\n- If board_game_expert holds a Queen (50% probability), he will likely call (70%) or raise (30%). If he calls or raises, I will win if the public card is a King or Jack (66.67% probability) or lose if the public card is a Queen (33.33% probability). Overall, the winning rate is 33.33% (50% * 66.67%), the losing rate is 16.67% (50% * 33.33%), and the draw rate is 0%.\n\nPlan 1 overall GoodGuy's Winning/Lose/Draw rates: Winning rate is 50% (16.67% + 33.33%), losing rate is 50% (33.33% + 16.67%), and draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I automatically lose the round regardless of board_game_expert's card or the public card. Therefore, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 2 overall GoodGuy's Winning/Lose/Draw rates: Winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n\nThe number of payoffs for each plan:\n- Plan 1: After the action, all chips in the pot would be 10. If win, the winning payoff would be 5. If lose, the lose payoff would be 5.\n- Plan 2: After the action, all chips in the pot would be 6. If lose, the lose payoff would be 3.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 50% * 5 - 50% * 5 = 0\n- Plan 2: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 0% * 0 - 100% * 3 = -3\n\nPlan Selection:\n- Plan 1 (Call) has an expected chips gain of 0, which is higher than Plan 2 (Fold) with an expected chips gain of -3. Therefore, the best strategy is to call."}}
{"message": "", "26_4": {"plan": "Plan 1: Raise\n- If board_game_expert holds a Queen (30% probability), he would likely call (60%) or raise (40%). If he calls, I would win as my King is higher than his Queen. If he raises, it would be a draw as we both hold Kings. The winning rate is 60%, the losing rate is 0%, and the draw rate is 40%.\n- If board_game_expert holds a King (70% probability), he would likely raise (80%) or call (20%). If he raises or calls, it would be a draw as we both hold Kings. 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 would lose regardless of what card board_game_expert holds. The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If board_game_expert holds a Queen (30% probability), he would likely call (60%) or raise (40%). If he calls, I would win as my King is higher than his Queen. If he raises, it would be a draw as we both hold Kings. The winning rate is 60%, the losing rate is 0%, and the draw rate is 40%.\n- If board_game_expert holds a King (70% probability), he would likely raise (80%) or call (20%). If he raises or calls, it would be a draw as we both hold Kings. The winning rate is 0%, the losing rate is 0%, and the draw rate is 100%.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 6 chips (half of the total pot). If I lose, the losing payoff would be 6 chips.\n- Plan 2: If I fold, I would lose 6 chips.\n- Plan 3: If I win, the winning payoff would be 6 chips. If I lose, the losing payoff would be 6 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.6 * 6 - 0 * 6 = 3.6 chips\n- Plan 2: Expected Chips Gain = 0 * 6 - 1 * 6 = -6 chips\n- Plan 3: Expected Chips Gain = 0.6 * 6 - 0 * 6 = 3.6 chips\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows:\n1. Plan 1: Raise (3.6 chips)\n2. Plan 3: Check (3.6 chips)\n3. Plan 2: Fold (-6 chips)\n\nTherefore, the plan with the highest estimated expected chips gain is either Plan 1: Raise or Plan 3: Check. Considering the strategy improvement, I should select Plan 1: Raise as it is more aggressive and could potentially lead to higher winnings in the long run."}}
{"message": "", "27_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (50% probability), he will likely call (30% probability) or raise (70% probability). If he calls, I will likely lose (as my Jack is lower than his King). If he raises, I will also likely lose. Therefore, the winning rate for this plan is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If board_game_expert holds a Queen (50% probability), he will likely call (60% probability) or raise (40% probability). If he calls, I will likely lose (as my Jack is lower than his Queen). If he raises, I will also likely lose. Therefore, the winning rate for this plan is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If board_game_expert holds a King (50% probability), he will likely call (80% probability) or raise (20% probability). If he calls, I will likely lose (as my Jack is lower than his King). If he raises, I will also likely lose. Therefore, the winning rate for this plan is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If board_game_expert holds a Queen (50% probability), he will likely call (70% probability) or fold (30% probability). If he calls, I will likely lose (as my Jack is lower than his Queen). If he folds, I will win. Therefore, the winning rate for this plan is 15% (50% * 30%), the losing rate is 85% (50% * 70% + 50% * 20%), and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put into the pot. Therefore, the winning rate for this plan is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 1.5 chips (half of the total pot of 3 chips). If I lose, the losing payoff would be 1.5 chips.\n- Plan 2: If I win, the winning payoff would be 2.5 chips (half of the total pot of 5 chips). If I lose, the losing payoff would be 2.5 chips.\n- Plan 3: If I lose, the losing payoff would be 1 chip (the chips I have already put into the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0% * 1.5 chips - 100% * 1.5 chips = -1.5 chips\n- Plan 2: 15% * 2.5 chips - 85% * 2.5 chips = -1.75 chips\n- Plan 3: 0% * 0 chips - 100% * 1 chip = -1 chip\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows: Plan 3 > Plan 1 > Plan 2. Therefore, I should choose Plan 3: Fold."}}
{"message": "", "28_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a Jack, he will likely fold (70% probability) or call (30% probability). If he folds, I win and the payoff would be 1.5 chips (half of the total pot). If he calls, the game goes to the second round and the outcome depends on the public card. \n- If board_game_expert holds a Queen, he will likely call (60% probability) or raise (40% probability). If he calls, the game goes to the second round and the outcome depends on the public card. If he raises, I can choose to fold, call, or raise in the next turn.\n- If board_game_expert holds a King, he will likely raise (70% probability) or call (30% probability). If he raises, I can choose to fold, call, or raise in the next turn. If he calls, the game goes to the second round and the outcome depends on the public card.\n\nPlan 2: Raise\n- If board_game_expert holds a Jack, he will likely fold (80% probability) or call (20% probability). If he folds, I win and the payoff would be 2 chips (half of the total pot). If he calls, the game goes to the second round and the outcome depends on the public card.\n- If board_game_expert holds a Queen, he will likely call (70% probability) or raise (30% probability). If he calls, the game goes to the second round and the outcome depends on the public card. If he raises, I can choose to fold, call, or raise in the next turn.\n- If board_game_expert holds a King, he will likely raise (80% probability) or call (20% probability). If he raises, I can choose to fold, call, or raise in the next turn. If he calls, the game goes to the second round and the outcome depends on the public card.\n\nPlan 3: Fold\n- If I fold, I lose and the payoff would be -1 chip (half of the total pot).\n\nExpected Chips Gain for Each Plan:\n- Plan 1: (0.7 * 1.5 + 0.3 * 0) * 0.7 + (0.6 * 0 + 0.4 * 0) * 0.3 + (0.7 * 0 + 0.3 * 0) * 0 = 0.735 chips\n- Plan 2: (0.8 * 2 + 0.2 * 0) * 0.7 + (0.7 * 0 + 0.3 * 0) * 0.3 + (0.8 * 0 + 0.2 * 0) * 0 = 1.12 chips\n- Plan 3: -1 * 1 = -1 chip\n\nPlan Selection:\n- Plan 2 > Plan 1 > Plan 3\n- Therefore, I should choose Plan 2: Raise."}}
{"message": "", "28_2": {"plan": "Plan 1: Call\n- If board_game_expert holds a Jack (10% probability), he would likely fold (80% probability). If he folds, I would win the pot, which is currently 10 chips. So, the winning rate for his Jack is 0.1 * 0.8 = 0.08. If he calls (20% probability), it would be a draw if the public card is a Jack, and I would lose if the public card is a Queen or King. So, the draw rate for his Jack is 0.1 * 0.2 * 1/3 = 0.007, and the lose rate for his Jack is 0.1 * 0.2 * 2/3 = 0.013.\n- If board_game_expert holds a Queen (45% probability), he would likely call (60% probability) or raise (40% probability). If he calls, I would win if the public card is a Jack, draw if the public card is a Queen, and lose if the public card is a King. So, the winning rate for his Queen is 0.45 * 0.6 * 1/3 = 0.09, the draw rate for his Queen is 0.45 * 0.6 * 1/3 = 0.09, and the lose rate for his Queen is 0.45 * 0.6 * 1/3 = 0.09. If he raises, I would call, and the outcomes would be the same. So, the overall winning rate for his Queen is 0.18, the draw rate for his Queen is 0.18, and the lose rate for his Queen is 0.18.\n- If board_game_expert holds a King (45% probability), he would likely raise (70% probability) or call (30% probability). If he raises, I would call, and I would win if the public card is a Jack, lose if the public card is a Queen or King. So, the winning rate for his King is 0.45 * 0.7 * 1/3 = 0.105, and the lose rate for his King is 0.45 * 0.7 * 2/3 = 0.21. If he calls, the outcomes would be the same. So, the overall winning rate for his King is 0.105, and the lose rate for his King is 0.21.\n\nPlan 1 overall GoodGuy's Winning/Lose/Draw rates:\n- Winning rate for plan 1: 0.08 + 0.18 + 0.105 = 0.365\n- Lose rate for plan 1: 0.013 + 0.18 + 0.21 = 0.403\n- Draw Rate for plan 1: 0.007 + 0.18 = 0.187\n\nPlan 2: Fold\n- If I fold, I would lose the pot, which is currently 10 chips. So, the lose rate for plan 2 is 1.\n\nPlan 2 overall GoodGuy's Winning/Lose/Draw rates:\n- Winning rate for plan 2: 0\n- Lose rate for plan 2: 1\n- Draw Rate for plan 2: 0\n\nThe number of payoffs for each plan:\n- Plan 1: After the action, all chips in the pot: If win, the winning payoff would be 10/2 = 5 chips. If lose, the lose payoff would be 10/2 = 5 chips.\n- Plan 2: After the action, all chips in the pot: If lose, the lose payoff would be 10/2 = 5 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0.365 * 5 - 0.403 * 5 = -0.19 chips\n- Plan 2: 0 - 1 * 5 = -5 chips\n\nPlan Selection:\n- Plan 1: Call\n- Plan 2: Fold\n\nThe rank of estimated expected chips gains for every plan is as follows:\n1. Plan 1: Call\n2. Plan 2: Fold\n\nTherefore, I should choose Plan 1: Call, as it has the highest estimated expected chips gain."}}
{"message": "", "28_4": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (80% probability), he would likely raise (70% probability) or call (30% probability). If he raises, I would lose (100% probability). If he calls, I would lose (100% probability).\n- If board_game_expert holds a Queen (20% probability), he would likely call (60% probability) or raise (40% probability). If he raises, I would lose (100% probability). If he calls, I would lose (100% probability).\n- Overall, the winning rate for plan 1 is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I would lose the game immediately. 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 board_game_expert holds a King (80% probability), he would likely raise (70% probability) or call (30% probability). If he raises, I would lose (100% probability). If he calls, I would lose (100% probability).\n- If board_game_expert holds a Queen (20% probability), he would likely call (60% probability) or raise (40% probability). If he raises, I would lose (100% probability). If he calls, I would lose (100% probability).\n- Overall, the winning rate for plan 3 is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 8 chips (half of the total pot). If I lose, the losing payoff would be 8 chips.\n- Plan 2: If I lose, the losing payoff would be 6 chips (half of the total pot).\n- Plan 3: If I win, the winning payoff would be 6 chips (half of the total pot). 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% * 8 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\nThe plan with the highest estimated expected chips gain is Plan 2 and Plan 3. However, considering the strategy improvement, I should choose Plan 2: Fold, to minimize losses."}}
