{"message": "", "1_1": {"plan": "Plan 1: Call\nIf I call, I will 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, they have a high chance of winning unless the public card is a Queen or Jack. If the public card is a Queen, I will win. If the public card is a Jack, it will be a draw. Therefore, the probabilities are: Win (33.33%), Lose (33.33%), Draw (33.33%).\n\nThe winning/losing/draw rates when board_game_expert holds a Queen: \nIf board_game_expert holds a Queen, we have the same card. Therefore, the outcome will depend on the public card. If the public card is a Queen, it will be a draw. If the public card is a King or Jack, it will be a loss. Therefore, the probabilities are: Win (0%), Lose (66.67%), Draw (33.33%).\n\nThe winning/losing/draw rates when board_game_expert holds a Jack: \nIf board_game_expert holds a Jack, they have the lowest card unless the public card is a Jack. If the public card is a Jack, I will lose. If the public card is a Queen or King, I will win. Therefore, the probabilities are: Win (66.67%), Lose (33.33%), Draw (0%).\n\nPlan 1 overall GoodGuy's Winning/Lose/Draw rates: \nWinning rate: (33.33% * 33.33%) + (0% * 33.33%) + (66.67% * 33.33%) = 33.33%\nLosing rate: (33.33% * 33.33%) + (66.67% * 33.33%) + (33.33% * 33.33%) = 44.44%\nDraw rate: (33.33% * 33.33%) + (33.33% * 33.33%) + (0% * 33.33%) = 22.22%\n\nPlan 2: Raise\nIf I raise, I will add 4 more chips to the pot, bringing the total pot to 12 chips. The analysis of winning/losing/draw rates when board_game_expert holds different cards is the same as in Plan 1.\n\nPlan 2 overall GoodGuy's Winning/Lose/Draw rates: \nWinning rate: 33.33%\nLosing rate: 44.44%\nDraw rate: 22.22%\n\nPlan 3: Fold\nIf I fold, I will lose the chips I have already put in the pot, and the game will end immediately. Therefore, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\nPlan 1: If win, the winning payoff would be 5 chips. If lose, the lose payoff would be 5 chips.\nPlan 2: If win, the winning payoff would be 6 chips. If lose, the lose payoff would be 6 chips.\nPlan 3: If win, the winning payoff would be 0 chips. If lose, the lose payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\nPlan 1: 33.33% * 5 - 44.44% * 5 = -0.56 chips\nPlan 2: 33.33% * 6 - 44.44% * 6 = -0.67 chips\nPlan 3: 0% * 0 - 100% * 2 = -2 chips\n\nPlan Selection:\nBased on the estimated expected chips gains, Plan 1 (Call) is the best strategy, followed by Plan 2 (Raise), and Plan 3 (Fold) is the worst strategy. Therefore, I will choose to call."}}
{"message": "", "1_3": {"plan": "Plan 1: Call\nIf I call, board_game_expert may believe I have a strong hand. If he holds a King, he may raise (probability 50%) or call (probability 50%). If he holds a Queen or Jack, he may raise (probability 25%) or call (probability 75%). \nThe winning/losing/drawing rates when board_game_expert holds a King: If he raises, I will lose (probability 100%). If he calls, I will lose (probability 100%). \nThe winning/losing/drawing rates when board_game_expert holds a Queen or Jack: If he raises, I will draw (probability 100%). If he calls, I will draw (probability 100%). \nOverall, the winning rate for plan 1 is 0%, the losing rate is 66.6%, and the drawing rate is 33.3%.\n\nPlan 2: Raise\nIf I raise, board_game_expert may believe I have a strong hand. If he holds a King, he may call (probability 75%) or fold (probability 25%). If he holds a Queen or Jack, he may call (probability 50%) or fold (probability 50%). \nThe winning/losing/drawing rates when board_game_expert holds a King: If he calls, I will lose (probability 100%). If he folds, I will win (probability 100%). \nThe winning/losing/drawing rates when board_game_expert holds a Queen or Jack: If he calls, I will draw (probability 100%). If he folds, I will win (probability 100%). \nOverall, the winning rate for plan 2 is 37.5%, the losing rate is 37.5%, and the drawing rate is 25%.\n\nPlan 3: Fold\nIf I fold, I will lose the game immediately. The winning rate for plan 3 is 0%, the losing rate is 100%, and the drawing rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\nPlan 1: If win, the winning payoff would be 6 chips. If lose, the lose payoff would be 4 chips.\nPlan 2: If win, the winning payoff would be 10 chips. If lose, the lose payoff would be 6 chips.\nPlan 3: If win, the winning payoff would be 0 chips. If lose, the lose payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\nPlan 1: 0% * 6 chips - 66.6% * 4 chips = -2.66 chips\nPlan 2: 37.5% * 10 chips - 37.5% * 6 chips = 1.5 chips\nPlan 3: 0% * 0 chips - 100% * 4 chips = -4 chips\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows: Plan 2 > Plan 1 > Plan 3. Therefore, the best strategy is to raise (Plan 2), as it has the highest estimated expected chips gain."}}
{"message": "", "2_1": {"plan": "Plan 1: Call\n- If board_game_expert holds a King: He will likely raise the bet (100% probability). If the public card is a King, I will win (50% probability) or draw (50% probability). If the public card is a Queen or Jack, I will win (100% probability). Overall, my winning rate is 75%, my losing rate is 0%, and my drawing rate is 25%.\n- If board_game_expert holds a Queen or Jack: He may raise the bet or call (50% probability each). If the public card is a King, I will win (100% probability). If the public card is a Queen or Jack, I will win (50% probability) or lose (50% probability). Overall, my winning rate is 75%, my losing rate is 25%, and my 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 (50% probability) or draw (50% probability). If the public card is a Queen or Jack, I will win (100% probability). Overall, my winning rate is 75%, my losing rate is 0%, and my drawing rate is 25%.\n- If board_game_expert holds a Queen or Jack: He may raise the bet or call (50% probability each). If the public card is a King, I will win (100% probability). If the public card is a Queen or Jack, I will win (50% probability) or lose (50% probability). Overall, my winning rate is 75%, my losing rate is 25%, and my drawing rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose all the chips in the pot. My winning rate is 0%, my losing rate is 100%, and my drawing rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 6 chips. If I lose, the losing payoff would be 4 chips.\n- Plan 2: If I win, the winning payoff would be 8 chips. If I lose, the losing payoff would be 6 chips.\n- Plan 3: If I fold, I will lose 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.75 * 6 - 0.25 * 4 = 3.5 chips\n- Plan 2: Expected Chips Gain = 0.75 * 8 - 0.25 * 6 = 4.5 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows:\n1. Plan 2: 4.5 chips\n2. Plan 1: 3.5 chips\n3. Plan 3: -2 chips\n\nTherefore, I should choose Plan 2 (Raise) as it has the highest estimated expected chips gain."}}
{"message": "", "2_3": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (50% probability), he will likely call (100% probability). If this happens, it will be a draw. The overall draw rate for this plan is 50%.\n- If board_game_expert holds a Queen or Jack (50% probability), we do not have enough information to infer his action. However, if he calls or folds, I will win as my card (King) is higher than the public card (Jack). The overall winning rate for this plan is 50%.\n\nPlan 2: Fold\n- If I fold, I will lose the round regardless of what card board_game_expert holds. The overall losing rate for this plan is 100%.\n\nPlan 3: Check\n- If board_game_expert holds a King (50% probability), he will likely raise (100% probability). If this happens, it will be a draw. The overall draw rate for this plan is 50%.\n- If board_game_expert holds a Queen or Jack (50% probability), we do not have enough information to infer his action. However, if he checks or folds, I will win as my card (King) is higher than the public card (Jack). The overall winning rate for this plan is 50%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the 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, I will lose the round and the losing payoff would be half of the total 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\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 50% * 6 chips - 0% * 6 chips = 3 chips\n- Plan 2: Expected Chips Gain = 0% * 6 chips - 100% * 6 chips = -6 chips\n- Plan 3: Expected Chips Gain = 50% * 6 chips - 0% * 6 chips = 3 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 both have the highest expected chips gain (3 chips), while Plan 2 has the lowest expected chips gain (-6 chips). Therefore, I should either raise (Plan 1) or check (Plan 3) in this round. Considering the strategy improvement, I should choose to raise (Plan 1) to potentially confuse board_game_expert and make him believe that I hold a King."}}
{"message": "", "3_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (10% probability), he will likely raise the bet (100% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, it's a draw. So, the winning rate is 0%, losing rate is 90%, and draw rate is 10%.\n- If board_game_expert holds a Queen (45% probability), he might call or raise. If the public card is a King or Queen, it's a draw. If the public card is a Jack, I win. So, the winning rate is 45%, losing rate is 0%, and draw rate is 45%.\n- If board_game_expert holds a Jack (45% probability), he might call or raise. If the public card is a King, I win. If the public card is a Queen or Jack, I lose. So, the winning rate is 45%, losing rate is 45%, and draw rate is 10%.\n- Overall, the winning rate for Plan 1 is 45%, the losing rate is 45%, and the draw rate is 10%.\n\nPlan 2: Raise\n- If board_game_expert holds a King (10% probability), he will likely call (100% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, it's a draw. So, the winning rate is 0%, losing rate is 90%, and draw rate is 10%.\n- If board_game_expert holds a Queen (45% probability), he might call or fold. If the public card is a King or Queen, it's a draw. If the public card is a Jack, I win. So, the winning rate is 45%, losing rate is 0%, and draw rate is 45%.\n- If board_game_expert holds a Jack (45% probability), he might call or fold. If the public card is a King, I win. If the public card is a Queen or Jack, I lose. So, the winning rate is 45%, losing rate is 45%, and draw rate is 10%.\n- Overall, the winning rate for Plan 2 is 45%, the losing rate is 45%, and the draw rate is 10%.\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%, losing rate is 100%, and draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips. If I lose, the losing payoff would be 2 chips.\n- Plan 2: If I win, the winning payoff would be 7 chips. If I lose, the losing payoff would be 6 chips.\n- Plan 3: If I fold, I will lose 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 45% * 3 - 45% * 2 = 0.45 chips\n- Plan 2: Expected Chips Gain = 45% * 7 - 45% * 6 = 0.45 chips\n- Plan 3: Expected Chips Gain = 0% * 0 - 100% * 2 = -2 chips\n\nPlan Selection:\n- Plan 1 and Plan 2 both have the highest expected chips gain of 0.45 chips, while Plan 3 has the lowest expected chips gain of -2 chips. Therefore, I should choose either Plan 1 or Plan 2. Considering the strategy improvement, I should choose Plan 2 (Raise) as it has the potential to confuse board_game_expert and disrupt his game pattern."}}
{"message": "", "3_2": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (70% probability), he will likely raise the bet (100% probability). If the public card is a King, I will lose (100% probability). If the public card is a Queen, I will win (100% probability). If the public card is a Jack, I will lose (100% probability). Overall, the winning rate is 35%, the losing rate is 70%, and the draw rate is 0%.\n- If board_game_expert holds a Queen (15% probability), he will likely raise the bet (100% probability). If the public card is a King, I will lose (100% probability). If the public card is a Queen, it will be a draw (100% probability). If the public card is a Jack, I will win (100% probability). Overall, the winning rate is 15%, the losing rate is 15%, and the draw rate is 15%.\n- If board_game_expert holds a Jack (15% probability), he will likely raise the bet (100% probability). If the public card is a King, I will lose (100% probability). If the public card is a Queen, I will win (100% probability). If the public card is a Jack, I will lose (100% probability). Overall, the winning rate is 15%, the losing rate is 30%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose the chips I have already put in the pot. The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, all chips in the pot: If win, the winning payoff would be 5 chips. If lose, the lose payoff would be 5 chips.\n- Plan 2: After the action, all chips in the pot: If lose, the lose payoff would be 6 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.35 * 5 - 0.70 * 5 = -1.75 chips\n- Plan 2: Expected Chips Gain = 0 * 0 - 1 * 6 = -6 chips\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain than Plan 2. Therefore, I should choose Plan 1: Call."}}
{"message": "", "3_4": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (100% probability), he will likely call my raise (100% probability). Given that I hold a Queen and the public card is a Queen, I will win this round (100% probability). \n- Overall winning rate for this plan is 100% (probability = 100% * 100%), lose rate is 0%, and draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will automatically lose this round regardless of what card board_game_expert holds. \n- Overall winning rate for this plan is 0%, lose rate is 100%, and draw rate is 0%.\n\nPlan 3: Check\n- If board_game_expert holds a King (100% probability), he will likely raise the bet (100% probability). Given that I hold a Queen and the public card is a Queen, I will win this round (100% probability). \n- Overall winning rate for this plan is 100% (probability = 100% * 100%), lose rate is 0%, and draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, all chips in the pot would be 14. If win, the winning payoff would be 7. If lose, the lose payoff would be 7.\n- Plan 2: After the action, all chips in the pot would be 6. If win, the winning payoff would be 3. If lose, the lose payoff would be 3.\n- Plan 3: After the action, all chips in the pot would be 6. If win, the winning payoff would be 3. If lose, the lose payoff would be 3.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected chips gain = winning rate * winning payoff - lose rate * lose payoff = 100% * 7 - 0% * 7 = 7\n- Plan 2: Expected chips gain = 0% * 3 - 100% * 3 = -3\n- Plan 3: Expected chips gain = 100% * 3 - 0% * 3 = 3\n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 1 > Plan 3 > Plan 2\n- Therefore, the plan with the highest estimated expected chips gain is Plan 1: Raise."}}
{"message": "", "4_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, he will likely raise the bet. If the public card is a King, I will lose. If the public card is a Queen or Jack, I have a chance to win. The winning/losing rate is 33.33% each.\n- If board_game_expert holds a Queen, he will likely call. If the public card is a Queen, I will lose. If the public card is a King or Jack, I have a chance to win. The winning/losing rate is 33.33% each.\n- If board_game_expert holds a Jack, he will likely raise the bet. If the public card is a Jack, I will win. If the public card is a King or Queen, I have a chance to lose. The winning/losing rate is 33.33% each.\n- Overall, the winning rate for plan 1 is 33.33%, the losing rate is 33.33%, and the draw rate is 33.33%.\n\nPlan 2: Raise\n- If board_game_expert holds a King, he will likely call. If the public card is a King, I will lose. If the public card is a Queen or Jack, I have a chance to win. The winning/losing rate is 33.33% each.\n- If board_game_expert holds a Queen, he will likely call. If the public card is a Queen, I will lose. If the public card is a King or Jack, I have a chance to win. The winning/losing rate is 33.33% each.\n- If board_game_expert holds a Jack, he will likely call. If the public card is a Jack, I will win. If the public card is a King or Queen, I have a chance to lose. The winning/losing rate is 33.33% each.\n- Overall, the winning rate for plan 2 is 33.33%, the losing rate is 33.33%, and the draw rate is 33.33%.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot. The losing rate is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be half of the total pot (3 chips). If lose, the lose 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 (6 chips). If lose, the lose payoff would be half of the total pot (6 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 = 33.33% * 3 chips - 33.33% * 3 chips = 0 chips\n- Plan 2: Expected Chips Gain = 33.33% * 6 chips - 33.33% * 6 chips = 0 chips\n- Plan 3: Expected Chips Gain = -2 chips\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 the better strategies. Between Plan 1 and Plan 2, Plan 2 has a higher potential payoff if I win, so I will choose Plan 2: Raise."}}
{"message": "", "4_2": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (40% probability), he will likely raise the bet in the second round regardless of the public card. If the public card is a King, I will lose (0% win, 100% lose, 0% draw). If the public card is a Queen or Jack, I have a chance to win if the public card is a Jack (50% win, 50% lose, 0% draw).\n- If board_game_expert holds a Jack (20% probability), he will likely call if I raise the bet. If the public card is a Jack, it will be a draw (0% win, 0% lose, 100% draw). If the public card is a Queen or King, I will lose (0% win, 100% lose, 0% draw).\n- If board_game_expert holds a Queen (40% probability), his actions are unpredictable. If the public card is a Queen, I will lose (0% win, 100% lose, 0% draw). If the public card is a King or Jack, I have a chance to win if the public card is a Jack (50% win, 50% lose, 0% draw).\nPlan 1 overall GoodGuy's Winning/Lose/Draw rates: Winning rate for plan 1 is 18%, Lose rate for plan 1 is 72%, Draw rate for plan 1 is 10%.\n\nPlan 2: Fold\n- If I fold, I will lose the chips I have already put in the pot. The winning rate, lose rate, and draw rate for this plan are all 0%.\n\nThe number of winning and lose 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 win, the winning payoff would be 0. If lose, the lose payoff would be 0.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Lose rate * Lose Payoff = 18% * (Half of the total pot) - 72% * (Half of the total pot) = -27% of the total pot.\n- Plan 2: Expected Chips Gain = 0.\n\nPlan Selection:\n- Plan 1 has a negative expected chips gain, while Plan 2 has a zero expected chips gain. Therefore, Plan 2 (Fold) is the better strategy in this situation."}}