{"message": "", "30_1": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (30% probability), he will likely raise (80% probability) or call (20% probability). If he raises, I will win if the public card is a King (33% probability), lose if it's a Queen or Jack (67% probability). If he calls, I will win if the public card is a King or Queen (67% probability), lose if it's a Jack (33% probability).\n- If board_game_expert holds a Queen (40% probability), he will likely call (70% probability) or raise (30% probability). If he calls or raises, I will win if the public card is a King or Queen (67% probability), lose if it's a Jack (33% probability).\n- If board_game_expert holds a Jack (30% probability), he will likely fold (80% probability) or call (20% probability). If he folds, I win. If he calls, I will win if the public card is a King or Queen (67% probability), lose if it's a Jack (33% probability).\n- Overall, the winning rate for Plan 1 is 70%, the losing rate is 30%, and the drawing rate is 0%.\n\nPlan 2: Raise\n- If board_game_expert holds a King (30% probability), he will likely raise (80% probability) or call (20% probability). If he raises, I will win if the public card is a King (33% probability), lose if it's a Queen or Jack (67% probability). If he calls, I will win if the public card is a King or Queen (67% probability), lose if it's a Jack (33% probability).\n- If board_game_expert holds a Queen (40% probability), he will likely call (70% probability) or raise (30% probability). If he calls or raises, I will win if the public card is a King or Queen (67% probability), lose if it's a Jack (33% probability).\n- If board_game_expert holds a Jack (30% probability), he will likely fold (80% probability) or call (20% probability). If he folds, I win. If he calls, I will win if the public card is a King or Queen (67% probability), lose if it's a Jack (33% probability).\n- Overall, the winning rate for Plan 2 is 70%, the losing rate is 30%, and the drawing rate is 0%.\n\nPlan 3: Fold\n- If I fold, I lose regardless of what board_game_expert holds or does. The losing rate for Plan 3 is 100%.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips (half of the total pot of 6 chips). If I lose, the losing payoff would be 2 chips (half of the total pot of 4 chips).\n- Plan 2: If I win, the winning payoff would be 4 chips (half of the total pot of 8 chips). If I lose, the losing payoff would be 3 chips (half of the total pot of 6 chips).\n- Plan 3: If I lose, the losing payoff would be 2 chips (half of the total pot of 4 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.7 * 3 - 0.3 * 2 = 1.7 chips\n- Plan 2: Expected Chips Gain = 0.7 * 4 - 0.3 * 3 = 2.1 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 2 > Plan 1 > Plan 3.\n- Therefore, I should select Plan 2 (Raise) as it has the highest estimated expected chips gain."}}
{"message": "", "30_3": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (60% probability), he will likely raise (80% probability) or call (20% probability). If he raises, we will have a draw. If he calls, I will win.\n- If board_game_expert holds a Queen (40% probability), he will likely fold (70% probability) or call (30% probability). If he folds, I will win. If he calls, I will win.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card board_game_expert holds.\n\nPlan 3: Check\n- If board_game_expert holds a King (60% probability), he will likely raise (70% probability) or call (30% probability). If he raises, we will have a draw. If he calls, I will win.\n- If board_game_expert holds a Queen (40% probability), he will likely raise (40% probability) or call (60% probability). If he raises, I will win. If he calls, I will win.\n\nThe number of 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 6 chips.\n- Plan 2: If I fold, I will lose 6 chips.\n- Plan 3: If I win, the winning payoff would be 6 chips. If I lose, the losing payoff would be 6 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.6 * 6 - 0.4 * 6 = 1.2 chips\n- Plan 2: Expected Chips Gain = -6 chips\n- Plan 3: Expected Chips Gain = 0.6 * 6 - 0.4 * 6 = 1.2 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 have the same expected chips gain, and both are better than Plan 2. However, considering the strategy improvement, Plan 1 (Raise) is more likely to confuse board_game_expert and potentially lead to more gains in the future games. Therefore, I will choose Plan 1: Raise."}}
{"message": "", "31_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, he will likely raise (80%) or call (20%). If he raises, I will likely 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 estimated winning/losing/draw rates are 20%/80%/0%.\n- If board_game_expert holds a Queen, he will likely raise (40%) or call (60%). If he raises, I will likely 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 estimated winning/losing/draw rates are 30%/70%/0%.\n- If board_game_expert holds a Jack, he will likely call (70%) or fold (30%). If he calls, it will be a draw if the public card is a Jack. If he folds, I will win. The estimated winning/losing/draw rates are 30%/0%/70%.\n\nPlan 2: Raise\n- If board_game_expert holds a King, he will likely call (70%) or raise (30%). If he calls, I will likely lose unless the public card is a Jack. If he raises, I will likely lose unless the public card is a Jack. The estimated winning/losing/draw rates are 10%/90%/0%.\n- If board_game_expert holds a Queen, he will likely call (70%) or fold (30%). If he calls, I will likely lose unless the public card is a Jack. If he folds, I will win. The estimated winning/losing/draw rates are 30%/70%/0%.\n- If board_game_expert holds a Jack, he will likely fold (80%) or call (20%). If he folds, I will win. If he calls, it will be a draw if the public card is a Jack. The estimated winning/losing/draw rates are 80%/0%/20%.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of what card board_game_expert holds. The estimated winning/losing/draw rates are 0%/100%/0%.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips (half of the total pot of 6 chips). If I lose, the loss payoff would be 3 chips.\n- Plan 2: If I win, the winning payoff would be 5 chips (half of the total pot of 10 chips). If I lose, the loss payoff would be 5 chips.\n- Plan 3: If I fold, I will lose 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.3 * 3 - 0.7 * 3 = -1.2 chips\n- Plan 2: Expected Chips Gain = 0.4 * 5 - 0.6 * 5 = -1 chips\n- Plan 3: Expected Chips Gain = 0 * 0 - 1 * 2 = -2 chips\n\nPlan Selection:\n- Plan 1: -1.2 chips\n- Plan 2: -1 chips\n- Plan 3: -2 chips\n\nBased on the estimated expected chips gain, Plan 2 (Raise) is the best strategy to follow in this round of the game."}}
{"message": "", "31_2": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (50% probability), he would likely call (60% probability) or fold (40% probability) in the second round if the public card is not a King. If I call, I would win if the public card is a Jack (33.33% probability), lose if the public card is a King (33.33% probability), and draw if the public card is a Queen (33.33% probability). \n- If board_game_expert holds a Queen (50% probability), he would likely call (50% probability) or fold (50% probability) in the second round if the public card is not a Queen. If I call, I would win if the public card is a Jack (33.33% probability), lose if the public card is a Queen (33.33% probability), and draw if the public card is a King (33.33% probability). \n\nPlan 2: Fold\n- If I fold, I would lose the game regardless of board_game_expert's cards or the public card. \n\nThe number of payoffs for each plan:\n- Plan 1: After the action, all chips in the pot would be 10. If win, the winning payoff would be 5. If lose, the lose payoff would be 5. \n- Plan 2: After the action, all chips in the pot would be 10. If lose, the lose payoff would be 5. \n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Lose rate * Lose Payoff = (33.33% * 5) - (33.33% * 5) = 0\n- Plan 2: Expected Chips Gain = - Lose rate * Lose Payoff = - 100% * 5 = -5\n\nPlan Selection:\n- Plan 1 (Call) is ranked first with an expected chips gain of 0.\n- Plan 2 (Fold) is ranked second with an expected chips gain of -5.\n\nTherefore, the best strategy would be to call."}}
{"message": "", "31_4": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King, he will likely call (60% probability) or fold (40% probability). If he calls, I will lose (as King is higher than Jack), if he folds, I will win. So, the winning rate is 40%, losing rate is 60%, and draw rate is 0%.\n- If board_game_expert holds a Queen, he will likely call (50% probability) or fold (50% probability). If he calls, I will lose (as Queen matches the public card), if he folds, I will win. So, the winning rate is 50%, losing rate is 50%, and draw rate is 0%.\n- If board_game_expert holds a Jack, he will likely call (20% probability) or fold (80% probability). If he calls, it will be a draw (as we both hold Jack), if he folds, I will win. So, the 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 board_game_expert holds. So, the winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n\nPlan 3: Check\n- If board_game_expert holds a King, he will likely call (60% probability) or fold (40% probability). If he calls, I will lose (as King is higher than Jack), if he folds, I will win. So, the winning rate is 40%, losing rate is 60%, and draw rate is 0%.\n- If board_game_expert holds a Queen, he will likely call (50% probability) or fold (50% probability). If he calls, I will lose (as Queen matches the public card), if he folds, I will win. So, the winning rate is 50%, losing rate is 50%, and draw rate is 0%.\n- If board_game_expert holds a Jack, he will likely call (20% probability) or fold (80% probability). If he calls, it will be a draw (as we both hold Jack), if he folds, I will win. So, the winning rate is 80%, losing rate is 0%, and draw rate is 20%.\n\nThe number of payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 6 chips (half of the total pot). If lose, the losing payoff would be 6 chips.\n- Plan 2: If lose, the losing payoff would be 6 chips.\n- Plan 3: If win, the winning payoff would be 6 chips. If 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 = 0.4 * 6 - 0.6 * 6 = -1.2 chips\n\nPlan Selection:\n- Plan 1: Expected Chips Gain = -1.2 chips\n- Plan 2: Expected Chips Gain = -6 chips\n- Plan 3: Expected Chips Gain = -1.2 chips\n\nBased on the estimated expected chips gain, Plan 1 and Plan 3 are the best strategies to follow. However, considering the strategy improvement, Plan 1 (Raise) would be the best strategy to follow as it can potentially confuse board_game_expert and make him fold."}}
{"message": "", "32_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, he will likely call (30%) or raise (70%). If he calls, I will likely win (33%) or lose (67%). If he raises, I will likely win (33%) or lose (67%). Overall, my winning rate is 33%, losing rate is 67%, and draw rate is 0%.\n- If board_game_expert holds a Queen, he will likely call (60%) or raise (40%). If he calls, it will be a draw (100%). If he raises, it will be a draw (100%). Overall, my winning rate is 0%, losing rate is 0%, and draw rate is 100%.\n- If board_game_expert holds a Jack, he will likely call (50%) or fold (50%). If he calls, I will likely win (67%) or lose (33%). If he folds, I will win (100%). Overall, my winning rate is 83.5%, losing rate is 16.5%, and draw rate is 0%.\n\nPlan 2: Raise\n- If board_game_expert holds a King, he will likely call (80%) or raise (20%). If he calls, I will likely win (33%) or lose (67%). If he raises, I will likely win (33%) or lose (67%). Overall, my winning rate is 33%, losing rate is 67%, and draw rate is 0%.\n- If board_game_expert holds a Queen, he will likely call (70%) or fold (30%). If he calls, it will be a draw (100%). If he folds, I will win (100%). Overall, my winning rate is 30%, losing rate is 0%, and draw rate is 70%.\n- If board_game_expert holds a Jack, he will likely fold (80%) or call (20%). If he folds, I will win (100%). If he calls, I will likely win (67%) or lose (33%). Overall, my winning rate is 86%, losing rate is 14%, and draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of what card board_game_expert holds. So, my winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips. If I lose, the losing payoff would be 2 chips.\n- Plan 2: If I win, the winning payoff would be 5 chips. If I lose, the losing payoff would be 4 chips.\n- Plan 3: If I lose, the losing payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 33% * 3 - 67% * 2 = -0.33 chips\n- Plan 2: Expected Chips Gain = 48.67% * 5 - 27% * 4 = 0.835 chips\n- Plan 3: Expected Chips Gain = 0% * 0 - 100% * 2 = -2 chips\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain, so I should choose Plan 2: Raise."}}
{"message": "", "32_2": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (40% probability), he would likely call (80%) or raise (20%). If he calls, I would win as I have a pair of Queens. If he raises, I would still win as I have a pair of Queens. Therefore, the winning rate for this plan is 100%.\n- If board_game_expert holds a Queen (35% probability), he would likely call (70%) or fold (20%). If he calls, it would be a draw as we both have a pair of Queens. If he folds, I would win. Therefore, the winning rate for this plan is 80% and the draw rate is 20%.\n- If board_game_expert holds a Jack (25% probability), he would likely fold (90%) or call (10%). If he folds, I would win. If he calls, I would still win as I have a pair of Queens. Therefore, the winning rate for this plan is 100%.\n\nPlan 2: Fold\n- If I fold, I would lose regardless of what card board_game_expert holds. Therefore, the losing rate for this plan is 100%.\n\nPlan 3: Check\n- If board_game_expert holds a King (40% probability), he would likely call (80%) or raise (20%). If he calls, I would win as I have a pair of Queens. If he raises, I would still win as I have a pair of Queens. Therefore, the winning rate for this plan is 100%.\n- If board_game_expert holds a Queen (35% probability), he would likely call (70%) or fold (20%). If he calls, it would be a draw as we both have a pair of Queens. If he folds, I would win. Therefore, the winning rate for this plan is 80% and the draw rate is 20%.\n- If board_game_expert holds a Jack (25% probability), he would likely fold (90%) or call (10%). If he folds, I would win. If he calls, I would still win as I have a pair of Queens. Therefore, the winning rate for this plan is 100%.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (8 chips). If I lose, the losing payoff would be half of the total pot (8 chips).\n- Plan 2: If I lose, the losing payoff would be half of the total pot (8 chips).\n- Plan 3: If I win, the winning payoff would be half of the total pot (8 chips). If I lose, the losing payoff would be half of the total pot (8 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 1.0 * 8 - 0 * 8 = 8 chips\n- Plan 2: Expected Chips Gain = 0 * 8 - 1.0 * 8 = -8 chips\n- Plan 3: Expected Chips Gain = 1.0 * 8 - 0 * 8 = 8 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 both have the highest expected chips gain of 8 chips, while Plan 2 has the lowest expected chips gain of -8 chips. Therefore, I should either raise (Plan 1) or check (Plan 3). Considering the strategy improvement, raising (Plan 1) would be the best option as it could pressure board_game_expert into folding."}}
{"message": "", "32_4": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (60% probability), he will likely call (90% probability). I will win as my pair of Queens beats his single King. The winning rate for his King is 0.6*0.9 = 54%.\n- If board_game_expert holds a Jack (40% probability), he will likely fold (90% probability). I will win as he folds. The winning rate for his Jack is 0.4*0.9 = 36%.\n- Overall, the winning rate for Plan 1 is 54% + 36% = 90%. There is no lose rate or draw rate as board_game_expert cannot beat my pair of Queens.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card board_game_expert holds. The lose rate is 100%.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the total chips in the pot would be 20 (my 12 chips + board_game_expert's 8 chips). The winning payoff would be half of the total pot, which is 10 chips.\n- Plan 2: If I lose, the total chips in the pot would be 12 (my 12 chips). The lose payoff would be half of the total pot, which is 6 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is winning rate * winning payoff = 0.9 * 10 = 9 chips.\n- Plan 2: The expected chips loss is lose rate * lose payoff = 1 * 6 = -6 chips.\n\nPlan Selection:\n- Plan 1 (Call) has the highest expected chips gain of 9 chips. Therefore, I should choose Plan 1."}}
{"message": "", "34_1": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (16.67% chance), he would likely call (70%) or raise (30%). If he calls, I would likely win (50%) or draw (50%). If he raises, I would likely win (50%) or draw (50%).\n- If board_game_expert holds a Queen (50% chance), he would likely call (70%) or fold (30%). If he calls, I would likely win (100%). If he folds, I would win by default.\n- If board_game_expert holds a Jack (33.33% chance), he would likely fold (80%) or call (20%). If he folds, I would win by default. If he calls, I would likely win (100%).\n\nPlan 2: Fold\n- If I fold, I would lose by default, regardless of what card board_game_expert holds.\n\nPlan 3: Check\n- If board_game_expert holds a King (16.67% chance), he would likely raise (80%) or check (20%). If he raises, I would likely win (50%) or draw (50%). If he checks, I would likely win (50%) or draw (50%).\n- If board_game_expert holds a Queen (50% chance), he would likely raise (40%) or check (60%). If he raises, I would likely win (100%). If he checks, I would likely win (100%).\n- If board_game_expert holds a Jack (33.33% chance), he would likely check (50%) or fold (50%). If he checks, I would likely win (100%). If he folds, I would win by default.\n\nPayoffs for each plan:\n- Plan 1: If I win, the pot would be 6 chips, and I would gain 3 chips. If I lose, I would lose 2 chips.\n- Plan 2: If I fold, I would lose 2 chips.\n- Plan 3: If I win, the pot would be 4 chips, and I would gain 2 chips. If I lose, I would lose 2 chips.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: (0.83 * 3) - (0.17 * 2) = 2.33 chips\n- Plan 2: -2 chips\n- Plan 3: (0.83 * 2) - (0.17 * 2) = 1.33 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I should choose to raise."}}
{"message": "", "35_1": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (70% probability), he will likely call (80%) or raise (20%). If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. The winning rate is 0.7*0.2*0.33 = 0.0462, the losing rate is 0.7*0.8*0.67 = 0.3756, and the draw rate is 0.\n- If board_game_expert holds a Queen (30% probability), he will likely call (80%) or fold (20%). If the public card is a King, I will lose. If the public card is a Queen or Jack, I will win. The winning rate is 0.3*0.8*0.67 = 0.1608, the losing rate is 0.3*0.2*0.33 = 0.0198, and the draw rate is 0.\n- Overall, the winning rate for Plan 1 is 0.207, the losing rate is 0.3954, and the draw rate is 0.\n\nPlan 2: Raise\n- If board_game_expert holds a King (70% probability), he will likely call (90%) or raise (10%). If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. The winning rate is 0.7*0.1*0.33 = 0.0231, the losing rate is 0.7*0.9*0.67 = 0.4233, and the draw rate is 0.\n- If board_game_expert holds a Queen (30% probability), he will likely call (80%) or fold (20%). If the public card is a King, I will lose. If the public card is a Queen or Jack, I will win. The winning rate is 0.3*0.8*0.67 = 0.1608, the losing rate is 0.3*0.2*0.33 = 0.0198, and the draw rate is 0.\n- Overall, the winning rate for Plan 2 is 0.1839, the losing rate is 0.4431, 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 1, and the draw rate is 0.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (6 chips). If I lose, the loss would be 2 chips.\n- Plan 2: If I win, the winning payoff would be half of the total pot (8 chips). If I lose, the loss would be 4 chips.\n- Plan 3: If I fold, the loss would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0.207 * 6 - 0.3954 * 2 = 0.2442\n- Plan 2: 0.1839 * 8 - 0.4431 * 4 = -0.0156\n- Plan 3: -2\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I should choose to call."}}
{"message": "", "35_3": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (80% probability), he will likely call (90% probability). If he calls, I will lose as his pair of Kings beats my single Jack. \n- If board_game_expert holds a Queen (10% probability), he will likely call (80% probability). If he calls, I will win as my Jack beats his Queen. \n- If board_game_expert holds a Jack (10% probability), he will likely fold (90% probability). If he folds, I will win as he forfeits the game. \n\nPlan 2: Raise\n- If board_game_expert holds a King (80% probability), he will likely call (90% probability). If he calls, I will lose as his pair of Kings beats my single Jack. \n- If board_game_expert holds a Queen (10% probability), he will likely fold (20% probability). If he folds, I will win as he forfeits the game. \n- If board_game_expert holds a Jack (10% probability), he will likely fold (90% probability). If he folds, I will win as he forfeits the game. \n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of what card board_game_expert holds. \n\nPayoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 12 chips (half of the total pot of 24 chips). If I lose, the losing payoff would be 12 chips. \n- Plan 2: If I win, the winning payoff would be 20 chips (half of the total pot of 40 chips). If I lose, the losing payoff would be 20 chips. \n- Plan 3: If I fold, I will lose 8 chips (the amount I have already put in the pot). \n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.1 * 12 - 0.8 * 12 = -8.4 chips\n- Plan 2: Expected Chips Gain = 0.2 * 20 - 0.8 * 20 = -12 chips\n- Plan 3: Expected Chips Gain = -8 chips\n\nPlan Selection:\nBased on the expected chips gain, Plan 1 (Call) is the best strategy as it has the highest expected chips gain (-8.4 chips). Plan 2 (Raise) is the second best strategy with an expected chips gain of -12 chips. Plan 3 (Fold) is the worst strategy with an expected chips gain of -8 chips. Therefore, I should choose Plan 1 (Call)."}}
{"message": "", "36_1": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (40% probability), he will likely raise (70%) or call (30%). If he raises, I will lose unless the public card is a King. If he calls, I will win unless the public card is a King. Therefore, the winning rate is 30%, the losing rate is 70%, and the draw rate is 0%.\n- If board_game_expert holds a Queen (60% probability), he will likely call (60%) or fold (40%). If he calls, I will win unless the public card is a Queen. If he folds, I will win. Therefore, the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If board_game_expert holds a King (40% probability), he will likely raise (70%) or call (30%). If he raises, I will lose unless the public card is a King. If he calls, I will win unless the public card is a King. Therefore, the winning rate is 30%, the losing rate is 70%, and the draw rate is 0%.\n- If board_game_expert holds a Queen (60% probability), he will likely call (70%) or fold (30%). If he calls, I will win unless the public card is a Queen. If he folds, I will win. Therefore, the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot. Therefore, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 6 chips (half of the total pot of 12 chips). If I lose, the losing payoff would be 6 chips.\n- Plan 2: If I win, the winning payoff would be 10 chips (half of the total pot of 20 chips). If I lose, the losing payoff would be 10 chips.\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 = 0.7 * 6 - 0.3 * 6 = 2.4 chips\n- Plan 2: Expected Chips Gain = 0.7 * 10 - 0.3 * 10 = 4 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, followed by Plan 1 (Call), and Plan 3 (Fold). Therefore, I should choose to raise."}}