{"message": "", "5_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (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 draw (50% chance) or lose (50% chance). Overall, the winning rate is 33%, the losing rate is 16.5%, and the draw rate is 16.5%.\n- If board_game_expert holds a Queen (33% chance), he will likely call (50% chance) or raise (50% chance). If the public card is a Queen, I will lose (100% chance). If the public card is not a Queen, I will win (50% chance) or draw (50% chance). Overall, the winning rate is 16.5%, the losing rate is 33%, and the draw rate is 16.5%.\n- If board_game_expert holds a Jack (33% chance), he will likely call (50% chance) or raise (50% chance). If the public card is a Jack, I will lose (100% chance). If the public card is not a Jack, I will win (50% chance) or draw (50% chance). Overall, the winning rate is 16.5%, the losing rate is 33%, and the draw rate is 16.5%.\n\nPlan 2: Raise\n- If board_game_expert holds a King (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 draw (50% chance) or lose (50% chance). Overall, the winning rate is 33%, the losing rate is 16.5%, and the draw rate is 16.5%.\n- If board_game_expert holds a Queen (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 (50% chance) or draw (50% chance). Overall, the winning rate is 16.5%, the losing rate is 33%, and the draw rate is 16.5%.\n- If board_game_expert holds a Jack (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 (50% chance) or draw (50% chance). Overall, the winning rate is 16.5%, the losing rate is 33%, and the draw rate is 16.5%.\n\nPlan 3: Fold\n- If I fold, I will lose 100% of the time. The losing rate is 100%, and there is no winning or draw rate.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips (half of the 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\nEstimated Expected Chips Gain for Each Plan:\n- Plan 1: (33% * 3 chips) - (16.5% * 3 chips) = 0.495 chips\n- Plan 2: (33% * 4 chips) - (16.5% * 4 chips) = 0.66 chips\n- Plan 3: -2 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest estimated expected chips gain, followed by Plan 1 (Call), and Plan 3 (Fold). Therefore, I should choose to raise."}}
{"message": "", "5_2": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (33% chance), he will call (100% chance). This will result in a draw (100% chance), as we both have a pair of Kings. \n- If board_game_expert holds a Queen (33% chance), he will call (100% chance). This will result in a win for me (100% chance), as my pair of Kings beats his high card Queen.\n- If board_game_expert holds a Jack (33% chance), he will call (100% chance). This will result in a win for me (100% chance), as my pair of Kings beats his high card Jack.\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of what card board_game_expert holds. \n\nPlan 3: Check\n- If board_game_expert holds a King (33% chance), he will raise (100% chance). This will result in a draw (100% chance), as we both have a pair of Kings. \n- If board_game_expert holds a Queen (33% chance), he will raise (50% chance) or call (50% chance). This will result in a win for me (100% chance), as my pair of Kings beats his high card Queen.\n- If board_game_expert holds a Jack (33% chance), he will raise (50% chance) or call (50% chance). This will result in a win for me (100% chance), as my pair of Kings beats his high card Jack.\n\nWinning/Lose Payoffs for Each Plan:\n- Plan 1: If I win, the pot will be 12 chips, so my winning payoff will be 6 chips. If I lose, the pot will be 12 chips, so my losing payoff will be 6 chips.\n- Plan 2: If I fold, I will lose the game, so my losing payoff will be 4 chips.\n- Plan 3: If I win, the pot will be 8 chips, so my winning payoff will be 4 chips. If I lose, the pot will be 8 chips, so my losing payoff will be 4 chips.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: (33% * 0 + 67% * 6 - 0% * 6) = 4.02 chips\n- Plan 2: (0% * 0 - 100% * 4) = -4 chips\n- Plan 3: (33% * 0 + 67% * 4 - 0% * 4) = 2.68 chips\n\nPlan Selection:\n- Plan 1: Raise\n- Plan 3: Check\n- Plan 2: Fold\n\nBased on the expected chips gain, I should choose Plan 1: Raise."}}
{"message": "", "5_4": {"plan": "Plan 1: 'Call'\n- The winning/losing/draw rates when board_game_expert holds a King: \n  - Based on board_game_expert's behaviour pattern, in the second round, because board_game_expert holds a King (100% probability) and the combination with the current public card (King), and if he sees my action ('call'), board_game_expert will do 'call' (100% probability). \n  - Considering the Single Game Win/Draw/Lose Rule, if we both hold a King and the public card is a King, it will be a draw (100% probability). \n  - Overall, the draw rate for his King is 100%.\n- Plan1 overall GoodGuy's Winning/Losing/Draw rates: the Winning rate for plan 1 is 0%; Lose rate for plan 1 is 0%; Draw Rate for plan 1 is 100%.\n\nPlan 2: 'Fold'\n- The winning/losing/draw rates when board_game_expert holds a King: \n  - Based on board_game_expert's behaviour pattern, in the second round, because board_game_expert holds a King (100% probability) and the combination with the current public card (King), and if he sees my action ('fold'), board_game_expert will win (100% probability). \n  - Overall, the lose rate for his King is 100%.\n- Plan2 overall GoodGuy's Winning/Losing/Draw rates: the Winning rate for plan 2 is 0%; Lose rate for plan 2 is 100%; Draw Rate for plan 2 is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan1: After the action 'call', all chips in the pot would be 24. If draw, the payoff would be 12 (half of the total pot).\n- Plan2: After the action 'fold', all chips in the pot would be 20. If lose, the payoff would be 0 (as I fold, I lose all the chips I have put into the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan1: Expected Chips Gain = Winning rate * Winning Payoff - Lose rate * Lose Payoff = 0% * 12 - 0% * 0 = 0\n- Plan2: Expected Chips Gain = Winning rate * Winning Payoff - Lose rate * Lose Payoff = 0% * 0 - 100% * 0 = 0\n\nPlan Selection:\n- Plan1 and Plan2 both have an expected chips gain of 0. However, considering the strategy improvement, Plan1 ('call') is a better choice as it keeps me in the game and gives me a chance to draw, while Plan2 ('fold') guarantees a loss. Therefore, I will choose Plan1 ('call')."}}
{"message": "", "6_1": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (20% chance), he will likely raise (100% chance). If the public card is a King, I will win (20% chance). If the public card is not a King, I will lose (80% chance). Overall, my winning rate is 20%*20% = 4%, and my losing rate is 20%*80% = 16%.\n- If board_game_expert holds a Queen (40% chance), he will likely call (100% chance). If the public card is a Queen, I will lose (40% chance). If the public card is not a Queen, I will win (60% chance). Overall, my winning rate is 40%*60% = 24%, and my losing rate is 40%*40% = 16%.\n- If board_game_expert holds a Jack (40% chance), he will likely raise (100% chance). If the public card is a Jack, I will win (40% chance). If the public card is not a Jack, I will win (60% chance). Overall, my winning rate is 40%*100% = 40%, and my losing rate is 0%.\n\nPlan 2: Raise\n- If board_game_expert holds a King (20% chance), he will likely call (100% chance). If the public card is a King, I will win (20% chance). If the public card is not a King, I will lose (80% chance). Overall, my winning rate is 20%*20% = 4%, and my losing rate is 20%*80% = 16%.\n- If board_game_expert holds a Queen (40% chance), he will likely call (100% chance). If the public card is a Queen, I will lose (40% chance). If the public card is not a Queen, I will win (60% chance). Overall, my winning rate is 40%*60% = 24%, and my losing rate is 40%*40% = 16%.\n- If board_game_expert holds a Jack (40% chance), he will likely call (100% chance). If the public card is a Jack, I will win (40% chance). If the public card is not a Jack, I will win (60% chance). Overall, my winning rate is 40%*100% = 40%, and my losing rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose 100% of the time.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If 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 gain = winning rate * winning payoff - losing rate * losing payoff = 68% * 6 - 32% * 6 = 2.16 chips.\n- Plan 2: Expected gain = winning rate * winning payoff - losing rate * losing payoff = 68% * 8 - 32% * 8 = 2.88 chips.\n- Plan 3: Expected gain = -2 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 choose Plan 2: Raise."}}
{"message": "", "6_3": {"plan": "Plan 1: Raise\n- If board_game_expert holds a Jack (100% probability), he will call (100% probability). Since my card is higher, I will win (100% probability). The overall winning rate for this plan is 100%.\n- The number of chips in the pot after raising would be 14. If I win, the winning payoff would be 7 chips. If I lose, the losing payoff would be 7 chips.\n- The expected chips gain for this plan is winning rate * winning payoff - losing rate * losing payoff = 1 * 7 - 0 * 7 = 7 chips.\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 plan is 100%.\n- The number of chips in the pot after folding would be 6. If I lose, the losing payoff would be 3 chips.\n- The expected chips loss for this plan is losing rate * losing payoff = 1 * 3 = 3 chips.\n\nPlan 3: Check\n- If board_game_expert holds a Jack (100% probability), he will call (100% probability). Since my card is higher, I will win (100% probability). The overall winning rate for this plan is 100%.\n- The number of chips in the pot after checking would be 6. If I win, the winning payoff would be 3 chips. If I lose, the losing payoff would be 3 chips.\n- The expected chips gain for this plan is winning rate * winning payoff - losing rate * losing payoff = 1 * 3 - 0 * 3 = 3 chips.\n\nPlan Selection:\nRanking the plans by expected chips gain, we get:\n1. Plan 1: Raise (7 chips)\n2. Plan 3: Check (3 chips)\n3. Plan 2: Fold (-3 chips)\n\nTherefore, the best plan is to raise."}}
{"message": "", "7_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, he will raise the bet in the first round. If I call, he will likely believe I have a Queen. In the second round, if the public card is a King, he will raise the bet again. If the public card is not a King, he will call the bet. My winning rate is 33.33%, losing rate is 33.33%, and draw rate is 33.33%.\n- If board_game_expert holds a Queen, he will call the bet in the first round. If I call, he will likely believe I have a Queen as well. In the second round, if the public card is a Queen, he will raise the bet. If the public card is not a Queen, he will call the bet. My winning rate is 33.33%, losing rate is 33.33%, and draw rate is 33.33%.\n- If board_game_expert holds a Jack, he will raise the bet in the first round. If I call, he will likely believe I have a Queen. In the second round, if the public card is a Jack, he will raise the bet again. If the public card is not a Jack, he will call the bet. My winning rate is 33.33%, losing rate is 33.33%, and draw rate is 33.33%.\n\nPlan 2: Raise\n- If board_game_expert holds a King, he will raise the bet in the first round. If I raise, he will likely believe I have a King or a Jack. In the second round, if the public card is a King, he will raise the bet again. If the public card is not a King, he will call the bet. My winning rate is 33.33%, losing rate is 33.33%, and draw rate is 33.33%.\n- If board_game_expert holds a Queen, he will call the bet in the first round. If I raise, he will likely believe I have a King or a Jack. In the second round, if the public card is a Queen, he will raise the bet. If the public card is not a Queen, he will call the bet. My winning rate is 33.33%, losing rate is 33.33%, and draw rate is 33.33%.\n- If board_game_expert holds a Jack, he will raise the bet in the first round. If I raise, he will likely believe I have a King or a Jack. In the second round, if the public card is a Jack, he will raise the bet again. If the public card is not a Jack, he will call the bet. My winning rate is 33.33%, losing rate is 33.33%, and draw rate is 33.33%.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of what card board_game_expert holds. My winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips. If I lose, the losing payoff would be 3 chips.\n- Plan 2: If I win, the winning payoff would be 7 chips. If I lose, the losing payoff would be 7 chips.\n- Plan 3: If I fold, I will lose 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: (33.33% * 3) - (33.33% * 3) = 0\n- Plan 2: (33.33% * 7) - (33.33% * 7) = 0\n- Plan 3: 0 - (100% * 1) = -1\n\nPlan Selection:\n- Plan 1: Rank 1\n- Plan 2: Rank 1\n- Plan 3: Rank 3\n\nBased on the estimated expected chips gain, I should choose either Plan 1 or Plan 2. Since Plan 2 involves a higher risk (more chips at stake), I will choose Plan 1: Call."}}
{"message": "", "7_2": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (25% chance), he will likely call (100% chance). If the public card is not a Queen, I will lose (100% chance). If the public card is a Queen, I will win (100% chance).\n- If board_game_expert holds a Queen (50% chance), he will likely call (100% chance). If the public card is not a Queen, I will lose (100% chance). If the public card is a Queen, it will be a draw (100% chance).\n- If board_game_expert holds a Jack (25% chance), he will likely call (100% chance). If the public card is not a Queen, I will lose (100% chance). If the public card is a Queen, I will win (100% chance).\n- Overall, the winning rate for Plan 1 is 37.5%, the losing rate is 62.5%, and the draw 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\nPlan 3: Check\n- If board_game_expert holds a King (25% chance), he will likely call (100% chance). If the public card is not a Queen, I will lose (100% chance). If the public card is a Queen, I will win (100% chance).\n- If board_game_expert holds a Queen (50% chance), he will likely call (100% chance). If the public card is not a Queen, I will lose (100% chance). If the public card is a Queen, it will be a draw (100% chance).\n- If board_game_expert holds a Jack (25% chance), he will likely call (100% chance). If the public card is not a Queen, I will lose (100% chance). If the public card is a Queen, I will win (100% chance).\n- Overall, the winning rate for Plan 3 is 37.5%, the losing rate is 62.5%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips. If I lose, the losing payoff would be 4 chips.\n- Plan 2: If I fold, I will lose 2 chips.\n- Plan 3: If I win, the winning payoff would be 2 chips. If I lose, the losing payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected gain = 37.5% * 4 chips - 62.5% * 4 chips = -1 chip\n- Plan 2: Expected gain = -2 chips\n- Plan 3: Expected gain = 37.5% * 2 chips - 62.5% * 2 chips = -0.5 chips\n\nPlan Selection:\n- Plan 1: -1 chip\n- Plan 2: -2 chips\n- Plan 3: -0.5 chips\n\nThe best plan is Plan 3 (Check), as it has the highest expected chips gain."}}
{"message": "", "8_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, he will raise (100%). I will win if the public card is a King (33.3%), draw if the public card is a Queen or Jack (66.7%).\n- If board_game_expert holds a Queen or Jack, he will call (100%). I will win if the public card is a King or Queen (66.7%), lose if the public card is a Jack (33.3%).\n\nPlan 2: Raise\n- If board_game_expert holds a King, he will call (100%). I will win if the public card is a King (33.3%), draw if the public card is a Queen or Jack (66.7%).\n- If board_game_expert holds a Queen or Jack, he will call (100%). I will win if the public card is a King or Queen (66.7%), lose if the public card is a Jack (33.3%).\n\nPlan 3: Fold\n- If I fold, I will lose the round regardless of what card board_game_expert holds or what the public card is.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips (half of the total pot of 6 chips). If I lose, the lose 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 lose payoff would be 3 chips (half of the total pot of 6 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 = 0.667 * 3 - 0.333 * 2 = 1.33 chips\n- Plan 2: Expected Chips Gain = 0.667 * 4 - 0.333 * 3 = 2.00 chips\n- Plan 3: Expected Chips Gain = -2 chips (since I will lose 2 chips if I fold)\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I will choose this plan."}}
{"message": "", "8_2": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King, he will raise (100% probability). If he raises, it will be a draw (100% probability), as we both have a pair of Kings. \n- If board_game_expert holds a Queen, he will call (100% probability). If he calls, I will win (100% probability), as my pair of Kings beats his Queen. \n- If board_game_expert holds a Jack, he will call (100% probability). If he calls, I will win (100% probability), as my pair of Kings beats his Jack. \n\nPlan 2: Fold\n- If I fold, I will lose (100% probability), regardless of what card board_game_expert holds. \n\nPlan 3: Check\n- If board_game_expert holds a King, he will raise (100% probability). If he raises, it will be a draw (100% probability), as we both have a pair of Kings. \n- If board_game_expert holds a Queen, he will call (100% probability). If he calls, I will win (100% probability), as my pair of Kings beats his Queen. \n- If board_game_expert holds a Jack, he will call (100% probability). If he calls, I will win (100% probability), as my pair of Kings beats his Jack. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (8 chips). If I lose, the lose payoff would be half of the total pot (8 chips).\n- Plan 2: If I lose, the lose 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 lose payoff would be half of the total pot (8 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning Rate * Winning Payoff - Lose Rate * Lose Payoff = (66.6% * 8 chips) - (0% * 8 chips) = 5.33 chips\n- Plan 2: Expected Chips Gain = Winning Rate * Winning Payoff - Lose Rate * Lose Payoff = (0% * 8 chips) - (100% * 8 chips) = -8 chips\n- Plan 3: Expected Chips Gain = Winning Rate * Winning Payoff - Lose Rate * Lose Payoff = (66.6% * 8 chips) - (0% * 8 chips) = 5.33 chips\n\nPlan Selection:\n- Plan 1: Expected Chips Gain = 5.33 chips\n- Plan 2: Expected Chips Gain = -8 chips\n- Plan 3: Expected Chips Gain = 5.33 chips\n\nBased on the estimated expected chips gains, Plan 1 and Plan 3 are the best strategies to follow, as they both have the highest expected chips gain. Plan 2 should be avoided, as it has a negative expected chips gain."}}
{"message": "", "8_4": {"plan": "Plan 1: Call\n- If board_game_expert holds Queen (50% probability), he will call (100% probability). I will win because my pair of Kings beats his Queen. The winning rate for this scenario is 50%.\n- If board_game_expert holds Jack (50% probability), he will call (100% probability). I will win because my pair of Kings beats his Jack. The winning rate for this scenario is 50%.\n\nPlan 1 overall GoodGuy's Winning/Lose/Draw rates: The Winning rate for plan 1 is 100% (50% + 50%); Lose rate for plan 1 is 0%; Draw Rate for plan 1 is 0%.\n\nPlan 2: Fold\n- If board_game_expert holds Queen (50% probability), he will call (100% probability). I will lose because I fold. The lose rate for this scenario is 50%.\n- If board_game_expert holds Jack (50% probability), he will call (100% probability). I will lose because I fold. The lose rate for this scenario is 50%.\n\nPlan 2 overall GoodGuy's Winning/Lose/Draw rates: The Winning rate for plan 2 is 0%; Lose rate for plan 2 is 100% (50% + 50%); Draw Rate for plan 2 is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, all chips in the pot would be 20 (12 chips from me and 8 chips from board_game_expert). If win, the winning payoff would be 10 (half of the total pot). If lose, the lose payoff would be 10.\n- Plan 2: After the action, all chips in the pot would be 12 (12 chips from me). If win, the winning payoff would be 6 (half of the total pot). If lose, the lose payoff would be 6.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = winning rate * Winning Payoff - lose rate * Lose Payoff = 100% * 10 - 0% * 10 = 10 chips\n- Plan 2: Expected Chips Gain = winning rate * Winning Payoff - lose rate * Lose Payoff = 0% * 6 - 100% * 6 = -6 chips\n\nPlan Selection: The rank of estimated expected chips gains for every plan is as follows: Plan 1 (10 chips) > Plan 2 (-6 chips). Therefore, I should select Plan 1 (Call) as it has the highest estimated expected chips gain."}}