{"message": "", "36_3": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King, he will likely raise (60%) or call (40%). If he raises, I will likely lose as we both have a King but he has more chips. If he calls, I will likely win as I have a higher card. \n- If board_game_expert holds a Jack, he will likely raise (70%) or call (30%). If he raises, I will likely lose as he has a pair of Jacks. If he calls, I will likely win as I have a higher card. \n\nPlan 2: Fold\n- If I fold, I will lose the current pot but save my remaining chips. This is a safe strategy but does not allow for potential gains. \n\nPlan 3: Check\n- If board_game_expert holds a King, he will likely raise (60%) or check (40%). If he raises, I will likely lose as we both have a King but he has more chips. If he checks, I will likely win as I have a higher card. \n- If board_game_expert holds a Jack, he will likely raise (70%) or check (30%). If he raises, I will likely lose as he has a pair of Jacks. If he checks, I will likely win as I have a higher card. \n\nPayoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (currently 12 chips, so 6 chips). If I lose, the losing payoff would be half of the total pot (6 chips).\n- Plan 2: If I fold, there is no winning payoff. 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 total pot (6 chips). If I lose, the losing payoff would be half of the total pot (6 chips).\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected gain = (0.4 * 6) - (0.6 * 6) = -1.2 chips\n- Plan 2: Expected gain = 0 - 6 = -6 chips\n- Plan 3: Expected gain = (0.4 * 6) - (0.6 * 6) = -1.2 chips\n\nPlan Selection:\nBased on the expected chips gain, Plan 1 and Plan 3 are the best strategies as they have the highest expected gain (-1.2 chips). However, considering the strategy improvement, Plan 1 (Raise) might be a better choice as it could potentially confuse board_game_expert and lead to a higher payoff in the future games."}}
{"message": "", "37_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, he would likely raise (70%) or call (30%). If he raises, I would likely lose this round. If he calls, I have a chance to win if the public card is a Queen. \n- If board_game_expert holds a Queen, he would likely call (60%) or raise (40%). If he raises, I would likely lose this round. If he calls, it would be a draw if the public card is not a Queen. \n- If board_game_expert holds a Jack, he would likely call (50%) or fold (50%). If he folds, I would win this round. If he calls, I have a chance to win if the public card is not a Jack. \n\nPlan 2: Raise\n- If board_game_expert holds a King, he would likely call (80%) or raise (20%). If he raises, I would likely lose this round. If he calls, I have a chance to win if the public card is a Queen. \n- If board_game_expert holds a Queen, he would likely call (70%) or fold (30%). If he folds, I would win this round. If he calls, it would be a draw if the public card is not a Queen. \n- If board_game_expert holds a Jack, he would likely fold (80%) or call (20%). If he folds, I would win this round. If he calls, I have a chance to win if the public card is not a Jack. \n\nPlan 3: Fold\n- If I fold, I would lose this round regardless of what card board_game_expert holds. \n\nThe number of payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 3 chips (half of the total pot of 6 chips). If lose, the lose payoff would be 2 chips (half of the total pot of 4 chips).\n- Plan 2: If win, the winning payoff would be 5 chips (half of the total pot of 10 chips). If lose, the lose payoff would be 3 chips (half of the total pot of 6 chips).\n- Plan 3: If lose, the lose payoff would be 2 chips (half of the total pot of 4 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.33*(3*0.5 - 2*0.5) + 0.33*(3*0.3 - 2*0.7) + 0.33*(3*0.5 - 2*0.5) = 0.33 chips\n- Plan 2: Expected Chips Gain = 0.33*(5*0.2 - 3*0.8) + 0.33*(5*0.3 - 3*0.7) + 0.33*(5*0.8 - 3*0.2) = 0.66 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain, so I would choose Plan 2: Raise."}}
{"message": "", "37_2": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (80% probability), he would likely call (90%) or raise (10%). If he calls, I would win (probability = 80% * 90% = 72%). If he raises, I would still win (probability = 80% * 10% = 8%).\n- If board_game_expert holds a Jack (20% probability), he would likely fold (90%) or call (10%). If he folds, I would win (probability = 20% * 90% = 18%). If he calls, I would still win (probability = 20% * 10% = 2%).\n\nPlan 2: Fold\n- If I fold, I would lose regardless of what board_game_expert holds.\n\nPlan 3: Check\n- If board_game_expert holds a King (80% probability), he would likely call (90%) or raise (10%). If he calls, I would win (probability = 80% * 90% = 72%). If he raises, I would still win (probability = 80% * 10% = 8%).\n- If board_game_expert holds a Jack (20% probability), he would likely fold (90%) or call (10%). If he folds, I would win (probability = 20% * 90% = 18%). If he calls, I would still win (probability = 20% * 10% = 2%).\n\nThe number of payoffs for each plan:\n- Plan 1: After the action, all chips in the pot would be 16. If win, the winning payoff would be 8. If lose, the lose payoff would be 8.\n- Plan 2: After the action, all chips in the pot would be 8. If lose, the lose payoff would be 4.\n- Plan 3: After the action, all chips in the pot would be 8. If win, the winning payoff would be 4. If lose, the lose payoff would be 4.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 72% * 8 + 8% * 8 - 0% * 8 = 6.4 chips\n- Plan 2: Expected Chips Gain = 0% * 4 - 100% * 4 = -4 chips\n- Plan 3: Expected Chips Gain = 72% * 4 + 8% * 4 - 0% * 4 = 3.2 chips\n\nPlan Selection:\n- Plan 1: Raise (Expected Chips Gain = 6.4)\n- Plan 3: Check (Expected Chips Gain = 3.2)\n- Plan 2: Fold (Expected Chips Gain = -4)\n\nTherefore, the best plan is to raise."}}
{"message": "", "37_4": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (100% probability), he will likely call (90% probability). If he calls, I will win because my pair of Queens beats his single King. Therefore, the winning rate for this plan is 90% (100% * 90%), the losing rate is 0%, and the draw rate is 10% (100% * 10%).\n- The total chips in the pot after I call will be 16 (my 12 chips + board_game_expert's 4 chips). If I win, the winning payoff would be 8 chips (half of the total pot). If I lose, the losing payoff would be 8 chips.\n- The expected chips gain for this plan is 7.2 chips (90% * 8 chips - 0% * 8 chips).\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- The total chips in the pot after I fold will be 12 (my 12 chips). If I lose, the losing payoff would be 6 chips (half of the total pot).\n- The expected chips loss for this plan is 6 chips (0% * 0 chips - 100% * 6 chips).\n\nPlan Selection:\n- Plan 1 (Call) has an expected chips gain of 7.2 chips.\n- Plan 2 (Fold) has an expected chips loss of 6 chips.\nTherefore, I should select Plan 1 (Call) as it has the highest estimated expected chips gain."}}
{"message": "", "38_1": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (57% probability), he will likely raise (70% probability). If the public card is a King, I will win (33% probability). If the public card is a Queen or Jack, I will lose (67% probability). \n- If board_game_expert holds a Queen (43% probability), he will likely call (70% probability). If the public card is a King, I will win (33% probability). If the public card is a Queen, it will be a draw (33% probability). If the public card is a Jack, I will win (33% probability). \n\nPlan 2: Raise\n- If board_game_expert holds a King (57% probability), he will likely raise (70% probability). If the public card is a King, I will win (33% probability). If the public card is a Queen or Jack, I will lose (67% probability). \n- If board_game_expert holds a Queen (43% probability), he will likely fold (30% probability). If the public card is a King, I will win (33% probability). If the public card is a Queen, it will be a draw (33% probability). If the public card is a Jack, I will win (33% probability). \n\nPlan 3: Fold\n- If I fold, I will lose the round regardless of board_game_expert's card or the public card. \n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (6 chips). If I lose, the losing payoff would be half of the total pot (6 chips).\n- Plan 2: If I win, the winning payoff would be half of the total pot (8 chips). If I lose, the losing payoff would be half of the total pot (8 chips).\n- Plan 3: If I fold, I will lose 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.57 * 0.7 * 0.33 * 6 - 0.57 * 0.7 * 0.67 * 6 = -0.57 chips\n- Plan 2: Expected Chips Gain = 0.57 * 0.7 * 0.33 * 8 - 0.57 * 0.7 * 0.67 * 8 = -0.76 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- Plan 1: -0.57 chips\n- Plan 2: -0.76 chips\n- Plan 3: -2 chips\n\nBased on the estimated expected chips gain, Plan 1 (Call) is the best strategy to follow."}}
{"message": "", "38_3": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King, he will likely raise (60% probability) or call (40% probability). If he raises, we will have a draw. If he calls, I will win. So, the winning rate is 40%, draw rate is 60%, and lose rate is 0%.\n- If board_game_expert holds a Queen, he will likely call (60% probability) or fold (40% probability). If he calls or folds, I will win. So, the winning rate is 100%, draw rate is 0%, and lose rate is 0%.\n- If board_game_expert holds a Jack, he will likely fold (90% probability) or call (10% probability). If he folds or calls, I will win. 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 lose regardless of what board_game_expert holds. So, the winning rate is 0%, draw rate is 0%, and lose rate is 100%.\n\nPlan 3: Check\n- If board_game_expert holds a King, he will likely raise (60% probability) or call (40% probability). If he raises, we will have a draw. If he calls, I will win. So, the winning rate is 40%, draw rate is 60%, and lose rate is 0%.\n- If board_game_expert holds a Queen, he will likely call (60% probability) or fold (40% probability). If he calls or folds, I will win. So, the winning rate is 100%, draw rate is 0%, and lose rate is 0%.\n- If board_game_expert holds a Jack, he will likely fold (90% probability) or call (10% probability). If he folds or calls, I will win. So, the winning rate is 100%, draw rate is 0%, and lose rate is 0%.\n\nThe number of payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 8 chips. If lose, the lose payoff would be 4 chips.\n- Plan 2: If lose, the lose payoff would be 4 chips.\n- Plan 3: If win, the winning payoff would be 4 chips. If lose, the lose payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.8 * 8 - 0 * 4 = 6.4 chips\n- Plan 2: Expected Chips Gain = 0 * 0 - 1 * 4 = -4 chips\n- Plan 3: Expected Chips Gain = 0.8 * 4 - 0 * 4 = 3.2 chips\n\nPlan Selection:\n- Plan 1: Raise\n- Plan 3: Check\n- Plan 2: Fold\n\nThe best plan is to raise, as it has the highest expected chips gain."}}