{"message": "", "9_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, he will likely raise in the next round. If the public card is a King, I will lose. If the public card is a Queen or Jack, I have a chance to win. \n- If board_game_expert holds a Queen or Jack, he will likely call in the next round. If the public card is a Queen or Jack, I will lose. If the public card is a King, I have a chance to win. \n\nPlan 2: Raise\n- If board_game_expert holds a King, he will likely call. If the public card is a King, I will lose. If the public card is a Queen or Jack, I have a chance to win. \n- If board_game_expert holds a Queen or Jack, he will likely call. If the public card is a Queen or Jack, I will lose. If the public card is a King, I have a chance to win. \n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put into the pot. However, I will not lose any more chips in this round. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot. If I lose, the lose 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 lose payoff would be half of the total pot. \n- Plan 3: If I fold, I will lose the chips I have already put into the pot. \n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning Rate * Winning Payoff - Lose Rate * Lose Payoff\n- Plan 2: Expected Chips Gain = Winning Rate * Winning Payoff - Lose Rate * Lose Payoff\n- Plan 3: Expected Chips Gain = - Chips I have already put into the pot\n\nPlan Selection:\n- I will select the plan with the highest expected chips gain. This will depend on the probabilities of board_game_expert's actions and the public card. I will need to consider both the potential payoff and the risk of each plan."}}
{"message": "", "9_2": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (33.33% probability), he will raise (100% probability). I will lose as his pair of Kings beats my single Jack. \n- If board_game_expert holds a Queen (33.33% probability), he will call (100% probability). I will win as my single Jack beats his single Queen.\n- If board_game_expert holds a Jack (33.33% probability), he will call (100% probability). It will be a draw as we both have a single Jack.\n\nPlan 2: Fold\n- If I fold, I will lose the current pot but avoid further losses. This is a safe strategy but does not allow for potential gains.\n\nPlan 3: Check\n- If board_game_expert holds a King (33.33% probability), he will raise (100% probability). I will lose as his pair of Kings beats my single Jack. \n- If board_game_expert holds a Queen (33.33% probability), he will check (100% probability). I will win as my single Jack beats his single Queen.\n- If board_game_expert holds a Jack (33.33% probability), he will check (100% probability). It will be a draw as we both have a single Jack.\n\nWinning/Lose Payoffs:\n- Plan 1: If I win, the pot will be 12 chips, so the winning payoff would be 6 chips. If I lose, the pot will be 12 chips, so the lose payoff would be 6 chips.\n- Plan 2: If I fold, there will be no change in my chips.\n- Plan 3: If I win, the pot will be 8 chips, so the winning payoff would be 4 chips. If I lose, the pot will be 8 chips, so the lose payoff would be 4 chips.\n\nExpected Chips Gain:\n- Plan 1: Expected gain = 33.33% * 6 chips - 33.33% * 6 chips = 0 chips\n- Plan 2: Expected gain = 0 chips\n- Plan 3: Expected gain = 33.33% * 4 chips - 33.33% * 4 chips = 0 chips\n\nPlan Selection:\nAll plans have an expected gain of 0 chips. However, considering the strategy improvement, Plan 2 (Fold) is the safest strategy as it avoids further losses. Therefore, I will choose Plan 2."}}
{"message": "", "10_1": {"plan": "Plan 1: Raise\n- If board_game_expert holds a Queen (50% chance), he will call (100% chance). If the public card is a King or Jack, I will win. If the public card is a Queen, I will lose. So, the winning rate is 66.67%, the losing rate is 33.33%, and the draw rate is 0%.\n- If board_game_expert holds a Jack (50% chance), he will call (100% chance). If the public card is a King or Queen, I will win. If the public card is a Jack, I will lose. So, the winning rate is 66.67%, the losing rate is 33.33%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose the round regardless of what card board_game_expert holds or what the public card is. 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 Queen (50% chance), he will call (100% chance). If the public card is a King or Jack, I will win. If the public card is a Queen, I will lose. So, the winning rate is 66.67%, the losing rate is 33.33%, and the draw rate is 0%.\n- If board_game_expert holds a Jack (50% chance), he will call (100% chance). If the public card is a King or Queen, I will win. If the public card is a Jack, I will lose. So, the winning rate is 66.67%, the losing rate is 33.33%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the 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 will lose the round and the losing payoff would be half of the total pot (2 chips).\n- Plan 3: 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\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: (66.67% * 6 chips) - (33.33% * 6 chips) = 2 chips\n- Plan 2: (0% * 2 chips) - (100% * 2 chips) = -2 chips\n- Plan 3: (66.67% * 4 chips) - (33.33% * 4 chips) = 1.33 chips\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows:\n1. Plan 1: Raise (2 chips)\n2. Plan 3: Check (1.33 chips)\n3. Plan 2: Fold (-2 chips)\n\nTherefore, the best plan to execute is Plan 1: Raise."}}
{"message": "", "11_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (probability 33.3%), he will raise in the 1st round (probability 100%). If I call, he will likely believe I hold a Queen or Jack and continue to raise in the 2nd round. If the public card is a King, I will lose (probability 33.3%). If the public card is a Queen or Jack, I will win (probability 66.7%).\n- If board_game_expert holds a Queen (probability 33.3%), he will call in the 1st round (probability 100%). If I call, he will likely believe I hold a Queen or Jack and continue to call in the 2nd round. If the public card is a Queen, it will be a draw (probability 33.3%). If the public card is a King or Jack, I will lose (probability 66.7%).\n- If board_game_expert holds a Jack (probability 33.3%), he will raise in the 1st round (probability 100%). If I call, he will likely believe I hold a Queen or Jack and continue to raise in the 2nd round. If the public card is a Jack, I will lose (probability 33.3%). If the public card is a King or Queen, I will win (probability 66.7%).\n\nPlan 2: Raise\n- If board_game_expert holds a King (probability 33.3%), he will raise in the 1st round (probability 100%). If I raise, he will likely believe I hold a King or Queen and continue to raise in the 2nd round. If the public card is a King, I will lose (probability 33.3%). If the public card is a Queen or Jack, I will win (probability 66.7%).\n- If board_game_expert holds a Queen (probability 33.3%), he will call in the 1st round (probability 100%). If I raise, he will likely believe I hold a King or Queen and continue to call in the 2nd round. If the public card is a Queen, it will be a draw (probability 33.3%). If the public card is a King or Jack, I will lose (probability 66.7%).\n- If board_game_expert holds a Jack (probability 33.3%), he will raise in the 1st round (probability 100%). If I raise, he will likely believe I hold a King or Queen and continue to raise in the 2nd round. If the public card is a Jack, I will lose (probability 33.3%). If the public card is a King or Queen, I will win (probability 66.7%).\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of what card board_game_expert holds or what the public card is.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips. If I lose, the losing payoff would be 2 chips.\n- Plan 2: If I win, the winning payoff would be 5 chips. If I lose, the losing payoff would be 4 chips.\n- Plan 3: If I fold, the losing payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.67 * 3 - 0.33 * 2 = 1.01 chips\n- Plan 2: Expected Chips Gain = 0.67 * 5 - 0.33 * 4 = 2.01 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": "", "11_2": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (50% chance), he will likely raise in the second round regardless of the public card. If the public card is a King, I will lose (33.3% chance). If the public card is a Queen, I will win (33.3% chance). If the public card is a Jack, I will lose (33.3% chance). \n- If board_game_expert holds a Jack (50% chance), he will likely check in the second round if the public card is not a Jack. If the public card is a Jack, I will lose (33.3% chance). If the public card is a Queen, I will win (33.3% chance). If the public card is a King, I will lose (33.3% chance). \n\nPlan 2: Fold\n- If I fold, I will lose the chips I have already put in the pot, but I will not lose any more chips in this round. \n\nExpected Chips Gain:\n- Plan 1: (33.3% * 10 chips) - (66.6% * 10 chips) = -3.3 chips\n- Plan 2: -4 chips\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain than Plan 2, so I should choose Plan 1. However, both plans have a negative expected chips gain, so I should be prepared to lose chips in this round. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 10 chips. If I lose, the lose payoff would be 10 chips.\n- Plan 2: If I fold, I will lose the 4 chips I have already put in the pot. \n\nIn conclusion, based on the current game status and the behavior patterns of both players, I should choose Plan 1: Call. However, I should be prepared to lose chips in this round."}}
{"message": "", "11_4": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (0% probability), he will fold (100% probability). I will win (100% probability). \n- If board_game_expert holds a Queen (0% probability), he will call (100% probability). I will win (100% probability).\n- If board_game_expert holds a Jack (100% probability), he will call (100% probability). I will win (100% probability).\nPlan1 overall GoodGuy's Winning/Lose/Draw rates: Winning rate (100%), Lose rate (0%), Draw Rate (0%).\n\nPlan 2: Fold\n- If board_game_expert holds a King (0% probability), he will check (100% probability). I will lose (100% probability).\n- If board_game_expert holds a Queen (0% probability), he will check (100% probability). I will lose (100% probability).\n- If board_game_expert holds a Jack (100% probability), he will check (100% probability). I will lose (100% probability).\nPlan2 overall GoodGuy's Winning/Lose/Draw rates: Winning rate (0%), Lose rate (100%), Draw Rate (0%).\n\nPlan 3: Check\n- If board_game_expert holds a King (0% probability), he will raise (100% probability). I will lose (100% probability).\n- If board_game_expert holds a Queen (0% probability), he will check (100% probability). I will win (100% probability).\n- If board_game_expert holds a Jack (100% probability), he will check (100% probability). I will win (100% probability).\nPlan3 overall GoodGuy's Winning/Lose/Draw rates: Winning rate (100%), Lose rate (0%), Draw Rate (0%).\n\nThe number of winning and lose payoffs for each plan:\n- Plan1: If win, the winning payoff would be 10 chips. If lose, the lose payoff would be 0 chips.\n- Plan2: If win, the winning payoff would be 0 chips. If lose, the lose payoff would be 6 chips.\n- Plan3: If win, the winning payoff would be 6 chips. If lose, the lose payoff would be 0 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan1: 100% * 10 chips - 0% * 0 chips = 10 chips\n- Plan2: 0% * 0 chips - 100% * 6 chips = -6 chips\n- Plan3: 100% * 6 chips - 0% * 0 chips = 6 chips\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows:\n1. Plan1: 10 chips\n2. Plan3: 6 chips\n3. Plan2: -6 chips\n\nTherefore, I should select Plan1 (Raise) as it has the highest estimated expected chips gain."}}
{"message": "", "12_1": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (50% probability), he will call (100% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I will win. So, the winning rate is 66.7%, the losing rate is 33.3%, and the draw rate is 0%.\n- If board_game_expert holds a Queen (50% probability), he will fold (50% probability) or call (50% probability). If he folds, I will win. If he calls and the public card is a Queen, I will lose. If the public card is a King or Jack, I will win. So, the winning rate is 83.3%, the losing rate is 16.7%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of board_game_expert's card or the public card. 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 (50% probability), he will raise (100% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I will win. So, the winning rate is 66.7%, the losing rate is 33.3%, and the draw rate is 0%.\n- If board_game_expert holds a Queen (50% probability), he will check (100% probability). If the public card is a Queen, I will lose. If the public card is a King or Jack, I will win. So, the winning rate is 66.7%, the losing rate is 33.3%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 4 chips. If lose, the lose payoff would be 4 chips.\n- Plan 2: If lose, the lose payoff would be 2 chips.\n- Plan 3: If win, the winning payoff would be 2 chips. If lose, the lose payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: (0.833 * 4) - (0.167 * 4) = 2.664 chips\n- Plan 2: 0 - (1 * 2) = -2 chips\n- Plan 3: (0.667 * 2) - (0.333 * 2) = 0.668 chips\n\nPlan Selection:\n- Plan 1: 2.664 chips\n- Plan 2: -2 chips\n- Plan 3: 0.668 chips\n\nBased on the estimated expected chips gain, I should choose Plan 1 (Raise) as it has the highest expected chips gain."}}
{"message": "", "14_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a Queen (50% probability), he will likely call (100% probability). If the public card is a Jack, I will win (33.33% probability). If the public card is a Queen or King, I will lose (66.67% probability). Overall, the winning rate is 16.67%, the losing rate is 33.33%, and the draw rate is 0%.\n- If board_game_expert holds a Jack (50% probability), he will likely call (100% probability). If the public card is a Jack, it will be a draw (33.33% probability). If the public card is a Queen or King, I will lose (66.67% probability). Overall, the winning rate is 0%, the losing rate is 33.33%, and the draw rate is 16.67%.\n\nPlan 2: Raise\n- If board_game_expert holds a Queen (50% probability), he will likely fold (50% probability) or call (50% probability). If he folds, I will win (100% probability). If he calls and the public card is a Jack, I will win (33.33% probability). If the public card is a Queen or King, I will lose (66.67% probability). Overall, the winning rate is 66.67%, the losing rate is 16.67%, and the draw rate is 0%.\n- If board_game_expert holds a Jack (50% probability), he will likely fold (100% probability). If he folds, I will win (100% probability). Overall, the winning rate is 50%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of what card 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 winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 2 chips. If I lose, the losing payoff would be 2 chips.\n- Plan 2: If I win, the winning payoff would be 6 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 = 16.67% * 2 - 33.33% * 2 = -0.33 chips\n- Plan 2: Expected Chips Gain = 58.33% * 6 - 8.33% * 6 = 3 chips\n- Plan 3: Expected Chips Gain = 0% * 0 - 100% * 2 = -2 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so it should be selected. Plan 1 (Call) is the second best option, and Plan 3 (Fold) is the worst option."}}
{"message": "", "14_2": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (50% probability), he will call (100% probability). I will lose as King is higher than Jack. \n- If board_game_expert holds a Queen (50% probability), he will call (100% probability). I will lose as Queen is higher than Jack. \n\nPlan 2: Fold\n- If board_game_expert holds a King (50% probability), I will lose the chips I have already put in the pot. \n- If board_game_expert holds a Queen (50% probability), I will lose the chips I have already put in the pot. \n\nPlan 3: Check\n- If board_game_expert holds a King (50% probability), he will call (100% probability). I will lose as King is higher than Jack. \n- If board_game_expert holds a Queen (50% probability), he will call (100% probability). I will lose as Queen is higher than Jack. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 8 chips. If lose, the lose payoff would be 8 chips.\n- Plan 2: If win, the winning payoff would be 0 chips. If lose, the lose payoff would be 4 chips.\n- Plan 3: If win, the winning payoff would be 8 chips. If lose, the lose payoff would be 8 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0% * 8 - 100% * 8 = -8 chips\n- Plan 2: Expected Chips Gain = 0% * 0 - 100% * 4 = -4 chips\n- Plan 3: Expected Chips Gain = 0% * 8 - 100% * 8 = -8 chips\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain (-4 chips), so I should choose Plan 2: Fold."}}
{"message": "", "15_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, he will raise in the second round if the public card is a King (100% probability). If the public card is not a King, and I call, he will call (100% probability). The winning rate is 0% (as his King beats my Queen), the draw rate is 0%, and the lose rate is 100%.\n- If board_game_expert holds a Queen, he will check in the second round if the public card is a Queen (100% probability). If the public card is not a Queen, and I call, he will fold (100% probability). The winning rate is 50% (as it depends on the public card), the draw rate is 50% (as we both hold Queens), and the lose rate is 0%.\n- If board_game_expert holds a Jack, he will check in the second round if the public card is a Jack (100% probability). If the public card is not a Jack, and I call, he will fold (100% probability). The winning rate is 100% (as my Queen beats his Jack), the draw rate is 0%, and the lose rate is 0%.\n\nPlan 2: Raise\n- If board_game_expert holds a King, he will call in the second round if the public card is a King (100% probability). If the public card is not a King, and I raise, he will call (100% probability). The winning rate is 0% (as his King beats my Queen), the draw rate is 0%, and the lose rate is 100%.\n- If board_game_expert holds a Queen, he will fold in the second round if the public card is a Queen (50% probability) or call (50% probability). If the public card is not a Queen, and I raise, he will fold (100% probability). The winning rate is 75% (as it depends on the public card and his action), the draw rate is 25% (as we both hold Queens and he may call), and the lose rate is 0%.\n- If board_game_expert holds a Jack, he will fold in the second round if the public card is a Jack (100% probability). If the public card is not a Jack, and I raise, he will fold (100% probability). The winning rate is 100% (as my Queen beats his Jack), the draw rate is 0%, and the lose rate is 0%.\n\nPlan 3: Fold\n- If I fold, the winning rate is 0%, the draw rate is 0%, and the lose rate is 100% regardless of what card board_game_expert holds.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 3 chips (half of the 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- 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 = 0.5 * 3 - 0.5 * 3 = 0\n- Plan 2: Expected Chips Gain = 0.75 * 5 - 0.25 * 5 = 2.5\n- Plan 3: Expected Chips Gain = 0 - 1 * 2 = -2\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so it should be selected."}}