{"message": "", "38_5": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (50% probability), he will likely raise (60% probability). If he raises, I will lose as his King matches my King, resulting in a draw. The overall losing rate for this scenario is 30% (50% * 60%).\n- If board_game_expert holds a Queen (40% probability), he will likely call (60% probability). If he calls, I will win as my King is higher than his Queen. The overall winning rate for this scenario is 24% (40% * 60%).\n- If board_game_expert holds a Jack (10% probability), he will likely fold (90% probability). If he folds, I will win as my King is higher than his Jack. The overall winning rate for this scenario is 9% (10% * 90%).\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of what card board_game_expert holds. The overall losing rate for this scenario is 100%.\n\nPayoffs for Each Plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (20/2 = 10 chips). If I lose, the losing payoff would be the chips I have already put in the pot (12 chips).\n- Plan 2: If I fold, I will lose the chips I have already put in the pot (12 chips).\n\nExpected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is the winning rate * winning payoff - losing rate * losing payoff = 24% * 10 - 30% * 12 = 0.6 chips.\n- Plan 2: The expected chips gain is the winning rate * winning payoff - losing rate * losing payoff = 0% * 0 - 100% * 12 = -12 chips.\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain (0.6 chips), so I should choose to 'call'."}}
{"message": "", "39_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, he will likely call (20% probability) or raise (80% probability). If he calls, I will likely win (50% probability) or lose (50% probability). If he raises, I will likely lose (100% probability). Overall, the winning rate is 10%, the losing rate is 90%, and the draw rate is 0%.\n- If board_game_expert holds a Queen, he will likely call (60% probability) or raise (40% probability). If he calls, I will likely win (50% probability) or lose (50% probability). If he raises, I will likely lose (100% probability). Overall, the winning rate is 30%, the losing rate is 70%, and the draw rate is 0%.\n- If board_game_expert holds a Jack, he will likely call (50% probability) or fold (50% probability). If he calls, I will likely win (50% probability) or draw (50% probability). If he folds, I will win (100% probability). Overall, the winning rate is 75%, the losing rate is 0%, and the draw rate is 25%.\n\nPlan 2: Raise\n- If board_game_expert holds a King, he will likely call (70% probability) or raise (30% probability). If he calls, I will likely lose (100% probability). If he raises, I will likely lose (100% probability). Overall, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If board_game_expert holds a Queen, he will likely call (70% probability) or fold (30% probability). If he calls, I will likely lose (100% probability). If he folds, I will win (100% probability). Overall, the winning rate is 30%, the losing rate is 70%, and the draw rate is 0%.\n- If board_game_expert holds a Jack, he will likely fold (80% probability) or call (20% probability). If he folds, I will win (100% probability). If he calls, I will likely win (50% probability) or draw (50% probability). Overall, the winning rate is 90%, the losing rate is 0%, and the draw rate is 10%.\n\nPlan 3: Fold\n- If I fold, I will lose (100% probability). The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips. If I lose, the losing payoff would be 2 chips.\n- Plan 2: If I win, the winning payoff would be 7 chips. If I lose, the losing payoff would be 6 chips.\n- Plan 3: If I lose, the losing payoff would be 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.38 chips\n- Plan 2: Expected Chips Gain = 1.2 chips\n- Plan 3: Expected Chips Gain = -1 chips\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows: Plan 2 > Plan 1 > Plan 3. Therefore, I should execute Plan 2, which is to raise."}}
{"message": "", "39_2": {"plan": "Plan 1: Raise\n- If board_game_expert holds a Queen (70% probability), he would likely call (70% probability) or fold (30% probability). If he calls, I would lose as his Queen outranks my Jack. If he folds, I would win the pot. \n- If board_game_expert holds a King (30% probability), he would likely call (70% probability) or raise (30% probability). In both cases, I would lose as his King outranks my Jack.\n\nPlan 2: Fold\n- If I fold, I would lose the current pot but minimize my losses.\n\nPlan 3: Check\n- If board_game_expert holds a Queen (70% probability), he would likely check as well, leading to a loss for me as his Queen outranks my Jack. \n- If board_game_expert holds a King (30% probability), he would likely check as well, leading to a loss for me as his King outranks my Jack.\n\nPayoffs for each plan:\n- Plan 1: If win, the winning payoff would be half of the total pot (8 chips). If lose, the loss payoff would be half of the total pot (8 chips).\n- Plan 2: If I fold, I would lose 4 chips from the pot.\n- Plan 3: If win, the winning payoff would be half of the total pot (8 chips). If lose, the loss payoff would be half of the total pot (8 chips).\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected gain = 0.7 * 0.3 * 8 - 0.7 * 0.7 * 8 - 0.3 * 8 = -5.6 chips\n- Plan 2: Expected loss = -4 chips\n- Plan 3: Expected gain = 0 - 0.7 * 8 - 0.3 * 8 = -8 chips\n\nPlan Selection:\n- Plan 1: Expected gain = -5.6 chips\n- Plan 2: Expected loss = -4 chips\n- Plan 3: Expected gain = -8 chips\n\nBased on the expected chips gain, Plan 2 (Fold) is the best strategy to minimize loss in this round."}}
{"message": "", "40_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, he will likely call (30%) or raise (70%). If he raises, I will call again in the next round. The winning rate is 50% (if the public card is a King), the losing rate is 0% (since my card is also a King), and the draw rate is 50% (if the public card is not a King).\n- If board_game_expert holds a Queen, he will likely call (60%) or raise (40%). If he raises, I will call again in the next round. The winning rate is 100% (since my card is a King), the losing rate is 0%, and the draw rate is 0%.\n- If board_game_expert holds a Jack, he will likely call (50%) or fold (50%). If he folds, I win the game. The winning rate is 100% (since my card is a King), the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If board_game_expert holds a King, he will likely call (80%) or raise (20%). If he raises, I will call in the next round. The winning rate is 50% (if the public card is a King), the losing rate is 0% (since my card is also a King), and the draw rate is 50% (if the public card is not a King).\n- If board_game_expert holds a Queen, he will likely call (70%) or fold (30%). If he folds, I win the game. The winning rate is 100% (since my card is a King), the losing rate is 0%, and the draw rate is 0%.\n- If board_game_expert holds a Jack, he will likely fold (80%) or call (20%). If he folds, I win the game. The winning rate is 100% (since my card is a King), the losing rate is 0%, and the draw rate is 0%.\n\nPlan 3: Fold\n- This plan is not reasonable since I hold a King, which is the highest rank in this game.\n\nThe number of payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 3 chips (half of the total pot of 6 chips). If lose, the lose payoff would be 3 chips.\n- Plan 2: If win, the winning payoff would be 5 chips (half of the total pot of 10 chips). If lose, the lose payoff would be 5 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.83 * 3 - 0 * 3 = 2.49 chips\n- Plan 2: Expected Chips Gain = 0.83 * 5 - 0 * 5 = 4.15 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I will choose this plan."}}
{"message": "", "40_2": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (40% probability), he would likely call (90%) or raise (10%). If he calls, we would draw. If he raises, we would draw. Overall, the draw rate is 100%.\n- If board_game_expert holds a Queen (35% probability), he would likely call (80%) or fold (20%). If he calls, I would lose. If he folds, I would win. Overall, the winning rate is 20% and the losing rate is 80%.\n- If board_game_expert holds a Jack (25% probability), he would likely fold (90%) or call (10%). If he folds, I would win. If he calls, I would win. Overall, the winning rate is 100%.\n\nPlan 2: Fold\n- If I fold, I would lose regardless of what card board_game_expert holds. The losing rate is 100%.\n\nPlan 3: Check\n- If board_game_expert holds a King (40% probability), he would likely call (90%) or raise (10%). If he calls, we would draw. If he raises, we would draw. Overall, the draw rate is 100%.\n- If board_game_expert holds a Queen (35% probability), he would likely call (80%) or fold (20%). If he calls, I would lose. If he folds, I would win. Overall, the winning rate is 20% and the losing rate is 80%.\n- If board_game_expert holds a Jack (25% probability), he would likely fold (90%) or call (10%). If he folds, I would win. If he calls, I would win. Overall, the winning rate is 100%.\n\nPayoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 8 chips (half of the total pot). If I lose, the losing payoff would be 8 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\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.2 * 8 - 0.8 * 8 = -4.8 chips\n- Plan 2: Expected Chips Gain = -4 chips\n- Plan 3: Expected Chips Gain = 0.2 * 4 - 0.8 * 4 = -2.4 chips\n\nPlan Selection:\n- Plan 1: -4.8 chips\n- Plan 2: -4 chips\n- Plan 3: -2.4 chips\n\nTherefore, the best plan is Plan 3: Check, as it has the highest expected chips gain."}}
{"message": "", "40_4": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (85% probability), he will likely call (90% probability). If he calls, I will win because my card is of higher rank. Therefore, the winning rate for this plan is 85% * 90% = 76.5%.\n- If board_game_expert holds a Queen (75% probability), he will likely call (80% probability). If he calls, I will lose because his card matches the public card. Therefore, the losing rate for this plan is 75% * 80% = 60%.\n- If board_game_expert holds a Jack (15% probability), he will likely fold (90% probability). If he folds, I will win because my card is of higher rank. Therefore, the winning rate for this plan is 15% * 90% = 13.5%.\n\nPlan 2: Raise\n- If board_game_expert holds a King (85% probability), he will likely call (90% probability). If he calls, I will win because my card is of higher rank. Therefore, the winning rate for this plan is 85% * 90% = 76.5%.\n- If board_game_expert holds a Queen (75% probability), he will likely fold (20% probability). If he folds, I will win because my card is of higher rank. Therefore, the winning rate for this plan is 75% * 20% = 15%.\n- If board_game_expert holds a Jack (15% probability), he will likely fold (90% probability). If he folds, I will win because my card is of higher rank. Therefore, the winning rate for this plan is 15% * 90% = 13.5%.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of what card board_game_expert holds. Therefore, the losing rate for this plan is 100%.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (12 chips). If I lose, the losing payoff would be half of the total pot (12 chips).\n- Plan 2: If I win, the winning payoff would be half of the total pot (16 chips). If I lose, the losing payoff would be half of the total pot (16 chips).\n- Plan 3: If I lose, the losing payoff would be half of the total pot (8 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 76.5% * 12 chips - 60% * 12 chips = 1.98 chips\n- Plan 2: Expected Chips Gain = 76.5% * 16 chips - 15% * 16 chips = 9.84 chips\n- Plan 3: Expected Chips Gain = -100% * 8 chips = -8 chips\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain (9.84 chips), followed by Plan 1 (1.98 chips), and Plan 3 (-8 chips). Therefore, I should choose Plan 2: Raise."}}
{"message": "", "41_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, he will likely raise (80% probability) or call (20% probability). If he raises, I will call again. If he calls, the round will end. The winning rate is 50% (if the public card is a King or lower than a Queen), the losing rate is 50% (if the public card is a Queen), and the draw rate is 0%.\n- If board_game_expert holds a Queen, he will likely call (60% probability) or raise (40% probability). If he raises, I will call again. If he calls, the round will end. The winning rate is 100% (as my card is higher), the losing rate is 0%, and the draw rate is 0%.\n- If board_game_expert holds a Jack, he will likely call (50% probability) or fold (50% probability). If he folds, I win the round. If he calls, the round will end. The winning rate is 100% (as my card is higher), the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If board_game_expert holds a King, he will likely call (70% probability) or raise (30% probability). If he raises, I will call. If he calls, the round will end. The winning rate is 50% (if the public card is a King or lower than a Queen), the losing rate is 50% (if the public card is a Queen), and the draw rate is 0%.\n- If board_game_expert holds a Queen, he will likely call (70% probability) or fold (30% probability). If he folds, I win the round. If he calls, the round will end. The winning rate is 100% (as my card is higher), the losing rate is 0%, and the draw rate is 0%.\n- If board_game_expert holds a Jack, he will likely fold (80% probability) or call (20% probability). If he folds, I win the round. If he calls, the round will end. The winning rate is 100% (as my card is higher), the losing rate is 0%, and the draw rate is 0%.\n\nPlan 3: Fold\n- This plan is not reasonable as I hold the highest rank card.\n\nThe number of payoffs for each plan:\n- Plan 1: If win, the winning payoff would be half of the total pot (3 chips). If lose, the losing payoff would be half of the total pot (3 chips).\n- Plan 2: If win, the winning payoff would be half of the total pot (4 chips). If lose, the losing payoff would be half of the total pot (4 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.83 * 3 - 0.17 * 3 = 2 chips\n- Plan 2: Expected Chips Gain = 0.83 * 4 - 0.17 * 4 = 3.32 chips\n\nPlan Selection:\n- Plan 2 (Raise) is the best strategy as it has the highest expected chips gain."}}
{"message": "", "41_2": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (47% probability), he will likely call (60% probability) or raise (40% probability) in the second round. If the public card is a King, I will win (probability = 47% * 100% = 47%). If the public card is a Queen or Jack, I will lose (probability = 47% * 0% = 0%). \n- If board_game_expert holds a Queen (24% probability), he will likely call (50% probability) or fold (50% probability) in the second round. If the public card is a Queen, I will lose (probability = 24% * 50% = 12%). If the public card is a King or Jack, I will win (probability = 24% * 50% = 12%). \n- If board_game_expert holds a Jack (29% probability), he will likely fold (90% probability) or call (10% probability) in the second round. If the public card is a Jack, I will lose (probability = 29% * 90% = 26.1%). If the public card is a King or Queen, I will win (probability = 29% * 10% = 2.9%). \n\nPlan 2: Fold\n- If I fold, I will lose the chips I have already put in the pot. The probability of this happening is 100%. \n\nThe number of payoffs for each plan:\n- Plan 1: After the action, all chips in the pot: If win, the winning payoff would be half of the total pot. If lose, the lose payoff would be half of the total pot. \n- Plan 2: After the action, all chips in the pot: If lose, the lose payoff would be the chips I have already put in the pot. \n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Lose rate * Lose Payoff = (61.9% * half of the total pot) - (38.1% * half of the total pot)\n- Plan 2: Expected Chips Gain = 0 - 100% * the chips I have already put in the pot\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain than Plan 2. Therefore, I should choose Plan 1: Call."}}
{"message": "", "41_4": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King, he will likely call (60% probability) or raise (40% probability). If he calls, I will win because my King is higher than his King. If he raises, I will still win because my King is higher than his King. So, the winning rate is 100%.\n- If board_game_expert holds a Queen, he will likely call (50% probability) or fold (50% probability). If he calls, I will lose because his Queen matches the public card. If he folds, I will win. So, the winning rate is 50% and the losing rate is 50%.\n- If board_game_expert holds a Jack, he will likely fold (90% probability) or call (10% probability). If he folds, I will win. If he calls, I will win because my King is higher than his Jack. So, the winning rate is 100%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card board_game_expert holds. So, the losing rate is 100%.\n\nPlan 3: Check\n- If board_game_expert holds a King, he will likely call (60% probability) or raise (40% probability). If he calls, I will win because my King is higher than his King. If he raises, I will still win because my King is higher than his King. So, the winning rate is 100%.\n- If board_game_expert holds a Queen, he will likely call (50% probability) or fold (50% probability). If he calls, I will lose because his Queen matches the public card. If he folds, I will win. So, the winning rate is 50% and the losing rate is 50%.\n- If board_game_expert holds a Jack, he will likely fold (90% probability) or call (10% probability). If he folds, I will win. If he calls, I will win because my King is higher than his Jack. So, the winning rate is 100%.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 6 chips (half of the total pot). If I lose, the losing payoff would be 6 chips.\n- Plan 2: If I lose, the losing payoff would be 6 chips.\n- Plan 3: If I win, the winning payoff would be 6 chips. If I lose, the losing payoff would be 6 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 1.0 * 6 - 0.5 * 6 = 3 chips\n- Plan 2: Expected Chips Gain = 0 * 6 - 1.0 * 6 = -6 chips\n- Plan 3: Expected Chips Gain = 1.0 * 6 - 0.5 * 6 = 3 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 have the highest expected chips gain, so I should choose either Plan 1 or Plan 3. However, considering the strategy improvement, I should choose Plan 1 (Raise) to put pressure on board_game_expert and potentially force a fold."}}
{"message": "", "43_1": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (20% probability), he will likely call (60% probability) or raise (40% probability). If he calls, I will likely lose (80% probability) unless the public card is a Jack (20% probability). If he raises, I will likely lose (100% probability).\n- If board_game_expert holds a Queen (40% probability), he will likely call (70% probability) or fold (30% probability). If he calls, I will likely lose (80% probability) unless the public card is a Jack (20% probability). If he folds, I will win (100% probability).\n- If board_game_expert holds a Jack (40% probability), he will likely fold (70% probability) or call (30% probability). If he folds, I will win (100% probability). If he calls, it will be a draw (100% probability).\n- Overall, the winning rate for Plan 1 is 20% * 40% + 40% * 30% + 40% * 70% = 46%. The losing rate is 20% * 60% + 40% * 70% = 34%. The draw rate is 40% * 30% = 12%.\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of board_game_expert's card. The losing rate is 100%.\n\nPlan 3: Check\n- If board_game_expert holds a King (20% probability), he will likely raise (70% probability) or check (30% probability). If he raises, I will likely lose (80% probability) unless the public card is a Jack (20% probability). If he checks, it will be a draw (100% probability).\n- If board_game_expert holds a Queen (40% probability), he will likely raise (40% probability) or check (60% probability). If he raises, I will likely lose (80% probability) unless the public card is a Jack (20% probability). If he checks, it will be a draw (100% probability).\n- If board_game_expert holds a Jack (40% probability), he will likely check (100% probability). It will be a draw (100% probability).\n- Overall, the winning rate for Plan 3 is 0%. The losing rate is 20% * 70% + 40% * 40% = 34%. The draw rate is 20% * 30% + 40% * 60% + 40% = 66%.\n\nThe number of payoffs for each plan:\n- Plan 1: If win, the winning payoff would be half of the total pot (6 chips). If lose, the lose payoff would be half of the total pot (6 chips).\n- Plan 2: If lose, the lose payoff would be half of the total pot (4 chips).\n- Plan 3: If lose, the lose payoff would be half of the total pot (4 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 46% * 6 - 34% * 6 = 0.72 chips\n- Plan 2: 0% * 4 - 100% * 4 = -4 chips\n- Plan 3: 0% * 4 - 34% * 4 = -1.36 chips\n\nPlan Selection:\n- Plan 1: Raise\n- Plan 3: Check\n- Plan 2: Fold\n\nThe plan with the highest estimated expected chips gain is Plan 1: Raise."}}
{"message": "", "44_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, he will likely raise (70% probability) or call (30% probability). If he raises, I will lose unless the public card is a Queen. If he calls, the game will be decided by the public card. \n- If board_game_expert holds a Queen, he will likely call (60% probability) or raise (40% probability). If he raises, I will lose unless the public card is a Queen. If he calls, the game will be a draw unless the public card is a King or Jack. \n- If board_game_expert holds a Jack, he will likely call (50% probability) or fold (50% probability). If he calls, I will win unless the public card is a King. If he folds, I will win. \n\nPlan 2: Raise\n- If board_game_expert holds a King, he will likely call (60% probability) or raise (40% probability). If he calls, I will lose unless the public card is a Queen. If he raises, I will lose unless the public card is a Queen. \n- If board_game_expert holds a Queen, he will likely call (70% probability) or fold (30% probability). If he calls, the game will be a draw unless the public card is a King or Jack. If he folds, I will win. \n- If board_game_expert holds a Jack, he will likely fold (80% probability) or call (20% probability). If he folds, I will win. If he calls, I will win unless the public card is a King. \n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of what card board_game_expert holds. \n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips (half of the total pot of 6 chips). If I lose, the losing payoff would be 2 chips (half of the total pot of 4 chips). \n- Plan 2: If I win, the winning payoff would be 4 chips (half of the total pot of 8 chips). If I lose, the losing payoff would be 3 chips (half of the total pot of 6 chips). \n- Plan 3: If I fold, I will lose 2 chips. \n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.5 * 3 - 0.5 * 2 = 0.5 chips\n- Plan 2: Expected Chips Gain = 0.6 * 4 - 0.4 * 3 = 1.2 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection: \n- Plan 2 (Raise) has the highest expected chips gain, so I should choose this plan."}}
{"message": "", "44_2": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (53.33% probability), he will likely call (70% probability) in the second round. If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. Therefore, the winning rate is 30%, the losing rate is 70%, and the drawing rate is 0%.\n- If board_game_expert holds a Queen (26.67% probability), he will likely call (60% probability) in the second round. If the public card is a King, I will lose. If the public card is a Queen or Jack, I will win. Therefore, the winning rate is 40%, the losing rate is 60%, and the drawing rate is 0%.\n- If board_game_expert holds a Jack (20% probability), he will likely fold (90% probability) in the second round. Therefore, the winning rate is 90%, the losing rate is 10%, and the drawing rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of what card board_game_expert holds. Therefore, the winning rate is 0%, the losing rate is 100%, and the drawing rate is 0%.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 10 chips (half of the total pot of 20 chips). If I lose, the losing payoff would be 10 chips.\n- Plan 2: If I fold, I will lose 4 chips (the chips I have already put into the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is (0.3 * 10 + 0.4 * 10 + 0.9 * 10) - (0.7 * 10 + 0.6 * 10 + 0.1 * 10) = 1.6 chips.\n- Plan 2: The expected chips loss is 4 chips.\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain than Plan 2. Therefore, I should choose Plan 1: Call."}}