{"message": "", "15_2": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, he will likely raise in the second round regardless of the public card. If the public card is a Queen, I will win (50% probability). If the public card is not a Queen, I will lose (50% probability). \n- If board_game_expert holds a Jack, he will likely check in the second round if the public card is a Jack, and fold if the public card is not a Jack. If the public card is a Queen, I will win (50% probability). If the public card is not a Queen, it will be a draw (50% probability). \n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of board_game_expert's card or the public card. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, all chips in the pot will be 10. If I win, the winning payoff would be 5. If I lose, the lose payoff would be 5. \n- Plan 2: After the action, all chips in the pot will be 10. If I lose, the lose payoff would be 5. \n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is (0.5 * 5) - (0.5 * 5) = 0\n- Plan 2: The expected chips loss is -5\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain than Plan 2. Therefore, I should choose Plan 1: Call."}}
{"message": "", "15_4": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (50% probability), he will likely call (100% probability). Given my strong hand, I will win (100% probability). \n- If board_game_expert holds a Jack (50% probability), he will likely fold (100% probability). Given my strong hand, I will win (100% probability). \n\nPlan 2: Fold\n- This plan is not reasonable given my strong hand. \n\nPlan 3: Check\n- If board_game_expert holds a King (50% probability), he will likely check (100% probability). Given my strong hand, I will win (100% probability). \n- If board_game_expert holds a Jack (50% probability), he will likely check (100% probability). Given my strong hand, I will win (100% probability). \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (currently 6 chips, so 3 chips). If I lose, the losing payoff would be half of the total pot (currently 6 chips, so 3 chips). \n- Plan 2: Not applicable as this plan is not reasonable. \n- Plan 3: If I win, the winning payoff would be half of the total pot (currently 6 chips, so 3 chips). If I lose, the losing payoff would be half of the total pot (currently 6 chips, so 3 chips). \n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate (100%) * Winning Payoff (3 chips) - Losing rate (0%) * Losing Payoff (3 chips) = 3 chips\n- Plan 2: Not applicable as this plan is not reasonable. \n- Plan 3: Expected Chips Gain = Winning rate (100%) * Winning Payoff (3 chips) - Losing rate (0%) * Losing Payoff (3 chips) = 3 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 both have the highest estimated expected chips gain of 3 chips. However, considering the strategy improvement, Plan 1 (Raise) is the better choice as it can 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, he would likely raise (80%) or call (20%). If he raises, I would lose as King is higher than Queen. If he calls, the outcome would depend on the public card. The overall winning rate is 20%, losing rate is 80%, and draw rate is 0%.\n- If board_game_expert holds a Queen, he would likely call (60%) or raise (40%). If he calls, it would be a draw. If he raises, the outcome would depend on the public card. The overall winning rate is 0%, losing rate is 40%, and draw rate is 60%.\n- If board_game_expert holds a Jack, he would likely call (70%) or raise (30%). If he calls or raises, I would win as Queen is higher than Jack. The overall winning rate is 100%, losing rate is 0%, and draw rate is 0%.\n\nPlan 2: Raise\n- If board_game_expert holds a King, he would likely raise (70%) or call (30%). If he raises or calls, I would lose as King is higher than Queen. The overall winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n- If board_game_expert holds a Queen, he would likely call (70%) or fold (30%). If he calls, it would be a draw. If he folds, I would win. The overall winning rate is 30%, losing rate is 0%, and draw rate is 70%.\n- If board_game_expert holds a Jack, he would likely call (60%) or fold (40%). If he calls or folds, I would win as Queen is higher than Jack. The overall winning rate is 100%, losing rate is 0%, and draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I would lose regardless of what card board_game_expert holds. The overall winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 3 chips. If lose, the lose payoff would be 2 chips.\n- Plan 2: If win, the winning payoff would be 6 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 = 20% * 3 - 80% * 2 = -1.2 chips\n- Plan 2: Expected Chips Gain = 43.3% * 6 - 33.3% * 4 = 0.6 chips\n- Plan 3: Expected Chips Gain = -100% * 2 = -2 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 choose Plan 2: Raise."}}
{"message": "", "17_2": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (18.75% chance), he would likely call (60%) or fold (40%). If he calls, I will lose. If he folds, I will win. So, the winning rate is 7.5% (18.75% * 40%), and the losing rate is 11.25% (18.75% * 60%).\n- If board_game_expert holds a Queen (43.75% chance), we will have a draw regardless of his action. So, the draw rate is 43.75%.\n- If board_game_expert holds a Jack (37.5% chance), he would likely call (40%) or fold (60%). If he calls, I will lose. If he folds, I will win. So, the winning rate is 22.5% (37.5% * 60%), and the losing rate is 15% (37.5% * 40%).\n\nPlan 2: Fold\n- If I fold, I will lose regardless of board_game_expert's card. So, the losing rate is 100%.\n\nPlan 3: Check\n- If board_game_expert holds a King (18.75% chance), he would likely call (60%) or fold (40%). If he calls, I will lose. If he folds, I will win. So, the winning rate is 7.5% (18.75% * 40%), and the losing rate is 11.25% (18.75% * 60%).\n- If board_game_expert holds a Queen (43.75% chance), we will have a draw regardless of his action. So, the draw rate is 43.75%.\n- If board_game_expert holds a Jack (37.5% chance), he would likely call (40%) or fold (60%). If he calls, I will lose. If he folds, I will win. So, the winning rate is 22.5% (37.5% * 60%), and the losing rate is 15% (37.5% * 40%).\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the 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 = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 30% * 8 - 26.25% * 8 = 0.3 chips\n- Plan 2: Expected Chips Gain = -100% * 4 = -4 chips\n- Plan 3: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 30% * 8 - 26.25% * 8 = 0.3 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 have the highest expected chips gain (0.3 chips), while Plan 2 has the lowest expected chips gain (-4 chips). Therefore, I should either raise (Plan 1) or check (Plan 3). Considering the strategy improvement, I should choose to raise (Plan 1) as it is more likely to confuse board_game_expert and potentially lead to a higher payoff in the long run."}}
{"message": "", "19_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, he will raise (100% probability). If the public card is a King, I will lose. If the public card is not a King, I have a chance to win if it's a Jack. \n- If board_game_expert holds a Queen or Jack, he will call (100% probability). If the public card is a Queen or Jack, I will lose. If the public card is a King, I have a chance to win.\n\nPlan 2: Raise\n- If board_game_expert holds a King, he will call (100% probability). If the public card is a King, I will lose. If the public card is not a King, I have a chance to win if it's a Jack. \n- If board_game_expert holds a Queen or Jack, he will raise (100% probability). If the public card is a Queen or Jack, I will lose. If the public card is a King, I have a chance to win.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot, but I will not lose any more chips. This is a safe strategy, but it does not give me a chance to win more chips.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips (half of the total pot of 6 chips). If I lose, the lose payoff would be 2 chips (half of the total pot of 4 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 lose 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 = 0.33 * 3 - 0.67 * 2 = -0.67 chips\n- Plan 2: Expected Chips Gain = 0.33 * 5 - 0.67 * 3 = -0.01 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain, so I will choose Plan 2: Raise."}}
{"message": "", "19_2": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (50% probability), he will raise in the second round regardless of the public card. If the public card is a King, I will lose (33.3% probability). If the public card is a Queen or a Jack, I will win (66.7% probability). \n- If board_game_expert holds a Jack (50% probability), he will raise in the second round if the public card is a Jack, and fold otherwise. If the public card is a Jack, it will be a draw (33.3% probability). If the public card is a Queen or a King, I will win (66.7% probability). \n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of board_game_expert's card or the public card. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the call 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 fold 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 = 0.5 * (0.667 * 5 - 0.333 * 5) + 0.5 * (0.667 * 5 - 0.333 * 5) = 1.67\n- Plan 2: Expected Chips Gain = -3\n\nPlan Selection:\n- Plan 1 (Call) has a higher expected chips gain than Plan 2 (Fold). Therefore, I should choose Plan 1."}}
{"message": "", "19_4": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (50% probability), he will call (100% probability). If I raise, the total chips in the pot will be 14. If I win, the winning payoff would be 7 chips. If I lose, the lose payoff would be 7 chips. The winning rate is 0% (since a King is higher than my Jack), the losing rate is 100%, and the draw rate is 0%. The expected chips gain for this plan is 0% * 7 - 100% * 7 = -7 chips.\n- If board_game_expert holds a Jack (50% probability), he will raise (100% probability). If I raise, the total chips in the pot will be 14. If I win, the winning payoff would be 7 chips. If I lose, the lose payoff would be 7 chips. The winning rate is 50% (since we both have a Jack), the losing rate is 0%, and the draw rate is 50%. The expected chips gain for this plan is 50% * 7 - 0% * 7 = 3.5 chips.\n\nPlan 2: Fold\n- If I fold, the total chips in the pot will remain 6. I will lose 3 chips regardless of what card board_game_expert holds. The expected chips gain for this plan is -3 chips.\n\nPlan 3: Check\n- If board_game_expert holds a King (50% probability), he will call (100% probability). If I check, the total chips in the pot will remain 6. If I win, the winning payoff would be 3 chips. If I lose, the lose payoff would be 3 chips. The winning rate is 0% (since a King is higher than my Jack), the losing rate is 100%, and the draw rate is 0%. The expected chips gain for this plan is 0% * 3 - 100% * 3 = -3 chips.\n- If board_game_expert holds a Jack (50% probability), he will raise (100% probability). If I check, the total chips in the pot will be 10. If I win, the winning payoff would be 5 chips. If I lose, the lose payoff would be 5 chips. The winning rate is 50% (since we both have a Jack), the losing rate is 0%, and the draw rate is 50%. The expected chips gain for this plan is 50% * 5 - 0% * 5 = 2.5 chips.\n\nPlan Selection:\nThe estimated expected chips gains for each plan are as follows:\n- Plan 1: -3.5 chips\n- Plan 2: -3 chips\n- Plan 3: -0.5 chips\n\nTherefore, the best plan to select in this situation is Plan 3: Check."}}
{"message": "", "20_1": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (80% probability), he will likely raise in the second round if the public card is a King (33.3% probability). If the public card is not a King, he will call if I raise (100% probability). Therefore, the winning rate for this plan is 0 (as I can't beat a King with my Queen), the draw rate is 0, and the lose rate is 80%.\n- If board_game_expert holds a Jack (20% probability), he will likely raise in the second round if the public card is a Jack (33.3% probability). If the public card is not a Jack, he will fold if I raise (100% probability). Therefore, the winning rate for this plan is 20%, the draw rate is 0, and the lose rate is 0.\n\nPlan 2: Raise\n- If board_game_expert holds a King (80% probability), he will likely call in the second round if the public card is a King (33.3% probability). If the public card is not a King, he will call if I raise (100% probability). Therefore, the winning rate for this plan is 0, the draw rate is 0, and the lose rate is 80%.\n- If board_game_expert holds a Jack (20% probability), he will likely raise in the second round if the public card is a Jack (33.3% probability). If the public card is not a Jack, he will fold if I raise (100% probability). Therefore, the winning rate for this plan is 20%, the draw rate is 0, and the lose rate is 0.\n\nPlan 3: Fold\n- If I fold, I automatically lose the game. Therefore, the winning rate for this plan is 0, the draw rate is 0, and the lose rate is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 6 chips (half of the total pot of 12 chips). If lose, the lose payoff would be 6 chips.\n- Plan 2: 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 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 = 20% * 6 chips - 80% * 6 chips = -3.6 chips\n- Plan 2: Expected Chips Gain = 20% * 8 chips - 80% * 8 chips = -4.8 chips\n- Plan 3: Expected Chips Gain = -2 chips (as I automatically lose if I fold)\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain (-3.6 chips), followed by Plan 3 (-2 chips), and Plan 2 (-4.8 chips). Therefore, I should choose Plan 1: Call."}}
{"message": "", "20_3": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, he will win. However, since I believe he holds a King with 100% probability, I can't avoid this outcome. The probability of winning is 0%, losing is 100%, and drawing is 0%.\n- If board_game_expert holds a Queen, we will draw. But since I believe he doesn't hold a Queen, the probability of this happening is 0%.\n- If board_game_expert holds a Jack, I will win. But since I believe he doesn't hold a Jack, the probability of this happening is 0%.\n\nPlan 2: Raise\n- If board_game_expert holds a King, he will call and win. The probability of winning is 0%, losing is 100%, and drawing is 0%.\n- If board_game_expert holds a Queen, he will fold and I will win. But since I believe he doesn't hold a Queen, the probability of this happening is 0%.\n- If board_game_expert holds a Jack, he will fold and I will win. But since I believe he doesn't hold a Jack, the probability of this happening is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of what card board_game_expert holds. The probability of winning is 0%, losing is 100%, and drawing is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 6 chips. If I lose, the lose payoff would be 6 chips.\n- Plan 2: If I win, the winning payoff would be 10 chips. If I lose, the lose payoff would be 10 chips.\n- Plan 3: If I lose, the lose payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0% * 6 chips - 100% * 6 chips = -6 chips\n- Plan 2: Expected Chips Gain = 0% * 10 chips - 100% * 10 chips = -10 chips\n- Plan 3: Expected Chips Gain = 0% * 0 chips - 100% * 4 chips = -4 chips\n\nPlan Selection:\n- Plan 1: -6 chips\n- Plan 2: -10 chips\n- Plan 3: -4 chips\n\nThe plan with the highest estimated expected chips gain is Plan 3: Fold. Although I will lose this game, I will lose the least amount of chips compared to the other plans. Therefore, I should choose to fold."}}
{"message": "", "21_1": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (0% probability), he will raise (100%). I will lose as King is higher than Queen. \n- If board_game_expert holds a Queen (100% probability), he will check (100%). It will be a draw as we both hold Queens. \n- If board_game_expert holds a Jack (0% probability), he will raise (100%). I will win as Queen is higher than Jack. \nOverall, the winning rate for plan 1 is 0%, the lose rate is 0%, and the draw rate is 100%. \n\nPlan 2: Fold\n- If I fold, I will automatically lose the round regardless of what card board_game_expert holds. \nOverall, the winning rate for plan 2 is 0%, the lose rate is 100%, and the draw rate is 0%. \n\nPlan 3: Check\n- If board_game_expert holds a King (0% probability), he will raise (100%). I will lose as King is higher than Queen. \n- If board_game_expert holds a Queen (100% probability), he will check (100%). It will be a draw as we both hold Queens. \n- If board_game_expert holds a Jack (0% probability), he will raise (100%). I will win as Queen is higher than Jack. \nOverall, the winning rate for plan 3 is 0%, the lose rate is 0%, and the draw rate is 100%. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 4 chips. If lose, the lose payoff would be 4 chips.\n- Plan 2: If win, the winning payoff would be 0 chips. If lose, the lose payoff would be 2 chips.\n- Plan 3: If win, the winning payoff would be 4 chips. If lose, the lose payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0% * 4 chips - 0% * 4 chips = 0 chips\n- Plan 2: 0% * 0 chips - 100% * 2 chips = -2 chips\n- Plan 3: 0% * 4 chips - 0% * 4 chips = 0 chips\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows:\n1. Plan 1 and Plan 3 (0 chips)\n2. Plan 2 (-2 chips)\n\nTherefore, I should select either Plan 1 (Raise) or Plan 3 (Check) as they have the highest estimated expected chips gain. Considering the strategy improvement, I would choose Plan 1 (Raise) to confuse board_game_expert."}}
{"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 overall winning rate is 30% * 1/3 (probability of Jack as public card) = 10%, losing rate is 70% * 2/3 (probability of King or Queen as public card) = 46.67%, and 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 lose unless the public card is a Jack. If he calls, I have a chance to win if the public card is a Jack. The overall winning rate is 60% * 1/3 = 20%, losing rate is 40% * 2/3 = 26.67%, and draw rate is 0%.\n- If board_game_expert holds a Jack, he will likely call (70% probability) or raise (30% probability). If he raises, it will be a draw unless the public card is a King or Queen. If he calls, it will be a draw. The overall winning rate is 0%, losing rate is 30% * 2/3 = 20%, and draw rate is 70% + 30% * 1/3 = 80%.\n\nPlan 2: Raise\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, I have a chance to win if the public card is a Jack. The overall winning rate is 40% * 1/3 = 13.33%, losing rate is 60% * 2/3 = 40%, and 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 have a chance to win if the public card is a Jack. The overall winning rate is 30% + 70% * 1/3 = 53.33%, losing rate is 70% * 2/3 = 46.67%, and draw rate is 0%.\n- If board_game_expert holds a Jack, he will likely fold (40% probability) or call (60% probability). If he folds, I will win. If he calls, it will be a draw. The overall winning rate is 40%, losing rate is 0%, and draw rate is 60%.\n\nPlan 3: Fold\n- If I fold, I will lose 2 chips regardless of board_game_expert's cards. The overall winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be half of the total pot (3 chips) = 1.5 chips. If lose, the lose payoff would be half of the total pot (3 chips) = 1.5 chips.\n- Plan 2: If win, the winning payoff would be half of the total pot (7 chips) = 3.5 chips. If lose, the lose payoff would be half of the total pot (7 chips) = 3.5 chips.\n- Plan 3: If lose, the lose payoff would be half of the total pot (2 chips) = 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 10% * 1.5 - 46.67% * 1.5 = -0.55 chips\n- Plan 2: Expected Chips Gain = 53.33% * 3.5 - 40% * 3.5 = 0.47 chips\n- Plan 3: Expected Chips Gain = -100% * 1 = -1 chip\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain, so 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 (100% probability). If he folds, I will win (100% probability).\n- If board_game_expert holds a Queen, he will likely call (50% probability) or fold (50% probability). If he calls, I will lose (100% probability). If he folds, I will win (100% probability).\n- If board_game_expert holds a Jack, he will likely call (40% probability) or fold (60% probability). If he calls, it will be a draw (100% probability). If he folds, I will win (100% probability).\n- Overall winning rate for Plan 1: (38.89% * 100%) + (38.89% * 100%) + (38.89% * 100%) = 38.89%\n- Overall losing rate for Plan 1: (22.22% * 100%) + (38.89% * 100%) = 61.11%\n- Overall draw rate for Plan 1: (38.89% * 100%) = 38.89%\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card board_game_expert holds.\n- Overall winning rate for Plan 2: 0%\n- Overall losing rate for Plan 2: 100%\n- Overall draw rate for Plan 2: 0%\n\nPlan 3: Check\n- If board_game_expert holds a King, he will likely raise (80% probability) or check (20% probability). If he raises, I will lose (100% probability). If he checks, I will lose (100% probability).\n- If board_game_expert holds a Queen, he will likely raise (70% probability) or check (30% probability). If he raises, I will lose (100% probability). If he checks, I will lose (100% probability).\n- If board_game_expert holds a Jack, he will likely raise (60% probability) or check (40% probability). If he raises, it will be a draw (100% probability). If he checks, it will be a draw (100% probability).\n- Overall winning rate for Plan 3: 0%\n- Overall losing rate for Plan 3: (22.22% * 100%) + (38.89% * 100%) = 61.11%\n- Overall draw rate for Plan 3: (38.89% * 100%) = 38.89%\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 4 chips. If lose, the lose payoff would be 4 chips.\n- Plan 2: If lose, the lose payoff would be 4 chips.\n- Plan 3: If lose, the lose payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: (38.89% * 4) - (61.11% * 4) = -0.89 chips\n- Plan 2: (0% * 4) - (100% * 4) = -4 chips\n- Plan 3: (0% * 4) - (61.11% * 4) = -2.44 chips\n\nPlan Selection:\n- Plan 1: -0.89 chips\n- Plan 2: -4 chips\n- Plan 3: -2.44 chips\n\nBased on the estimated expected chips gain, Plan 1 (Raise) is the best strategy to use in this situation."}}
{"message": "", "22_4": {"plan": "Plan 1: Call\n- If board_game_expert holds a Queen (70% probability), he will likely raise (70% probability). Considering the game rules, I will lose this round (probability = 70% * 70% = 49%).\n- If board_game_expert holds a Jack (30% probability), he will likely call (40% probability) or fold (60% probability). Considering the game rules, I will draw this round if he calls (probability = 30% * 40% = 12%) and win if he folds (probability = 30% * 60% = 18%).\n\nPlan 2: Fold\n- If I fold, I will lose this round regardless of board_game_expert's cards or actions.\n\nWinning/Lose/Draw rates for Plan 1: \n- Winning rate: 18%\n- Lose rate: 49%\n- Draw rate: 12%\n\nWinning/Lose/Draw rates for Plan 2: \n- Winning rate: 0%\n- Lose rate: 100%\n- Draw rate: 0%\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (12 chips + 8 chips) / 2 = 10 chips. If I lose, the lose payoff would be half of the total pot (12 chips + 8 chips) / 2 = 10 chips.\n- Plan 2: If I lose, the lose payoff would be half of the total pot (12 chips + 8 chips) / 2 = 10 chips.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = winning rate * Winning Payoff - lose rate * Lose Payoff = 18% * 10 chips - 49% * 10 chips = -3.1 chips\n- Plan 2: Expected Chips Gain = winning rate * Winning Payoff - lose rate * Lose Payoff = 0% * 10 chips - 100% * 10 chips = -10 chips\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain (-3.1 chips) than Plan 2 (-10 chips). Therefore, I should choose Plan 1: Call."}}
{"message": "", "23_1": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King, he will likely raise (70%) or call (30%). If he raises, I will lose unless the public card is a Queen. If he calls, I will win unless the public card is a King. The overall winning rate is 30%, losing rate is 70%, and draw rate is 0%.\n- If board_game_expert holds a Queen, he will likely call (70%) or fold (30%). If he calls, the game will be a draw unless the public card is a King or Jack. If he folds, I will win. The overall winning rate is 30%, losing rate is 0%, and draw rate is 70%.\n- If board_game_expert holds a Jack, he will likely call (60%) or fold (40%). If he calls, I will win unless the public card is a Jack. If he folds, I will win. The overall winning rate is 60%, losing rate is 0%, and draw rate is 40%.\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of board_game_expert's card. The overall 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%) or call (20%). If he raises, I will lose unless the public card is a Queen. If he calls, I will win unless the public card is a King. The overall winning rate is 20%, losing rate is 80%, and draw rate is 0%.\n- If board_game_expert holds a Queen, he will likely call (60%) or raise (40%). If he calls, the game will be a draw unless the public card is a King or Jack. If he raises, I will lose unless the public card is a Queen. The overall winning rate is 20%, losing rate is 40%, and draw rate is 40%.\n- If board_game_expert holds a Jack, he will likely call (70%) or raise (30%). If he calls, I will win unless the public card is a Jack. If he raises, I will lose unless the public card is a Queen. The overall winning rate is 40%, losing rate is 30%, and draw rate is 30%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 4 chips. If lose, the lose payoff would be 2 chips.\n- Plan 2: If lose, the lose payoff would be 2 chips.\n- Plan 3: If win, the winning payoff would be 2 chips. If lose, the lose payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.3 * 4 - 0.7 * 2 = -0.2 chips\n- Plan 2: Expected Chips Gain = -2 chips\n- Plan 3: Expected Chips Gain = 0.2 * 2 - 0.8 * 2 = -1.2 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I should choose to raise."}}
{"message": "", "24_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 have a 50% chance of winning (if the public card is a King or not a King). If he calls, I have a 100% chance of winning (since my card is a King and his is also a King, but the public card is not a King). Overall, the winning rate for this plan is 60%.\n- If board_game_expert holds a Queen, he would likely raise (40%) or call (60%). If he raises, I have a 50% chance of winning (if the public card is a King or a Queen). If he calls, I have a 100% chance of winning (since my card is a King and his is a Queen, and the public card is not a Queen). Overall, the winning rate for this plan is 70%.\n- If board_game_expert holds a Jack, he would likely raise (30%) or call (70%). If he raises, I have a 50% chance of winning (if the public card is a King or a Jack). If he calls, I have a 100% chance of winning (since my card is a King and his is a Jack, and the public card is not a Jack). Overall, the winning rate for this plan is 80%.\n\nPlan 2: Raise\n- If board_game_expert holds a King, he would likely raise (60%) or call (40%). If he raises, I have a 50% chance of winning (if the public card is a King or not a King). If he calls, I have a 100% chance of winning (since my card is a King and his is also a King, but the public card is not a King). Overall, the winning rate for this plan is 70%.\n- If board_game_expert holds a Queen, he would likely call (70%) or fold (30%). If he calls, I have a 100% chance of winning (since my card is a King and his is a Queen, and the public card is not a Queen). If he folds, I win by default. Overall, the winning rate for this plan is 100%.\n- If board_game_expert holds a Jack, he would likely call (60%) or fold (40%). If he calls, I have a 100% chance of winning (since my card is a King and his is a Jack, and the public card is not a Jack). If he folds, I win by default. Overall, the winning rate for this plan is 100%.\n\nPlan 3: Fold\n- This plan is not advisable as I hold a King, which is the highest rank card. Folding would result in a 100% loss rate.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 3 chips (half of the total pot of 6 chips). If lose, the lose payoff would be 3 chips.\n- Plan 2: If win, the winning payoff would be 4 chips (half of the total pot of 8 chips). If lose, the lose payoff would be 4 chips.\n- Plan 3: If fold, there would be no payoff as I would lose by default.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.7 * 3 - 0.3 * 3 = 1.2 chips\n- Plan 2: Expected Chips Gain = 0.9 * 4 - 0.1 * 4 = 3.6 chips\n- Plan 3: Expected Chips Gain = 0 - 1 * 2 = -2 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain and is therefore the best strategy. Plan 1 (Call) is the second best strategy, and Plan 3 (Fold) is the worst strategy."}}
{"message": "", "24_2": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (22.2% probability), he would likely call (60%) or fold (40%). If he calls, we would draw. If he folds, I would win. So, the winning rate is 22.2% * 40% = 8.88%, the draw rate is 22.2% * 60% = 13.32%, and the lose rate is 0%.\n- If board_game_expert holds a Queen (38.9% probability), he would likely call (50%) or fold (50%). If he calls, I would lose. If he folds, I would win. So, the winning rate is 38.9% * 50% = 19.45%, the draw rate is 0%, and the lose rate is 38.9% * 50% = 19.45%.\n- If board_game_expert holds a Jack (33.3% probability), he would likely call (40%) or fold (60%). If he calls, I would win. If he folds, I would win. So, the winning rate is 33.3% * 100% = 33.3%, the draw rate is 0%, and the lose rate is 0%.\n\nPlan 2: Fold\n- If I fold, I would lose regardless of what card board_game_expert holds. So, the winning rate is 0%, the draw rate is 0%, and the lose rate is 100%.\n\nPlan 3: Check\n- If board_game_expert holds a King (22.2% probability), he would likely raise (80%) or check (20%). If he raises, I would lose. If he checks, we would draw. So, the winning rate is 0%, the draw rate is 22.2% * 20% = 4.44%, and the lose rate is 22.2% * 80% = 17.76%.\n- If board_game_expert holds a Queen (38.9% probability), he would likely raise (50%) or check (50%). If he raises, I would lose. If he checks, I would lose. So, the winning rate is 0%, the draw rate is 0%, and the lose rate is 38.9% * 100% = 38.9%.\n- If board_game_expert holds a Jack (33.3% probability), he would likely raise (40%) or check (60%). If he raises, I would win. If he checks, I would win. So, the winning rate is 33.3% * 100% = 33.3%, the draw rate is 0%, and the lose rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be half of the total pot (8 chips). If lose, the lose payoff would be half of the total pot (8 chips).\n- Plan 2: If lose, the lose payoff would be half of the total pot (4 chips).\n- Plan 3: If win, the winning payoff would be half of the total pot (4 chips). 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: Expected Chips Gain = 8 * 61.63% - 8 * 19.45% = 3.34 chips\n- Plan 2: Expected Chips Gain = -4 * 100% = -4 chips\n- Plan 3: Expected Chips Gain = 4 * 37.74% - 4 * 56.66% = -0.76 chips\n\nPlan Selection:\n- Plan 1: Raise (3.34 chips)\n- Plan 3: Check (-0.76 chips)\n- Plan 2: Fold (-4 chips)\n\nThe best plan is to raise."}}
{"message": "", "24_4": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (32% probability), he will likely call (60%). If he calls, I will lose (as his King is higher than my King). If he folds (40%), I will win. So, the winning rate is 12.8%, losing rate is 19.2%, and draw rate is 0%.\n- If board_game_expert holds a Queen (35% probability), he will likely call (50%) or fold (50%). If he calls, I will lose (as his pair of Queens is higher than my single King). If he folds, I will win. So, the winning rate is 17.5%, losing rate is 17.5%, and draw rate is 0%.\n- If board_game_expert holds a Jack (24% probability), he will likely call (40%) or fold (60%). If he calls, I will win (as my King is higher than his Jack). If he folds, I will win. So, the winning rate is 21.6%, losing rate is 0%, and draw rate is 0%.\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 winning and lose payoffs for each plan:\n- Plan 1: After the call, all chips in the pot would be 24. If win, the winning payoff would be 12. If lose, the lose payoff would be 12.\n- Plan 2: After the fold, all chips in the pot would be 20. If lose, the lose payoff would be 10.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 0.516 * 12 - 0.368 * 12 = 1.776\n- Plan 2: Expected Chips Gain = 0 * Winning Payoff - 1 * Losing Payoff = -10\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain than Plan 2. Therefore, I should choose Plan 1: Call."}}
{"message": "", "25_1": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (20% probability), he would likely call (70%) or raise (30%). If he calls, I would likely win (80%) or draw (20%). If he raises, I would likely win (70%) or draw (30%). Overall, the winning rate is 0.2*(0.7*0.8+0.3*0.7)=0.122, the draw rate is 0.2*(0.7*0.2+0.3*0.3)=0.038, and the lose rate is 0.\n- If board_game_expert holds a Queen (40% probability), he would likely call (50%) or fold (50%). If he calls, I would likely win (100%). If he folds, I would also win (100%). Overall, the winning rate is 0.4*(0.5*1+0.5*1)=0.4, the draw rate is 0, and the lose rate is 0.\n- If board_game_expert holds a Jack (40% probability), he would likely fold (60%) or call (40%). If he folds, I would win (100%). If he calls, I would also win (100%). Overall, the winning rate is 0.4*(0.6*1+0.4*1)=0.4, the draw rate is 0, and the lose rate is 0.\nPlan1 overall GoodGuy's Winning/Lose/Draw rates: the Winning rate for plan 1 is 0.122+0.4+0.4=0.922; Lose rate for plan 1 is 0; Draw Rate for plan 1 is 0.038.\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 draw rate is 0, and the lose rate is 1.\n\nPlan 3: Check\n- If board_game_expert holds a King (20% probability), he would likely raise (80%) or call (20%). If he raises, I would likely win (80%) or draw (20%). If he calls, I would likely win (70%) or draw (30%). Overall, the winning rate is 0.2*(0.8*0.8+0.2*0.7)=0.124, the draw rate is 0.2*(0.8*0.2+0.2*0.3)=0.04, and the lose rate is 0.\n- If board_game_expert holds a Queen (40% probability), he would likely raise (40%) or call (60%). If he raises, I would likely win (100%). If he calls, I would also win (100%). Overall, the winning rate is 0.4*(0.4*1+0.6*1)=0.4, the draw rate is 0, and the lose rate is 0.\n- If board_game_expert holds a Jack (40% probability), he would likely raise (30%) or call (70%). If he raises, I would win (100%). If he calls, I would also win (100%). Overall, the winning rate is 0.4*(0.3*1+0.7*1)=0.4, the draw rate is 0, and the lose rate is 0.\nPlan3 overall GoodGuy's Winning/Lose/Draw rates: the Winning rate for plan 3 is 0.124+0.4+0.4=0.924; Lose rate for plan 3 is 0; Draw Rate for plan 3 is 0.04.\n\nThe number of winning and lose payoffs for each plan:\n- Plan1: After the action, all chips in the pot: If win, the winning payoff would be 4 (half of the total pot); If lose, the lose payoff would be 2 (half of the total pot).\n- Plan2: After the action, all chips in the pot: If win, the winning payoff would be 2 (half of the total pot); If lose, the lose payoff would be 2 (half of the total pot).\n- Plan3: After the action, all chips in the pot: If win, the winning payoff would be 2 (half of the total pot); If lose, the lose payoff would be 2 (half of the total pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan1: 0.922*4-0*2=3.688\n- Plan2: 0*2-1*2=-2\n- Plan3: 0.924*2-0*2=1.848\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is: Plan1 > Plan3 > Plan2. Therefore, I should select Plan1 (Raise) as it has the highest estimated expected chips gain."}}
{"message": "", "26_0": {"plan": "Plan 1: Call\n- If board_game_expert holds 'SK', he will likely raise (100% probability). If the public card is 'HQ', he will call (100% probability). My winning rate is 0% (as his card is higher), losing rate is 100%, and draw rate is 0%.\n- If board_game_expert holds 'QH', he will likely check (50% probability) or call (50% probability). If the public card is 'JH', he will check (100% probability). My winning rate is 100% (as my card is higher), losing rate is 0%, and draw rate is 0%.\n\nPlan 2: Raise\n- If board_game_expert holds 'SK', he will likely call (100% probability). If the public card is 'HQ', he will call (100% probability). My winning rate is 0% (as his card is higher), losing rate is 100%, and draw rate is 0%.\n- If board_game_expert holds 'QH', he will likely fold (100% probability). My winning rate is 100% (as he will fold), losing rate is 0%, and draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the round regardless of what card board_game_expert holds. My winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If 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 4 chips (half of the total pot of 8 chips). If lose, the lose payoff would be 4 chips.\n- Plan 3: If I fold, I will lose 1 chip (the chip I put in as the small blind).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 100% * 3 chips - 0% * 3 chips = 3 chips\n- Plan 2: Expected Chips Gain = 100% * 4 chips - 0% * 4 chips = 4 chips\n- Plan 3: Expected Chips Gain = 0% * 0 chips - 100% * 1 chip = -1 chip\n\nPlan Selection:\nRanking the plans by expected chips gain, we get Plan 2 > Plan 1 > Plan 3. Therefore, the best plan to execute is Plan 2: Raise."}}
{"message": "", "26_2": {"plan": "Plan 1: Call\n- If board_game_expert holds 'SK': He will likely raise (100% probability). If the public card is a 'HQ', he will call (100% probability). My winning rate is 50% (if the public card is a King), losing rate is 50% (if the public card is a Queen or Jack), and draw rate is 0%.\n- If board_game_expert holds 'QH': He will likely check (50% probability) or call (50% probability). If the public card is a 'JH', he will check (100% probability). My winning rate is 100% (since I hold a King), losing rate is 0%, and draw rate is 0%.\n\nPlan 2: Fold\n- If board_game_expert holds 'SK': My winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n- If board_game_expert holds 'QH': My winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n\nWinning/Lose 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 win, the winning payoff would be 3. If lose, the lose payoff would be 3.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.75 * 5 - 0.25 * 5 = 2.5\n- Plan 2: Expected Chips Gain = 0 * 3 - 1 * 3 = -3\n\nPlan Selection:\nBased on the expected chips gain, Plan 1 (Call) is the better strategy."}}
{"message": "", "26_4": {"plan": "Plan 1: Raise\n- If board_game_expert holds 'SK': He will call (100% probability). If the next public card is a King, I will win (25% probability), if it's a Queen, I will lose (25% probability), and if it's a Jack, I will win (50% probability). Overall, my winning rate is 75%, losing rate is 25%, and draw rate is 0%.\n- If board_game_expert holds 'QH': He will fold (100% probability). I will win (100% probability). Overall, my winning rate is 100%, losing rate is 0%, and draw rate is 0%.\n\nPlan 2: Fold\n- If board_game_expert holds 'SK' or 'QH': I will lose (100% probability). Overall, my winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n\nPlan 3: Check\n- If board_game_expert holds 'SK': He will raise (100% probability). If the next public card is a King, I will win (25% probability), if it's a Queen, I will lose (25% probability), and if it's a Jack, I will win (50% probability). Overall, my winning rate is 75%, losing rate is 25%, and draw rate is 0%.\n- If board_game_expert holds 'QH': He will check (100% probability). If the next public card is a King, I will win (25% probability), if it's a Queen, I will lose (25% probability), and if it's a Jack, I will win (50% probability). Overall, my winning rate is 75%, losing rate is 25%, and draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 10 chips. If lose, the lose payoff would be 10 chips.\n- Plan 2: If lose, the lose payoff would be 6 chips.\n- Plan 3: If win, the winning payoff would be 6 chips. If lose, the lose payoff would be 6 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.75 * 10 - 0.25 * 10 = 5 chips\n- Plan 2: Expected Chips Gain = 0 - 1 * 6 = -6 chips\n- Plan 3: Expected Chips Gain = 0.75 * 6 - 0.25 * 6 = 3 chips\n\nPlan Selection:\n- Plan 1: 5 chips\n- Plan 2: -6 chips\n- Plan 3: 3 chips\n\nBased on the expected chips gain, I should select Plan 1 (Raise) as it has the highest expected chips gain."}}