{"message": "", "44_4": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (probability 1/3), he will likely call (70% probability) or raise (30% probability). If he calls, we will draw and split the pot. If he raises, I will lose.\n- If board_game_expert holds a Queen (probability 1/3), he will likely call (60% probability) or fold (40% probability). If he calls, we will draw and split the pot. If he folds, I will win.\n- If board_game_expert holds a Jack (probability 1/3), he will likely fold (90% probability) or call (10% probability). If he folds, I will win. If he calls, he will win due to having a pair.\n\nPlan 2: Raise\n- If board_game_expert holds a King (probability 1/3), he will likely call (60% probability) or raise (40% probability). If he calls, we will draw and split the pot. If he raises, I will lose.\n- If board_game_expert holds a Queen (probability 1/3), he will likely fold (40% probability) or call (60% probability). If he folds, I will win. If he calls, we will draw and split the pot.\n- If board_game_expert holds a Jack (probability 1/3), he will likely fold (90% probability) or call (10% probability). If he folds, I will win. If he calls, he will win due to having a pair.\n\nPlan 3: Fold\n- If I fold, I will lose the round regardless of what card board_game_expert holds.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 8 chips (half of the total pot of 16 chips). If I lose, the losing payoff would be 10 chips (the amount I have already put in the pot).\n- Plan 2: If I win, the winning payoff would be 12 chips (half of the total pot of 24 chips). If I lose, the losing payoff would be 14 chips (the amount I would have put in the pot).\n- Plan 3: If I fold, the losing payoff would be 10 chips (the amount I have already put in the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = (1/3 * 0.7 * 8) - (1/3 * 0.3 * 10) = 0.6 chips\n- Plan 2: Expected Chips Gain = (1/3 * 0.6 * 12) - (1/3 * 0.4 * 14) = 0.4 chips\n- Plan 3: Expected Chips Gain = -10 chips (as I will lose the amount I have already put in the pot)\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I should choose to call."}}
{"message": "", "45_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (20% chance), he would likely call (30%) or raise (70%). If he calls, I would likely win (50%) or draw (50%). If he raises, I would likely win (50%) or draw (50%).\n- If board_game_expert holds a Queen (40% chance), he would likely call (60%) or raise (40%). If he calls, I would likely win (100%). If he raises, I would likely win (100%).\n- If board_game_expert holds a Jack (40% chance), he would likely call (50%) or fold (50%). If he calls, I would likely win (100%). If he folds, I would win by default.\n\nPlan 2: Raise\n- If board_game_expert holds a King (20% chance), he would likely call (80%) or raise (20%). If he calls, I would likely win (50%) or draw (50%). If he raises, I would likely win (50%) or draw (50%).\n- If board_game_expert holds a Queen (40% chance), he would likely call (70%) or fold (30%). If he calls, I would likely win (100%). If he folds, I would win by default.\n- If board_game_expert holds a Jack (40% chance), he would likely fold (80%) or call (20%). If he folds, I would win by default. If he calls, I would likely win (100%).\n\nPlan 3: Fold\n- If I fold, I would lose by default.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips (half of the total pot of 6 chips). If I lose, the loss payoff would be 3 chips.\n- Plan 2: If I win, the winning payoff would be 7 chips (half of the total pot of 14 chips). If I lose, the loss payoff would be 7 chips.\n- Plan 3: If I fold, the loss payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.9 * 3 - 0.1 * 3 = 2.4 chips\n- Plan 2: Expected Chips Gain = 0.95 * 7 - 0.05 * 7 = 6.3 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I would choose this plan."}}
{"message": "", "45_2": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (50% chance), he will likely call (80%) or raise (20%). If he calls, I will win (50%) or draw (50%). If he raises, I will win (50%) or draw (50%). Overall, my winning rate is 50%, my losing rate is 0%, and my drawing rate is 50%.\n- If board_game_expert holds a Queen (50% chance), he will likely call (70%) or fold (30%). If he calls, I will win (100%). If he folds, I will win (100%). Overall, my winning rate is 100%, my losing rate is 0%, and my drawing rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose 100% of the time, regardless of what card board_game_expert holds.\n\nPayoffs for each plan:\n- Plan 1: If I win, the pot will be 10 chips, so my winning payoff would be 5 chips. If I lose, the pot will be 10 chips, so my losing payoff would be 5 chips.\n- Plan 2: If I fold, I will lose the 6 chips I have already put into the pot.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: My expected chips gain is (50% * 5 chips) - (0% * 5 chips) = 2.5 chips.\n- Plan 2: My expected chips gain is 0% * 0 chips - 100% * 6 chips = -6 chips.\n\nPlan Selection:\n- Plan 1 has an expected chips gain of 2.5 chips, while Plan 2 has an expected chips gain of -6 chips. Therefore, I should choose Plan 1: Call."}}
{"message": "", "45_4": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (60% chance), he will likely raise (90% chance). If he raises, I will lose (probability = 60% * 90% = 54%). If he calls (10% chance), it will be a draw (probability = 60% * 10% = 6%).\n- If board_game_expert holds a Queen (40% chance), he will likely call (50% chance) or fold (50% chance). If he calls, I will win (probability = 40% * 50% = 20%). If he folds, I will also win (probability = 40% * 50% = 20%).\n- Overall, the winning rate for plan 1 is 40%, the losing rate is 54%, and the draw rate is 6%.\n\nPlan 2: Raise\n- If board_game_expert holds a King (60% chance), he will likely call (80% chance) or raise (20% chance). If he calls, it will be a draw (probability = 60% * 80% = 48%). If he raises, I will lose (probability = 60% * 20% = 12%).\n- If board_game_expert holds a Queen (40% chance), he will likely call (70% chance) or fold (30% chance). If he calls, I will win (probability = 40% * 70% = 28%). If he folds, I will also win (probability = 40% * 30% = 12%).\n- Overall, the winning rate for plan 2 is 40%, the losing rate is 12%, and the draw rate is 48%.\n\nPlan 3: Fold\n- If I fold, I will lose all the chips I have already put into the pot. The losing rate for plan 3 is 100%.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (10 + 6 + 6 = 22, half is 11). If I lose, the losing payoff would be half of the total pot (11).\n- Plan 2: If I win, the winning payoff would be half of the total pot (10 + 6 + 8 = 24, half is 12). If I lose, the losing payoff would be half of the total pot (12).\n- Plan 3: If I fold, I will lose all the chips I have already put into the pot (10).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = winning rate * Winning Payoff - losing rate * Losing Payoff = 40% * 11 - 54% * 11 = -1.54\n- Plan 2: Expected Chips Gain = 40% * 12 - 12% * 12 = 3.6\n- Plan 3: Expected Chips Gain = -10\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain (3.6), followed by Plan 1 (-1.54) and Plan 3 (-10). Therefore, I should choose Plan 2: Raise."}}
{"message": "", "46_1": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (20% probability), he will likely raise (70% probability) or call (30% probability). If he raises, I will lose (probability = 20% * 70% = 14%). If he calls, I will win (probability = 20% * 30% = 6%).\n- If board_game_expert holds a Queen (60% probability), he will likely call (70% probability) or fold (30% probability). If he calls, it will be a draw (probability = 60% * 70% = 42%). If he folds, I will win (probability = 60% * 30% = 18%).\n- If board_game_expert holds a Jack (70% probability), he will likely fold (80% probability) or call (20% probability). If he folds, I will win (probability = 70% * 80% = 56%). If he calls, I will win (probability = 70% * 20% = 14%).\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card board_game_expert holds. The lose rate is 100%.\n\nPlan 3: Check\n- If board_game_expert holds a King (20% probability), he will likely raise (80% probability) or call (20% probability). If he raises, I will lose (probability = 20% * 80% = 16%). If he calls, I will lose (probability = 20% * 20% = 4%).\n- If board_game_expert holds a Queen (60% probability), he will likely call (60% probability) or raise (40% probability). If he calls, it will be a draw (probability = 60% * 60% = 36%). If he raises, I will lose (probability = 60% * 40% = 24%).\n- If board_game_expert holds a Jack (70% probability), he will likely call (70% probability) or fold (30% probability). If he calls, I will win (probability = 70% * 70% = 49%). If he folds, I will win (probability = 70% * 30% = 21%).\n\nThe number of payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 6 chips. If lose, the lose payoff would be 4 chips.\n- Plan 2: If lose, the lose payoff would be 2 chips.\n- Plan 3: If win, the winning payoff would be 4 chips. If lose, the lose payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 6 * (6% + 18% + 56% + 14%) - 4 * 14% = 5.36 chips\n- Plan 2: Expected Chips Gain = -2 * 100% = -2 chips\n- Plan 3: Expected Chips Gain = 4 * (49% + 21%) - 2 * (16% + 4% + 24%) = 1.4 chips\n\nPlan Selection:\n- Plan 1: 5.36 chips\n- Plan 2: -2 chips\n- Plan 3: 1.4 chips\n\nThe rank of estimated expected chips gains for every plan is Plan 1 > Plan 3 > Plan 2. Therefore, the best strategy is to raise (Plan 1)."}}
{"message": "", "47_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (probability 0%), he will 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, lose if it is a King, and draw if it is a Jack. \n- If board_game_expert holds a Queen (probability 40%), he will call (70% probability) or fold (30% probability). 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. If he folds, I will win. \n- If board_game_expert holds a Jack (probability 60%), he will fold (80% probability) or call (20% probability). If he folds, I will win. If he calls, I will win if the public card is a Queen or King, and draw if it is a Jack. \n\nPlan 2: Raise\n- If board_game_expert holds a King (probability 0%), he will 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, lose if it is a King, and draw if it is a Jack. \n- If board_game_expert holds a Queen (probability 40%), he will fold (30% probability) or call (70% probability). If he folds, I will win. 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. \n- If board_game_expert holds a Jack (probability 60%), he will fold (80% probability) or call (20% probability). If he folds, I will win. If he calls, I will win if the public card is a Queen or King, and draw if it is a Jack. \n\nPlan 3: Fold\n- If I fold, I will lose the 2 chips I have already put in the pot. \n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips (half of the total pot of 6 chips). If I lose, the losing payoff would be 2 chips (the chips I have already put in the pot).\n- Plan 2: If I win, the winning payoff would be 5 chips (half of the total pot of 10 chips). If I lose, the losing payoff would be 6 chips (the chips I have already put in the pot plus the 4 chips I raised).\n- Plan 3: If I fold, the losing payoff would be 2 chips (the chips I have already put in the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.4 * 3 - 0.6 * 2 = 0.6 chips\n- Plan 2: Expected Chips Gain = 0.4 * 5 - 0.6 * 6 = -1.6 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- Plan 1 (Call) has the highest expected chips gain, so I will choose this plan."}}
{"message": "", "47_2": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (20% probability), he will likely raise (60% probability) or call (40% probability). If he raises, I will lose (as his King beats my Queen). If he calls, I will also lose unless the next public card is a Queen. So, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If board_game_expert holds a Queen (40% probability), he will likely call (60% probability) or fold (40% probability). If he calls, it will be a draw unless the next public card is a Queen (then I win). If he folds, I win. So, the winning rate is 40%, the losing rate is 0%, and the draw rate is 60%.\n- If board_game_expert holds a Jack (40% probability), he will likely fold (80% probability) or call (20% probability). If he folds, I win. If he calls, I win unless the next public card is a Jack (then I lose). So, the winning rate is 80%, the losing rate is 20%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I lose the chips I have already put in the pot. So, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If board_game_expert holds a King (20% probability), he will likely raise (60% probability) or check (40% probability). If he raises, I will lose (as his King beats my Queen). If he checks, I will also lose unless the next public card is a Queen. So, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If board_game_expert holds a Queen (40% probability), he will likely check (60% probability) or raise (40% probability). If he checks, it will be a draw unless the next public card is a Queen (then I win). If he raises, I lose. So, the winning rate is 20%, the losing rate is 40%, and the draw rate is 40%.\n- If board_game_expert holds a Jack (40% probability), he will likely check (80% probability) or raise (20% probability). If he checks, I win unless the next public card is a Jack (then I lose). If he raises, I lose. So, the winning rate is 60%, the losing rate is 40%, and the draw rate is 0%.\n\nThe number of payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 6 chips (half of the total pot of 12 chips). If I lose, the losing payoff would be 6 chips.\n- Plan 2: If I fold, I lose the 2 chips I have already put in the pot.\n- Plan 3: If I win, the winning payoff would be 4 chips (half of the total pot of 8 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 = 0.8*6 - 1*6 = -1.2 chips\n- Plan 2: Expected Chips Gain = 0 - 1*2 = -2 chips\n- Plan 3: Expected Chips Gain = 0.6*4 - 0.4*4 = 0.8 chips\n\nPlan Selection:\n- Plan 1: -1.2 chips\n- Plan 2: -2 chips\n- Plan 3: 0.8 chips\n\nTherefore, the best plan is Plan 3: Check."}}
{"message": "", "49_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, he would likely raise (40% probability) or call (60% probability). If he raises, I would likely lose unless the public card is a Jack. If he calls, I would have a chance to win if the public card is a Jack. The winning/losing rates would be 33%/67%.\n- If board_game_expert holds a Queen, he would likely raise (40% probability) or call (60% probability). If he raises, I would likely lose unless the public card is a Jack. If he calls, I would have a chance to win if the public card is a Jack. The winning/losing rates would be 33%/67%.\n- If board_game_expert holds a Jack, he would likely call (50% probability) or fold (50% probability). If he calls, it would be a draw if the public card is a Jack. If he folds, I would win. The winning/draw/losing rates would be 50%/33%/17%.\n\nPlan 2: Raise\n- If board_game_expert holds a King, he would likely call (70% probability) or raise (30% probability). If he calls, I would likely lose unless the public card is a Jack. If he raises, I would likely lose. The winning/losing rates would be 33%/67%.\n- If board_game_expert holds a Queen, he would likely call (70% probability) or fold (30% probability). If he calls, I would likely lose unless the public card is a Jack. If he folds, I would win. The winning/losing rates would be 33%/67%.\n- If board_game_expert holds a Jack, he would likely fold (80% probability) or call (20% probability). If he folds, I would win. If he calls, it would be a draw if the public card is a Jack. The winning/draw/losing rates would be 80%/13%/7%.\n\nPlan 3: Fold\n- If I fold, I would lose the chips I have already put in the pot. The losing rate would be 100%.\n\nThe number of 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 = 33% * 3 - 67% * 2 = -0.33 chips\n- Plan 2: Expected Chips Gain = 59% * 5 - 41% * 4 = 0.95 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I would choose Plan 2."}}
{"message": "", "49_2": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King, he would likely call (60% probability) or fold (40% probability). If he calls, I would lose (100% probability). If he folds, I would win (100% probability). \n- If board_game_expert holds a Queen, he would likely call (50% probability) or fold (50% probability). If he calls, I would lose (100% probability). If he folds, I would win (100% probability). \n- If board_game_expert holds a Jack, he would likely fold (60% probability) or call (40% probability). If he calls, it would be a draw (100% probability). If he folds, I would win (100% probability). \n\nPlan 2: Fold\n- If I fold, I would lose (100% probability) regardless of what card board_game_expert holds.\n\nPlan 3: Check\n- If board_game_expert holds a King, he would likely raise (90% probability) or call (10% probability). If he raises, I would lose (100% probability). If he calls, I would lose (100% probability). \n- If board_game_expert holds a Queen, he would likely call (50% probability) or fold (50% probability). If he calls, I would lose (100% probability). If he folds, I would win (100% probability). \n- If board_game_expert holds a Jack, he would likely fold (60% probability) or call (40% probability). If he calls, it would be a draw (100% probability). If he folds, I would win (100% probability). \n\nPayoffs for each plan:\n- Plan 1: If win, the winning payoff would be 8 chips. If lose, the losing payoff would be 8 chips.\n- Plan 2: If lose, the losing payoff would be 4 chips.\n- Plan 3: If win, the winning payoff would be 8 chips. If lose, the losing payoff would be 8 chips.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: (0.7 * 8) - (0.3 * 8) = 3.2 chips\n- Plan 2: -4 chips\n- Plan 3: (0.7 * 8) - (0.3 * 8) = 3.2 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 have the highest expected chips gain, so I would choose either of these plans. However, considering the strategy improvement, I would choose Plan 1 (Raise) to pressure board_game_expert into folding or calling with a weaker hand."}}
{"message": "", "49_4": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (90% probability), he will likely raise (90% probability). I will lose as his King matches the public card. \n- If board_game_expert holds a Queen (10% probability), he will likely call (50% probability) or fold (50% probability). I will win if he folds, but lose if he calls as his Queen is higher than my Jack.\n- If board_game_expert holds a Jack (0% probability), he will likely fold (60% probability) or call (40% probability). I will win if he folds, but it will be a draw if he calls as we both hold a Jack.\n\nPlan 2: Fold\n- If board_game_expert holds a King (90% probability), I will lose less chips by folding.\n- If board_game_expert holds a Queen (10% probability), I will lose less chips by folding.\n- If board_game_expert holds a Jack (0% probability), I will lose less chips by folding.\n\nThe number of payoffs for each plan:\nPlan 1: After the action, all chips in the pot: If win, the winning payoff would be 10 chips (half of the total pot). If lose, the lose payoff would be 10 chips.\nPlan 2: After the action, all chips in the pot: If win, the winning payoff would be 0 chips as I fold. If lose, the lose payoff would be 4 chips (the amount I have already put in the pot).\n\nEstimate Expected Chips Gain for Each Plan:\nPlan 1: Expected Chips Gain = 0.1 * 10 - 0.9 * 10 = -8 chips\nPlan 2: Expected Chips Gain = 0 * 0 - 1 * 4 = -4 chips\n\nPlan Selection:\nPlan 2 (Fold) has the highest estimated expected chips gain (-4 chips), so I should choose Plan 2."}}
{"message": "", "50_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, he is likely to raise (70% probability). If the public card is a King, I will lose. If the public card is a Queen, I will win. If the public card is a Jack, I will lose. The overall winning rate is 30%, losing rate is 70%.\n- If board_game_expert holds a Queen, he is likely to 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 win. The overall winning rate is 60%, drawing rate is 40%.\n- If board_game_expert holds a Jack, he is likely to call (70% probability) or fold (30% probability). If the public card is a Queen or King, I will win. If the public card is a Jack, I will lose. The overall winning rate is 70%, losing rate is 30%.\n\nPlan 2: Raise\n- If board_game_expert holds a King, he is likely to raise (80% probability) or call (20% probability). If the public card is a King, I will lose. If the public card is a Queen, I will win. If the public card is a Jack, I will lose. The overall winning rate is 20%, losing rate is 80%.\n- If board_game_expert holds a Queen, he is likely to call (70% probability) or fold (30% 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 70%, drawing rate is 30%.\n- If board_game_expert holds a Jack, he is likely to fold (80% probability) or call (20% probability). If the public card is a Queen or King, I will win. If the public card is a Jack, I will lose. The overall winning rate is 80%, losing rate is 20%.\n\nPlan 3: Fold\n- If I fold, I will lose the pot. The overall losing rate is 100%.\n\nThe number of 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 lose, the losing payoff would be 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.6 * 3 - 0.4 * 1 = 1.4 chips\n- Plan 2: Expected Chips Gain = 0.7 * 5 - 0.3 * 2 = 3.1 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": "", "50_2": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (30% probability), he would likely raise (60% probability). I would lose this round as his King outranks my Queen. \n- If board_game_expert holds a Queen (65% probability), he would likely call (60% probability). This would result in a draw as we both hold Queens. \n- If board_game_expert holds a Jack (5% probability), he would likely fold (80% probability). I would win this round as my Queen outranks his Jack. \n\nPlan 2: Fold\n- If I fold, I would automatically lose this round regardless of what card board_game_expert holds. \n\nPlan 3: Check\n- If board_game_expert holds a King (30% probability), he would likely raise (60% probability). I would lose this round as his King outranks my Queen. \n- If board_game_expert holds a Queen (65% probability), he would likely call (60% probability). This would result in a draw as we both hold Queens. \n- If board_game_expert holds a Jack (5% probability), he would likely fold (80% probability). I would win this round as my Queen outranks his Jack. \n\nPayoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (8 chips). If I lose, the losing payoff would be half of the total pot (8 chips).\n- Plan 2: If I fold, I would lose my current stake in the pot (4 chips).\n- Plan 3: If I win, the winning payoff would be half of the total pot (8 chips). If I lose, the losing payoff would be half of the total pot (8 chips).\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected gain = 0.05 * 8 - 0.30 * 8 = -2 chips\n- Plan 2: Expected loss = -4 chips\n- Plan 3: Expected gain = 0.05 * 8 - 0.30 * 8 = -2 chips\n\nPlan Selection:\nBased on the expected chips gain, Plan 1 and Plan 3 are equally preferable, while Plan 2 is the least preferable. However, considering the strategy improvement, I should play more aggressively when I have a high-ranking card. Therefore, I would choose Plan 1: Raise."}}