{"message": "", "27_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (20% probability), he would likely call (30%) or raise (70%). If he calls, I would have a 33% chance of winning (if the public card is a Jack), 33% chance of losing (if the public card is a King), and 33% chance of drawing (if the public card is a Queen). If he raises, I would have a 33% chance of winning, 33% chance of losing, and 33% chance of drawing. Overall, my winning rate for his King is 20% * 33% = 6.6%, losing rate is 6.6%, and drawing rate is 6.6%.\n- If board_game_expert holds a Queen (30% probability), he would likely call (60%) or raise (40%). If he calls, I would have a 33% chance of winning, 33% chance of losing, and 33% chance of drawing. If he raises, I would have a 33% chance of winning, 33% chance of losing, and 33% chance of drawing. Overall, my winning rate for his Queen is 30% * 33% = 9.9%, losing rate is 9.9%, and drawing rate is 9.9%.\n- If board_game_expert holds a Jack (50% probability), he would likely call (50%) or fold (50%). If he calls, I would have a 33% chance of winning, 33% chance of losing, and 33% chance of drawing. If he folds, I would win. Overall, my winning rate for his Jack is 50% * 33% = 16.5%, losing rate is 16.5%, and drawing rate is 16.5%.\nPlan 1 overall GoodGuy's Winning/Lose/Draw rates: Winning rate for plan 1 is 6.6% + 9.9% + 16.5% = 33%, Lose rate for plan 1 is 33%, and Draw Rate for plan 1 is 33%.\n\nPlan 2: Raise\n- If board_game_expert holds a King (20% probability), he would likely call (80%) or raise (20%). If he calls, I would have a 33% chance of winning, 33% chance of losing, and 33% chance of drawing. If he raises, I would have a 33% chance of winning, 33% chance of losing, and 33% chance of drawing. Overall, my winning rate for his King is 20% * 33% = 6.6%, losing rate is 6.6%, and drawing rate is 6.6%.\n- If board_game_expert holds a Queen (30% probability), he would likely call (70%) or fold (30%). If he calls, I would have a 33% chance of winning, 33% chance of losing, and 33% chance of drawing. If he folds, I would win. Overall, my winning rate for his Queen is 30% * 33% = 9.9%, losing rate is 9.9%, and drawing rate is 9.9%.\n- If board_game_expert holds a Jack (50% probability), he would likely fold (70%) or call (30%). If he folds, I would win. If he calls, I would have a 33% chance of winning, 33% chance of losing, and 33% chance of drawing. Overall, my winning rate for his Jack is 50% * 33% = 16.5%, losing rate is 16.5%, and drawing rate is 16.5%.\nPlan 2 overall GoodGuy's Winning/Lose/Draw rates: Winning rate for plan 2 is 6.6% + 9.9% + 16.5% = 33%, Lose rate for plan 2 is 33%, and Draw Rate for plan 2 is 33%.\n\nPlan 3: Fold\n- If I fold, I would lose regardless of what card board_game_expert holds. Therefore, my winning rate for this plan is 0%, losing rate is 100%, and drawing rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, all chips in the pot: If win, the winning payoff would be 3 chips. If lose, the lose payoff would be 3 chips.\n- Plan 2: After the action, all chips in the pot: If win, the winning payoff would be 6 chips. If lose, the lose payoff would be 6 chips.\n- Plan 3: After the action, all chips in the pot: If lose, the lose payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Lose rate * Lose Payoff = 33% * 3 - 33% * 3 = 0 chips\n- Plan 2: Expected Chips Gain = 33% * 6 - 33% * 6 = 0 chips\n- Plan 3: Expected Chips Gain = 0% * 0 - 100% * 2 = -2 chips\n\nPlan Selection:\n- Plan 1 and Plan 2 both have an expected chips gain of 0, while Plan 3 has an expected chips loss of 2. Therefore, either Plan 1 or Plan 2 would be the best choice. Since Plan 2 has a higher potential payoff if I win, I would choose Plan 2: Raise."}}
{"message": "", "27_2": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King, he would likely check (60%) or fold (40%). If he checks, I would lose (as King is higher than Jack). If he folds, I would 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 would likely check (50%) or fold (50%). If he checks, I would lose (as Queen matches the public card). If he folds, I would 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 would likely fold (60%) or check (40%). If he folds, I would win. If he checks, it would be a draw (as we both hold 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 would 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 would likely check (60%) or fold (40%). If he checks, I would lose (as King is higher than Jack). If he folds, I would 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 would likely check (50%) or fold (50%). If he checks, I would lose (as Queen matches the public card). If he folds, I would 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 would likely fold (60%) or check (40%). If he folds, I would win. If he checks, it would be a draw (as we both hold Jack). So, the winning rate is 60%, losing rate is 0%, and draw rate is 40%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 4 chips (half of the total pot). 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 = 0.4 * 4 - 0.6 * 4 = -0.8 chips\n- Plan 2: Expected Chips Gain = 0 - 1 * 4 = -4 chips\n- Plan 3: Expected Chips Gain = 0.5 * 4 - 0.5 * 4 = 0 chips\n\nPlan Selection:\n- Plan 1: -0.8 chips\n- Plan 2: -4 chips\n- Plan 3: 0 chips\n\nBased on the estimated expected chips gain, Plan 3 (Check) is the best strategy to use in this situation."}}
{"message": "", "27_4": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (20% probability), he will likely check (60%) or fold (40%). If he checks, 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 (80% probability), he will likely raise (80%) or check (20%). If he raises or checks, I will lose (as Queen is higher than Jack). So, the winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n\nPlan 2: Raise\n- If board_game_expert holds a King (20% probability), he will likely call (80%) or raise (20%). If he calls or raises, I will lose (as King is higher than Jack). So, the winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n- If board_game_expert holds a Queen (80% probability), he will likely call (70%) or fold (30%). If he calls, I will lose (as Queen is higher than Jack). If he folds, I will win. So, the winning rate is 30%, losing rate is 70%, and draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put into the pot. So, the winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be half of the total pot (12 chips). If lose, the lose payoff would be half of the total pot (12 chips).\n- Plan 2: If win, the winning payoff would be half of the total pot (16 chips). If lose, the lose payoff would be half of the total pot (16 chips).\n- Plan 3: If lose, the lose payoff would be the chips I have already put into the pot (4 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.4 * 12 - 0.6 * 12 = -2.4 chips\n- Plan 2: Expected Chips Gain = 0.3 * 16 - 0.7 * 16 = -6.4 chips\n- Plan 3: Expected Chips Gain = -4 chips\n\nPlan Selection:\n- Plan 1: -2.4 chips\n- Plan 2: -6.4 chips\n- Plan 3: -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 Plan 1: Call."}}
{"message": "", "28_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 have a 33.33% chance of winning if the public card is a Jack. If he raises, I have a 33.33% chance of winning if the public card is a Jack. Overall, my winning rate is 33.33%, lose rate is 66.67%, and draw rate is 0%.\n- If board_game_expert holds a Queen, he will likely call (60%) or raise (40%). If he calls, I have a 33.33% chance of winning if the public card is a Jack. If he raises, I have a 33.33% chance of winning if the public card is a Jack. Overall, my winning rate is 33.33%, lose rate is 66.67%, and draw rate is 0%.\n- If board_game_expert holds a Jack, he will likely call (50%) or fold (50%). If he calls, I have a 50% chance of winning if the public card is a Jack. If he folds, I win the round. Overall, my winning rate is 50%, lose rate is 0%, and draw rate is 50%.\nPlan 1 overall GoodGuy's Winning/Lose/Draw rates: Winning rate is 38.89%, Lose rate is 44.44%, Draw rate is 16.67%.\n\nPlan 2: Raise\n- If board_game_expert holds a King, he will likely call (80%) or raise (20%). If he calls, I have a 33.33% chance of winning if the public card is a Jack. If he raises, I have a 33.33% chance of winning if the public card is a Jack. Overall, my winning rate is 33.33%, lose rate is 66.67%, and draw rate is 0%.\n- If board_game_expert holds a Queen, he will likely call (70%) or fold (30%). If he calls, I have a 33.33% chance of winning if the public card is a Jack. If he folds, I win the round. Overall, my winning rate is 43.33%, lose rate is 46.67%, and draw rate is 10%.\n- If board_game_expert holds a Jack, he will likely fold (70%) or call (30%). If he folds, I win the round. If he calls, I have a 50% chance of winning if the public card is a Jack. Overall, my winning rate is 60%, lose rate is 0%, and draw rate is 40%.\nPlan 2 overall GoodGuy's Winning/Lose/Draw rates: Winning rate is 45.56%, Lose rate is 37.78%, Draw rate is 16.67%.\n\nPlan 3: Fold\n- If I fold, I lose the round regardless of what card board_game_expert holds. Therefore, my winning rate is 0%, lose rate is 100%, and draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 3 chips. If lose, the lose payoff would be 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 I fold, I lose 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 38.89% * 3 - 44.44% * 2 = 0.67 chips\n- Plan 2: Expected Chips Gain = 45.56% * 5 - 37.78% * 4 = 0.78 chips\n- Plan 3: Expected Chips Gain = 0% * 0 - 100% * 2 = -2 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest estimated expected chips gain, so I should choose this plan."}}
{"message": "", "28_2": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (40% probability), he will likely check (60%) or fold (40%) in the second round if the public card is not a King. If the public card is a King, he will likely raise (90%) or check (10%). The winning rate for this plan is 40% (probability of him holding a King) * 60% (probability of him checking if the public card is not a King) = 24%. The losing rate is 40% * 40% = 16%. The draw rate is 0% as there is no possibility of a draw in this situation.\n- If board_game_expert holds a Queen (60% probability), he will likely check (50%) or fold (50%) in the second round if the public card is not a Queen. If the public card is a Queen, he will likely raise (80%) or check (20%). The winning rate for this plan is 60% * 50% = 30%. The losing rate is 60% * 50% = 30%. The draw rate is 0%.\n- Overall, the winning rate for Plan 1 is 24% + 30% = 54%. The losing rate is 16% + 30% = 46%. The draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose the 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 winning and lose payoffs for each plan:\n- Plan 1: After the call 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 fold action, all chips in the pot would be 6. If I lose, the losing payoff would be 3 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is winning rate * winning payoff - losing rate * losing payoff = 54% * 5 - 46% * 5 = 0.4 chips.\n- Plan 2: The expected chips gain is -100% * 3 = -3 chips.\n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 1 > Plan 2.\n- Therefore, I should select Plan 1 (Call) as it has the highest estimated expected chips gain."}}
{"message": "", "28_4": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King, he will likely check (60%) or fold (40%). If he checks, I will lose as his King is higher than my Jack. If he folds, I will win. Therefore, the winning rate is 40%, the losing rate is 60%, and the draw rate is 0%.\n- If board_game_expert holds a Queen, he will likely check (50%) or fold (50%). If he checks, I will lose as his Queen is higher than my Jack. If he folds, I will win. Therefore, the winning rate is 50%, the losing rate is 50%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will 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, he will likely check (60%) or fold (40%). If he checks, I will lose as his King is higher than my Jack. If he folds, I will win. Therefore, the winning rate is 40%, the losing rate is 60%, and the draw rate is 0%.\n- If board_game_expert holds a Queen, he will likely check (50%) or fold (50%). If he checks, I will lose as his Queen is higher than my Jack. If he folds, I will win. Therefore, the winning rate is 50%, the losing rate is 50%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If 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 = 0.4 * 6 - 0.6 * 6 = -1.2 chips\n- Plan 2: Expected Chips Gain = 0 - 1 * 6 = -6 chips\n- Plan 3: Expected Chips Gain = 0.45 * 6 - 0.55 * 6 = -0.6 chips\n\nPlan Selection:\n- Plan 1: -1.2 chips\n- Plan 2: -6 chips\n- Plan 3: -0.6 chips\n\nTherefore, the best plan is Plan 3: Check, as it has the highest expected chips gain."}}
{"message": "", "30_1": {"plan": "Make Reasonable Plans:\n\nPlan 1: Call\n- This action will match the current bet and continue the game. This is a safe move as I hold a King, the highest rank card.\n\nPlan 2: Raise\n- This action will increase the bet by 4 chips, potentially pressuring board_game_expert into folding. This is a more aggressive move, but could result in a larger pot if board_game_expert decides to call.\n\nPlan 3: Fold\n- This action will forfeit the current game. This is not a recommended move as I hold a King, the highest rank card.\n\nPotential board_game_expert's actions and Estimate Winning/Lose/Draw Rate for Each Plan:\n\nPlan 1: Call\n- If board_game_expert holds a King (41.2% probability), he will likely call (60% probability). This would result in a draw.\n- If board_game_expert holds a Queen (23.5% probability), he will likely fold (70% probability). This would result in a win for me.\n- If board_game_expert holds a Jack (35.3% probability), he will likely fold (80% probability). This would result in a win for me.\n\nPlan 2: Raise\n- If board_game_expert holds a King (41.2% probability), he will likely call (60% probability). This would result in a draw.\n- If board_game_expert holds a Queen (23.5% probability), he will likely fold (70% probability). This would result in a win for me.\n- If board_game_expert holds a Jack (35.3% probability), he will likely fold (80% probability). This would result in a win for me.\n\nPlan 3: Fold\n- If I fold, board_game_expert will win regardless of his card.\n\nThe number of winning and lose payoffs for each plan:\n\nPlan 1: Call\n- If win, the winning payoff would be half of the total pot (6 chips).\n- If lose, the lose payoff would be half of the total pot (6 chips).\n\nPlan 2: Raise\n- If win, the winning payoff would be half of the total pot (8 chips).\n- If lose, the lose payoff would be half of the total pot (8 chips).\n\nPlan 3: Fold\n- If I fold, I will lose 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n\nPlan 1: Call\n- Expected Chips Gain = Winning Rate * Winning Payoff - Lose Rate * Lose Payoff\n- Expected Chips Gain = (0.588 * 6) - (0 * 6) = 3.528 chips\n\nPlan 2: Raise\n- Expected Chips Gain = (0.588 * 8) - (0 * 8) = 4.704 chips\n\nPlan 3: Fold\n- Expected Chips Gain = -4 chips\n\nPlan Selection:\n\nRank of estimated expected chips gains:\n1. Plan 2: Raise\n2. Plan 1: Call\n3. Plan 3: Fold\n\nTherefore, the plan with the highest estimated expected chips gain is Plan 2: Raise. This is the plan I should execute."}}
{"message": "", "30_3": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (41.18% probability), he will likely call (60% probability). This will result in a draw. If he folds (40% probability), I will win.\n- If board_game_expert holds a Queen (23.53% probability), he will likely fold (70% probability), resulting in my win. If he calls (30% probability), I will also win as my card is higher.\n- If board_game_expert holds a Jack (35.29% probability), he will likely fold (80% probability), resulting in my win. If he calls (20% probability), he will win as his card matches the public card.\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 (41.18% probability), he will likely check (60% probability), resulting in a draw. If he raises (40% probability), I will call and it will result in a draw.\n- If board_game_expert holds a Queen (23.53% probability), he will likely check (50% probability), resulting in my win. If he raises (50% probability), I will call and win as my card is higher.\n- If board_game_expert holds a Jack (35.29% probability), he will likely check (70% probability), resulting in his win. If he raises (30% probability), I will fold and lose.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (6 chips + my raise of 8 chips = 14 chips, half is 7 chips). If I lose, the lose payoff would be half of the total pot (6 chips + my raise of 8 chips = 14 chips, half is 7 chips).\n- Plan 2: If I fold, I will lose my current pot of 6 chips.\n- Plan 3: If I win, the winning payoff would be half of the total pot (6 chips, half is 3 chips). If I lose, the lose payoff would be half of the total pot (6 chips, half is 3 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = (winning rate * winning payoff) - (losing rate * losing payoff) = (0.6471 * 7 chips) - (0.3529 * 7 chips) = 2.0588 chips\n- Plan 2: Expected Chips Gain = -6 chips (as I will lose my current pot)\n- Plan 3: Expected Chips Gain = (0.6471 * 3 chips) - (0.3529 * 3 chips) = 0.8824 chips\n\nPlan Selection:\n- Plan 1: Raise (Expected Chips Gain = 2.0588 chips)\n- Plan 3: Check (Expected Chips Gain = 0.8824 chips)\n- Plan 2: Fold (Expected Chips Gain = -6 chips)\n\nBased on the estimated expected chips gains, I should choose Plan 1: Raise."}}
{"message": "", "31_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (20% probability), he will likely call (70% probability) or raise (30% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I have a 50% chance of winning (if he calls) or losing (if he raises). \n- If board_game_expert holds a Queen (60% probability), he will likely call (50% probability) or fold (50% probability). If the public card is a Queen, I will lose. If the public card is a King or Jack, I have a 50% chance of winning (if he calls or folds). \n- If board_game_expert holds a Jack (20% probability), he will likely fold (60% probability) or call (40% probability). If the public card is a Jack, it's a draw. If the public card is a King or Queen, I have a 60% chance of winning (if he folds) or 40% chance of losing (if he calls). \n\nPlan 2: Raise\n- If board_game_expert holds a King (20% probability), he will likely call (70% probability) or raise (30% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I have a 70% chance of winning (if he calls) or 30% chance of losing (if he raises). \n- If board_game_expert holds a Queen (60% probability), he will likely fold (50% probability) or call (50% probability). If the public card is a Queen, I will lose. If the public card is a King or Jack, I have a 50% chance of winning (if he folds or calls). \n- If board_game_expert holds a Jack (20% probability), he will likely fold (60% probability) or call (40% probability). If the public card is a Jack, it's a draw. If the public card is a King or Queen, I have a 60% chance of winning (if he folds) or 40% chance of losing (if he calls). \n\nPlan 3: Fold\n- If I fold, I will lose the 2 chips I have already put into the pot. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips (half of the 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 5 chips (half of the total pot of 10 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 the 2 chips I have already put into the pot. \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 = 0.5 * 5 - 0.5 * 4 = 0.5 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- Plan 1 and Plan 2 both have the highest expected chips gain of 0.5 chips, so I should choose between these two plans based on my strategy improvement. Since board_game_expert tends to fold when he sees a raise and I hold a Jack, I should choose Plan 2: Raise to pressure him into folding."}}
{"message": "", "31_2": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (30% probability), he will likely raise (40% probability) or check (60% 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 to win (if the public card is a Jack) or lose (if the public card is a Queen). \n- If board_game_expert holds a Queen (40% probability), he will likely check (70% probability) or fold (30% 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 to win (if the public card is a Jack) or draw (if the public card is a King). \n- If board_game_expert holds a Jack (30% probability), he will likely check (80% probability) or fold (20% probability) in the second round. If the public card is a Jack, I will win. If the public card is not a Jack, I have a 50% chance to lose (if the public card is a King) or draw (if the public card is a Queen). \n\nPlan 2: Fold\n- If I fold, I will lose the game and the chips I have already put in the pot. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (currently 10 chips, so 5 chips). If I lose, the lose payoff would be half of the total pot (currently 10 chips, so 5 chips). \n- Plan 2: If I fold, I will lose the 4 chips I have already put in the pot. \n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is (0.3 * 0.5 * 5) + (0.4 * 0.5 * 5) + (0.3 * 1 * 5) - (0.3 * 0.5 * 5) - (0.4 * 0.5 * 5) - (0.3 * 0 * 5) = 1.5 chips. \n- Plan 2: The expected chips gain is -4 chips. \n\nPlan Selection:\n- Plan 1 has a higher expected chips gain than Plan 2, so I should choose Plan 1 and call."}}
{"message": "", "31_4": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King, he will likely check (60% probability) or raise (40% probability). If he checks, I will lose (100% probability). If he raises, I will lose (100% probability). Overall, my winning rate is 0%, losing rate is 100%, and drawing rate is 0%.\n- If board_game_expert holds a Jack, he will likely check (80% probability) or fold (20% probability). If he checks, I will draw (100% probability). If he folds, I will win (100% probability). Overall, my winning rate is 20%, losing rate is 0%, and drawing rate is 80%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card board_game_expert holds. My winning rate is 0%, losing rate is 100%, and drawing rate is 0%.\n\nPlan 3: Check\n- If board_game_expert holds a King, he will likely check (60% probability) or raise (40% probability). If he checks, I will lose (100% probability). If he raises, I will lose (100% probability). Overall, my winning rate is 0%, losing rate is 100%, and drawing rate is 0%.\n- If board_game_expert holds a Jack, he will likely check (80% probability) or fold (20% probability). If he checks, I will draw (100% probability). If he folds, I will win (100% probability). Overall, my winning rate is 20%, losing rate is 0%, and drawing rate is 80%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 6 chips. If I lose, the losing payoff would be 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 = 20% * 6 chips - 100% * 6 chips = -4 chips\n- Plan 2: Expected Chips Gain = 0% * 6 chips - 100% * 6 chips = -6 chips\n- Plan 3: Expected Chips Gain = 20% * 6 chips - 100% * 6 chips = -4 chips\n\nPlan Selection:\n- Plan 1: -4 chips\n- Plan 2: -6 chips\n- Plan 3: -4 chips\n\nBased on the expected chips gain, Plan 2 is the worst strategy. Plan 1 and Plan 3 are equally good, but considering the strategy improvement, I should choose Plan 1: Raise."}}
{"message": "", "32_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, he would likely raise (40%) or call (60%). If he raises, I would likely lose (probability = 0.4 * 0.4 = 0.16). If he calls, I would likely win if the public card is a Queen (probability = 0.6 * 0.33 = 0.198), and lose if the public card is a King or Jack (probability = 0.6 * 0.67 = 0.402).\n- If board_game_expert holds a Queen, he would likely raise (40%) or call (60%). If he raises, I would likely draw (probability = 0.4 * 0.4 = 0.16). If he calls, I would likely win if the public card is a Jack (probability = 0.6 * 0.33 = 0.198), and draw if the public card is a Queen or lose if it's a King (probability = 0.6 * 0.67 = 0.402).\n- If board_game_expert holds a Jack, he would likely fold (30%) or call (70%). If he folds, I would win (probability = 0.3). If he calls, I would likely win if the public card is a Queen or Jack (probability = 0.7 * 0.67 = 0.469), and lose if the public card is a King (probability = 0.7 * 0.33 = 0.231).\n- Overall, the winning rate for plan 1 is 0.198 + 0.198 + 0.3 + 0.469 = 1.165, the losing rate is 0.16 + 0.402 + 0.16 + 0.402 + 0.231 = 1.355, and the draw rate is 0.16 + 0.402 = 0.562.\n\nPlan 2: Raise\n- If board_game_expert holds a King, he would likely call (70%) or fold (30%). If he calls, I would likely lose (probability = 0.7 * 0.4 = 0.28). If he folds, I would win (probability = 0.3).\n- If board_game_expert holds a Queen, he would likely call (50%) or fold (50%). If he calls, I would likely draw (probability = 0.5 * 0.4 = 0.2). If he folds, I would win (probability = 0.5).\n- If board_game_expert holds a Jack, he would likely fold (60%) or call (40%). If he folds, I would win (probability = 0.6). If he calls, I would likely win if the public card is a Queen or Jack (probability = 0.4 * 0.67 = 0.268), and lose if the public card is a King (probability = 0.4 * 0.33 = 0.132).\n- Overall, the winning rate for plan 2 is 0.3 + 0.5 + 0.6 + 0.268 = 1.668, the losing rate is 0.28 + 0.2 + 0.132 = 0.612, and the draw rate is 0.2.\n\nPlan 3: Fold\n- If I fold, I would lose regardless of what card board_game_expert holds. The losing rate is 1.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be half of the total pot (3 chips) = 1.5 chips. If lose, the lose payoff would be half of the total pot (3 chips) = 1.5 chips.\n- Plan 2: If win, the winning payoff would be half of the total pot (6 chips) = 3 chips. If lose, the lose payoff would be half of the total pot (6 chips) = 3 chips.\n- Plan 3: If lose, the lose payoff would be half of the total pot (2 chips) = 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = winning rate * Winning Payoff - lose rate * Lose Payoff = 1.165 * 1.5 - 1.355 * 1.5 = -0.285 chips\n- Plan 2: Expected Chips Gain = 1.668 * 3 - 0.612 * 3 = 3.168 chips\n- Plan 3: Expected Chips Gain = -1 * 1 = -1 chip\n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 2 > Plan 1 > Plan 3.\n- Therefore, I should choose Plan 2: Raise, as it has the highest estimated expected chips gain."}}
{"message": "", "32_2": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King, he would likely check (60%) or fold (40%). If he checks, I will win as my pair of Queens beats his King. If he folds, I will also win as he forfeits the game. Therefore, the winning rate for this plan is 100%.\n- If board_game_expert holds a Jack, he would likely check (80%) or fold (20%). If he checks, I will win as my pair of Queens beats his Jack. If he folds, I will also win as he forfeits the game. Therefore, the winning rate for this plan is also 100%.\n\nPlan 2: Fold\n- If I fold, I will automatically lose the game 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, he would likely check (60%) or fold (40%). If he checks, I will win as my pair of Queens beats his King. If he folds, I will also win as he forfeits the game. Therefore, the winning rate for this plan is 100%.\n- If board_game_expert holds a Jack, he would likely check (80%) or fold (20%). If he checks, I will win as my pair of Queens beats his Jack. If he folds, I will also win as he forfeits the game. Therefore, the winning rate for this plan is also 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (currently 8 chips, so 4 chips). If I lose, the losing payoff would be half of the total pot (currently 8 chips, so 4 chips).\n- Plan 2: If I fold, I will lose my current bet of 4 chips.\n- Plan 3: If I win, the winning payoff would be half of the total pot (currently 8 chips, so 4 chips). If I lose, the losing payoff would be half of the total pot (currently 8 chips, so 4 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning Rate * Winning Payoff - Losing Rate * Losing Payoff = 100% * 4 chips - 0% * 4 chips = 4 chips\n- Plan 2: Expected Chips Gain = Winning Rate * Winning Payoff - Losing Rate * Losing Payoff = 0% * 4 chips - 100% * 4 chips = -4 chips\n- Plan 3: Expected Chips Gain = Winning Rate * Winning Payoff - Losing Rate * Losing Payoff = 100% * 4 chips - 0% * 4 chips = 4 chips\n\nPlan Selection:\n- Plan 1 (Raise) and Plan 3 (Check) both have the highest expected chips gain of 4 chips. However, considering the strategy improvement, Plan 1 (Raise) is the better choice as it applies more pressure on board_game_expert and potentially forces him to fold. Therefore, I will choose Plan 1 (Raise)."}}
{"message": "", "32_4": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (30% probability), he will likely check (60%) or fold (40%). If he checks, I will win (probability = 0.3 * 0.6 = 0.18). If he folds, I will also win (probability = 0.3 * 0.4 = 0.12). So, the overall winning rate for this plan if he holds a King is 0.3.\n- If board_game_expert holds a Queen (65% probability), it will result in a draw. So, the draw rate for this plan if he holds a Queen is 0.65.\n- If board_game_expert holds a Jack (5% probability), he will likely check (80%) or fold (20%). If he checks, I will win (probability = 0.05 * 0.8 = 0.04). If he folds, I will also win (probability = 0.05 * 0.2 = 0.01). So, the overall winning rate for this plan if he holds a Jack is 0.05.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card board_game_expert holds. So, the lose rate for this plan is 1.\n\nThe number of winning and lose 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 (20/2 = 10 chips). If lose, the lose payoff would be half of the total pot (20/2 = 10 chips).\n- Plan 2: After the action, all chips in the pot: If lose, the lose payoff would be half of the total pot (20/2 = 10 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = winning rate * Winning Payoff - lose rate * Lose Payoff = (0.35 * 10) - (0 * 10) = 3.5 chips\n- Plan 2: Expected Chips Gain = winning rate * Winning Payoff - lose rate * Lose Payoff = (0 * 10) - (1 * 10) = -10 chips\n\nPlan Selection:\n- Plan 1 has an expected chips gain of 3.5 chips, while Plan 2 has an expected chips loss of 10 chips. Therefore, Plan 1 (Call) is the better strategy."}}
{"message": "", "34_1": {"plan": "Plan 1: Raise\n- If board_game_expert holds a Queen (54% probability), he will likely call (70% probability) or fold (30% probability). If he calls, I will likely win (2/3 probability) or lose (1/3 probability). If he folds, I will win. \n- If board_game_expert holds a Jack (46% probability), he will likely call (60% probability) or fold (40% probability). If he calls, I will likely win (2/3 probability) or lose (1/3 probability). If he folds, 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 Queen (54% probability), he will likely call (60% probability), raise (30% probability), or fold (10% probability). If he calls or raises, I will likely win (2/3 probability) or lose (1/3 probability). If he folds, I will win. \n- If board_game_expert holds a Jack (46% probability), he will likely call (50% probability), raise (20% probability), or fold (30% probability). If he calls or raises, I will likely win (2/3 probability) or lose (1/3 probability). If he folds, I will win. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, all chips in the pot: If win, the winning payoff would be 4 chips. If lose, the lose payoff would be 4 chips. \n- Plan 2: After the action, all chips in the pot: If lose, the lose payoff would be 2 chips. \n- Plan 3: After the action, all chips in the pot: If win, the winning payoff would be 2 chips. If lose, the lose payoff would be 2 chips. \n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.54*(0.7*4 + 0.3*4) + 0.46*(0.6*4 + 0.4*4) = 3.68 chips\n- Plan 2: Expected Chips Gain = -2 chips\n- Plan 3: Expected Chips Gain = 0.54*(0.6*2 + 0.3*2) + 0.46*(0.5*2 + 0.2*2) = 1.48 chips\n\nPlan Selection:\n- Plan 1: Raise (3.68 chips)\n- Plan 3: Check (1.48 chips)\n- Plan 2: Fold (-2 chips)\n\nBased on the estimated expected chips gain, I should choose Plan 1: Raise."}}
{"message": "", "35_1": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (35% probability), he will likely raise (20% probability) or call (80% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I have a 50% chance of winning or drawing. \n- If board_game_expert holds a Queen (20% probability), he will likely fold (50% probability) or call (50% probability). If the public card is a Queen, I will lose. If the public card is a King or Jack, I have a 50% chance of winning or drawing. \n- If board_game_expert holds a Jack (45% probability), he will likely fold (60% probability) or call (40% probability). If the public card is a Jack, it's a draw. If the public card is a King or Queen, I will lose. \n\nPlan 2: Raise\n- If board_game_expert holds a King (35% probability), he will likely call (80% probability) or raise (20% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I have a 50% chance of winning or drawing. \n- If board_game_expert holds a Queen (20% probability), he will likely fold (50% probability) or call (50% probability). If the public card is a Queen, I will lose. If the public card is a King or Jack, I have a 50% chance of winning or drawing. \n- If board_game_expert holds a Jack (45% probability), he will likely fold (60% probability) or call (40% probability). If the public card is a Jack, it's a draw. If the public card is a King or Queen, I will lose. \n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 6 chips. If I lose, the lose payoff would be 4 chips.\n- Plan 2: If I win, the winning payoff would be 10 chips. If I lose, the lose payoff would be 6 chips.\n- Plan 3: If I fold, I will lose 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.35*(0.2*6 - 0.8*4) + 0.2*(0.5*6 - 0.5*4) + 0.45*(0.4*6 - 0.6*4) = -0.8 chips\n- Plan 2: Expected Chips Gain = 0.35*(0.2*10 - 0.8*6) + 0.2*(0.5*10 - 0.5*6) + 0.45*(0.4*10 - 0.6*6) = -1.2 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I will choose Plan 1: Call."}}
{"message": "", "35_3": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (80% probability), he will likely raise (90% probability). I will lose this round (probability = 0.8 * 0.9 = 0.72). If he calls (10% probability), I will also lose (probability = 0.8 * 0.1 = 0.08).\n- If board_game_expert holds a Queen (10% probability), he will likely call (70% probability). I will win this round (probability = 0.1 * 0.7 = 0.07). If he folds (30% probability), I will also win (probability = 0.1 * 0.3 = 0.03).\n- If board_game_expert holds a Jack (10% probability), it will be a draw regardless of his action.\n- Overall, the winning rate for Plan 1 is 0.1, the losing rate is 0.8, and the draw rate is 0.1.\n\nPlan 2: Raise\n- If board_game_expert holds a King (80% probability), he will likely call (80% probability). I will lose this round (probability = 0.8 * 0.8 = 0.64). If he raises (20% probability), I will also lose (probability = 0.8 * 0.2 = 0.16).\n- If board_game_expert holds a Queen (10% probability), he will likely fold (30% probability). I will win this round (probability = 0.1 * 0.3 = 0.03). If he calls (70% probability), I will also win (probability = 0.1 * 0.7 = 0.07).\n- If board_game_expert holds a Jack (10% probability), it will be a draw regardless of his action.\n- Overall, the winning rate for Plan 2 is 0.1, the losing rate is 0.8, and the draw rate is 0.1.\n\nPlan 3: Fold\n- If I fold, I will lose this round regardless of board_game_expert's card and action. The losing rate for Plan 3 is 1.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 6 chips. If lose, the lose payoff would be 4 chips.\n- Plan 2: If win, the winning payoff would be 10 chips. If lose, the lose payoff would be 8 chips.\n- Plan 3: If lose, the lose payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.1 * 6 - 0.8 * 4 = -2.4 chips\n- Plan 2: Expected Chips Gain = 0.1 * 10 - 0.8 * 8 = -5.2 chips\n- Plan 3: Expected Chips Gain = -1 * 4 = -4 chips\n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 1 > Plan 3 > Plan 2.\n- Therefore, I should select Plan 1 (Call) as it has the highest estimated expected chips gain."}}
{"message": "", "36_1": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (50% probability), he will likely raise (30% probability) or call (70% probability). If he raises, I will lose (probability = 50% * 30% = 15%). If he calls, it will be a draw (probability = 50% * 70% = 35%).\n- If board_game_expert holds a Queen (25% probability), he will likely fold (50% probability) or call (50% probability). If he folds, I will win (probability = 25% * 50% = 12.5%). If he calls, I will win (probability = 25% * 50% = 12.5%).\n- If board_game_expert holds a Jack (25% probability), he will likely fold (40% probability) or call (60% probability). If he folds, I will win (probability = 25% * 40% = 10%). If he calls, I will win (probability = 25% * 60% = 15%).\n- Overall, the winning rate for Plan 1 is 40%, the losing rate is 15%, and the draw rate is 35%.\n\nPlan 2: Raise\n- If board_game_expert holds a King (50% probability), he will likely raise (30% probability) or call (70% probability). If he raises, I will lose (probability = 50% * 30% = 15%). If he calls, it will be a draw (probability = 50% * 70% = 35%).\n- If board_game_expert holds a Queen (25% probability), he will likely fold (50% probability) or call (50% probability). If he folds, I will win (probability = 25% * 50% = 12.5%). If he calls, I will win (probability = 25% * 50% = 12.5%).\n- If board_game_expert holds a Jack (25% probability), he will likely fold (40% probability) or call (60% probability). If he folds, I will win (probability = 25% * 40% = 10%). If he calls, I will win (probability = 25% * 60% = 15%).\n- Overall, the winning rate for Plan 2 is 40%, the losing rate is 15%, and the draw rate is 35%.\n\nPlan 3: Fold\n- If I fold, I will lose all the chips I have put in the pot. The losing rate for Plan 3 is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the 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 lose, the losing payoff would be the chips I have put in the pot (2 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 40% * 6 - 15% * 6 = 1.5 chips\n- Plan 2: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 40% * 8 - 15% * 8 = 2 chips\n- Plan 3: Expected Chips Gain = -100% * 2 = -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": "", "36_3": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (40% chance), he would likely check (60%) or raise (40%). If he checks, I would win as my card is higher. If he raises, it would be a draw as we both hold a King. \n- If board_game_expert holds a Queen (20% chance), he would likely check (70%) or fold (30%). If he checks or folds, I would win as my card is higher. \n- If board_game_expert holds a Jack (40% chance), he would likely raise (80%) or check (20%). If he raises or checks, he would win as his card 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 (40% chance), he would likely check (60%) or raise (40%). If he checks, I would win as my card is higher. If he raises, it would be a draw as we both hold a King. \n- If board_game_expert holds a Queen (20% chance), he would likely check (70%) or fold (30%). If he checks or folds, I would win as my card is higher. \n- If board_game_expert holds a Jack (40% chance), he would likely raise (80%) or check (20%). If he raises or checks, he would win as his card matches the public card. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 6 chips. If I lose, the lose 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 lose 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 highest expected chips gain, so I would choose either of these plans. However, considering the strategy improvement, I would choose Plan 1 (Raise) as it could pressure board_game_expert into folding if he holds a Queen."}}
{"message": "", "37_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, I have a chance to win if the public card is a Queen or Jack. The overall winning rate is 30% (probability of him calling * probability of public card being a Queen or Jack), losing rate is 70% (probability of him raising), and 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 lose unless the public card is a Queen. If he calls, I have a chance to win if the public card is a Queen or Jack. The overall winning rate is 60% (probability of him calling * probability of public card being a Queen or Jack), losing rate is 40% (probability of him raising), and draw rate is 0%.\n- If board_game_expert holds a Jack, he will likely call (50% probability) or raise (50% probability). If he raises, I will lose unless the public card is a Queen. If he calls, I have a chance to win if the public card is a Queen or Jack. The overall winning rate is 50% (probability of him calling * probability of public card being a Queen or Jack), losing rate is 50% (probability of him raising), and draw rate is 0%.\n\nPlan 2: Raise\n- If board_game_expert holds a King, he will likely call (80% probability) or raise (20% probability). If he raises, I will lose unless the public card is a Queen. If he calls, I have a chance to win if the public card is a Queen or Jack. The overall winning rate is 20% (probability of him raising * probability of public card being a Queen or Jack), losing rate is 80% (probability of him calling), 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 folds, I will win. If he calls, I have a chance to win if the public card is a Queen or Jack. The overall winning rate is 50% (probability of him folding + probability of him calling * probability of public card being a Queen or Jack), losing rate is 50% (probability of him calling), and draw rate is 0%.\n- If board_game_expert holds a Jack, he will likely call (40% probability) or fold (60% probability). If he folds, I will win. If he calls, I have a chance to win if the public card is a Queen or Jack. The overall winning rate is 60% (probability of him folding + probability of him calling * probability of public card being a Queen or Jack), losing rate is 40% (probability of him calling), and draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of what card board_game_expert holds. The overall winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 3 chips (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 4 chips (half of the total pot of 8 chips). If lose, the lose payoff would be 4 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 = 30% * 3 - 70% * 3 = -1.2 chips\n- Plan 2: Expected Chips Gain = 50% * 4 - 50% * 4 = 0 chips\n- Plan 3: Expected Chips Gain = 0% * 0 - 100% * 2 = -2 chips\n\nPlan Selection:\n- Plan 1: -1.2 chips\n- Plan 2: 0 chips\n- Plan 3: -2 chips\n\nBased on the estimated expected chips gain, Plan 2 (Raise) is the best strategy to use in this situation."}}
{"message": "", "37_2": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King, he will likely check (60% probability) or fold (40% probability). Given my strong hand, I will win if he checks and also win if he folds. So, the winning rate is 100%.\n- If board_game_expert holds a Queen, he will likely raise (80% probability) or check (20% probability). Given we both have the same hand, it will be a draw regardless of his action. So, the draw rate is 100%.\n- If board_game_expert holds a Jack, he will likely check (80% probability) or fold (20% probability). Given my strong hand, I will win if he checks and also win if he folds. So, the winning rate is 100%.\n\nPlan 2: Check\n- If board_game_expert holds a King, he will likely check (60% probability) or fold (40% probability). Given my strong hand, I will win if he checks and also win if he folds. So, the winning rate is 100%.\n- If board_game_expert holds a Queen, he will likely raise (80% probability) or check (20% probability). Given we both have the same hand, it will be a draw regardless of his action. So, the draw rate is 100%.\n- If board_game_expert holds a Jack, he will likely check (80% probability) or fold (20% probability). Given my strong hand, I will win if he checks and also win if he folds. So, the winning rate is 100%.\n\nPlan 3: Fold\n- This plan is not reasonable given my strong hand.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (8 chips). If I lose, the lose 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 (8 chips). If I lose, the lose payoff would be half of the total pot (8 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Lose rate * Lose Payoff = 1.0 * 8 - 0 * 8 = 8 chips\n- Plan 2: Expected Chips Gain = Winning rate * Winning Payoff - Lose rate * Lose Payoff = 1.0 * 8 - 0 * 8 = 8 chips\n\nPlan Selection:\n- Both Plan 1 and Plan 2 have the same expected chips gain. However, considering the strategy improvement, I should choose Plan 1: Raise to pressure board_game_expert into folding."}}
{"message": "", "37_4": {"plan": "Plan 1: Call\n- If board_game_expert holds a Queen (60% probability), he will likely call (50% probability) or fold (50% probability). If he calls, we will draw (50% probability). If he folds, I will win (50% probability).\n- If board_game_expert holds a King (40% probability), he will likely call (80% probability) or raise (20% probability). If he calls, I will lose (80% probability). If he raises, I will lose (20% probability).\n- Overall, the winning rate for plan 1 is 30% (60% * 50%), the losing rate is 36% (40% * 90%), and the draw rate is 30% (60% * 50%).\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card board_game_expert holds. The losing rate for plan 2 is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the call, 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 fold, all chips in the pot would be 20. If lose, the lose payoff would be 10.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 30% * 10 - 36% * 10 = -0.6\n- Plan 2: Expected Chips Gain = 0% * 10 - 100% * 10 = -10\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain (-0.6) than Plan 2 (-10). Therefore, I should choose Plan 1: Call."}}
{"message": "", "38_1": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (70% probability), he will likely call (60% probability). If the public card is a King, I will win (100% probability). If the public card is not a King, I will win (50% probability). Overall winning rate for this plan is 70% * 60% * 75% = 31.5%.\n- If board_game_expert holds a Queen (20% probability), he will likely call (50% probability). If the public card is a Queen, I will lose (100% probability). If the public card is not a Queen, I will win (50% probability). Overall winning rate for this plan is 20% * 50% * 25% = 2.5%.\n- If board_game_expert holds a Jack (10% probability), he will likely call (40% probability). If the public card is a Jack, I will lose (100% probability). If the public card is not a Jack, I will win (50% probability). Overall winning rate for this plan is 10% * 40% * 25% = 1%.\n\nPlan 2: Raise\n- If board_game_expert holds a King (70% probability), he will likely fold (40% probability). If the public card is a King, I will win (100% probability). If the public card is not a King, I will win (50% probability). Overall winning rate for this plan is 70% * 40% * 75% = 21%.\n- If board_game_expert holds a Queen (20% probability), he will likely fold (50% probability). If the public card is a Queen, I will lose (100% probability). If the public card is not a Queen, I will win (50% probability). Overall winning rate for this plan is 20% * 50% * 25% = 2.5%.\n- If board_game_expert holds a Jack (10% probability), he will likely fold (60% probability). If the public card is a Jack, I will lose (100% probability). If the public card is not a Jack, I will win (50% probability). Overall winning rate for this plan is 10% * 60% * 25% = 1.5%.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of board_game_expert's card or the public card. Overall winning rate for this plan is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 6 chips. If lose, the lose payoff would be 6 chips.\n- Plan 2: If win, the winning payoff would be 10 chips. If lose, the lose payoff would be 10 chips.\n- Plan 3: If win, the winning payoff would be 0 chips. If lose, the lose payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 31.5% * 6 - 68.5% * 6 = -2.22 chips\n- Plan 2: Expected Chips Gain = 25% * 10 - 75% * 10 = -5 chips\n- Plan 3: Expected Chips Gain = 0% * 0 - 100% * 2 = -2 chips\n\nPlan Selection:\n- Plan 1: Rank 1\n- Plan 3: Rank 2\n- Plan 2: Rank 3\n\nBased on the above analysis, I should choose Plan 1 (Call) as it has the highest expected chips gain."}}
{"message": "", "38_3": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King, he will likely check (50% probability) or fold (50% probability). If he checks, I will win (50% probability) or lose (50% probability). If he folds, I will win (100% probability). Overall, my winning rate is 75%, losing rate is 25%, and draw rate is 0%.\n- If board_game_expert holds a Queen, he will likely raise (70% probability) or check (30% probability). If he raises, I will lose (100% probability). If he checks, I will win (50% probability) or lose (50% probability). Overall, my winning rate is 15%, losing rate is 85%, and draw rate is 0%.\n- If board_game_expert holds a Jack, he will likely check (70% probability) or fold (30% probability). If he checks, I will win (100% probability). If he folds, I will win (100% probability). Overall, my winning rate is 100%, losing rate is 0%, and draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose (100% probability) regardless of what card board_game_expert holds.\n\nPlan 3: Check\n- If board_game_expert holds a King, he will likely check (50% probability) or fold (50% probability). If he checks, I will win (50% probability) or lose (50% probability). If he folds, I will win (100% probability). Overall, my winning rate is 75%, losing rate is 25%, and draw rate is 0%.\n- If board_game_expert holds a Queen, he will likely raise (70% probability) or check (30% probability). If he raises, I will lose (100% probability). If he checks, I will win (50% probability) or lose (50% probability). Overall, my winning rate is 15%, losing rate is 85%, and draw rate is 0%.\n- If board_game_expert holds a Jack, he will likely check (70% probability) or fold (30% probability). If he checks, I will win (100% probability). If he folds, I will win (100% probability). Overall, my winning rate is 100%, losing rate is 0%, and draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 8 chips. If I lose, the losing payoff would be 4 chips.\n- Plan 2: If I lose, the losing payoff would be 4 chips.\n- Plan 3: If I win, the winning payoff would be 4 chips. If I lose, the losing payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.75 * 8 - 0.25 * 4 = 5 chips\n- Plan 2: Expected Chips Gain = -4 chips\n- Plan 3: Expected Chips Gain = 0.75 * 4 - 0.25 * 4 = 2 chips\n\nPlan Selection:\n- Plan 1: Raise (Expected Chips Gain = 5 chips)\n- Plan 3: Check (Expected Chips Gain = 2 chips)\n- Plan 2: Fold (Expected Chips Gain = -4 chips)\n\nTherefore, I should choose Plan 1: Raise, as it has the highest expected chips gain."}}
{"message": "", "38_5": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (40% probability), he will likely check (50% probability). If he checks, I will win (probability = 40% * 50% = 20%). If he folds (50% probability), I will also win (probability = 40% * 50% = 20%). Overall, the winning rate for his King is 40%.\n- If board_game_expert holds a Queen (35% probability), he will likely fold (40% probability). If he folds, I will win (probability = 35% * 40% = 14%). If he checks (60% probability), I will lose (probability = 35% * 60% = 21%). Overall, the winning rate for his Queen is 14%, and the losing rate is 21%.\n- If board_game_expert holds a Jack (25% probability), he will likely fold (30% probability). If he folds, I will win (probability = 25% * 30% = 7.5%). If he checks (70% probability), I will win (probability = 25% * 70% = 17.5%). Overall, the winning rate for his Jack is 25%.\n\nPlan 1 overall GoodGuy's Winning/Lose/Draw rates: \n- Winning rate for plan 1: 40% (King) + 14% (Queen) + 25% (Jack) = 79%\n- Losing rate for plan 1: 21% (Queen) = 21%\n- Draw rate for plan 1: 0%\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card board_game_expert holds. Therefore, the losing rate for plan 2 is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the call 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 fold action, all chips in the pot would be 20. If lose, the lose payoff would be 12.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Lose Payoff = 79% * 10 - 21% * 10 = 5.8\n- Plan 2: Expected Chips Gain = Losing rate * Lose Payoff = 100% * 12 = -12\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain than Plan 2. Therefore, I should choose Plan 1: Call."}}
{"message": "", "39_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (40% probability), he will likely raise (80% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. The overall winning rate is 20%, losing rate is 80%, and drawing rate is 0%.\n- If board_game_expert holds a Queen (40% probability), he will likely fold (50% probability) or call (50% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. The overall winning rate is 20%, losing rate is 80%, and drawing rate is 0%.\n- If board_game_expert holds a Jack (20% probability), he will likely fold (60% probability) or call (40% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, it will be a draw. The overall winning rate is 0%, losing rate is 80%, and drawing rate is 20%.\n\nPlan 2: Raise\n- If board_game_expert holds a King (40% probability), he will likely call (70% probability) or raise (30% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. The overall winning rate is 20%, losing rate is 80%, and drawing rate is 0%.\n- If board_game_expert holds a Queen (40% probability), he will likely fold (50% probability) or call (50% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. The overall winning rate is 20%, losing rate is 80%, and drawing rate is 0%.\n- If board_game_expert holds a Jack (20% probability), he will likely fold (60% probability) or call (40% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, it will be a draw. The overall winning rate is 0%, losing rate is 80%, and drawing rate is 20%.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of the card board_game_expert holds. The overall winning rate is 0%, losing rate is 100%, and drawing rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips. If I lose, the losing payoff would be 2 chips.\n- Plan 2: If I win, the winning payoff would be 7 chips. If I lose, the losing payoff would be 6 chips.\n- Plan 3: If I fold, I will lose 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 20% * 3 - 80% * 2 = -1.2 chips\n- Plan 2: Expected Chips Gain = 20% * 7 - 80% * 6 = -3.6 chips\n- Plan 3: Expected Chips Gain = -1 chip\n\nPlan Selection:\nBased on the estimated expected chips gains, Plan 1 (Call) is the best strategy to follow in this situation."}}
{"message": "", "39_2": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (25% probability), he will call (60% probability) or raise (40% probability). If he calls, I will lose (100% probability). If he raises, I will also lose (100% probability). Overall, I will lose (100% probability).\n- If board_game_expert holds a Queen (35% probability), he will fold (60% probability) or call (40% probability). If he folds, I will win (100% probability). If he calls, I will lose (100% probability). Overall, I will win (60% probability) and lose (40% probability).\n- If board_game_expert holds a Jack (40% probability), he will 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). Overall, I will win (70% probability) and draw (30% probability).\n- Winning payoff: 4 chips. Losing payoff: 4 chips.\n\nPlan 2: Fold\n- If I fold, I will lose (100% probability). Losing payoff: 2 chips.\n\nPlan 3: Check\n- If board_game_expert holds a King (25% probability), he will raise (80% probability) or check (20% probability). If he raises, I will lose (100% probability). If he checks, I will also lose (100% probability). Overall, I will lose (100% probability).\n- If board_game_expert holds a Queen (35% probability), he will raise (30% probability) or check (70% probability). If he raises, I will lose (100% probability). If he checks, I will lose (100% probability). Overall, I will lose (100% probability).\n- If board_game_expert holds a Jack (40% probability), he will raise (20% probability) or check (80% probability). If he raises, I will lose (100% probability). If he checks, it will be a draw (100% probability). Overall, I will lose (20% probability) and draw (80% probability).\n- Winning payoff: 2 chips. Losing payoff: 2 chips.\n\nExpected Chips Gain:\n- Plan 1: 0.25 * (-4) + 0.35 * (0.6 * 4 - 0.4 * 4) + 0.4 * (0.7 * 4) = 0.4 chips\n- Plan 2: -2 chips\n- Plan 3: 0.25 * (-2) + 0.35 * (-2) + 0.4 * 0 = -1.35 chips\n\nPlan Selection:\n- Plan 1 > Plan 3 > Plan 2\n- Therefore, I should choose Plan 1: Raise."}}
{"message": "", "40_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, keeping the pot small. If he calls, I will also call, matching his bet. The winning rate is 50% (if the public card is a King), the losing rate is 50% (if the public card is not a King), 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, keeping the pot small. If he calls, I will also call, matching his bet. The winning rate is 100% (as my King beats his Queen), 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 raise (50% probability). If he raises, I will call, keeping the pot small. If he calls, I will also call, matching his bet. The winning rate is 100% (as my King beats his Jack), 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, keeping the pot small. If he calls, I will raise, increasing the pot. The winning rate is 50% (if the public card is a King), the losing rate is 50% (if the public card is not a King), and the draw rate is 0%.\n- If board_game_expert holds a Queen, he will likely fold (50% probability) or call (50% probability). If he folds, I will win the pot. If he calls, I will raise, increasing the pot. The winning rate is 100% (as my King beats his Queen), the losing rate is 0%, and the draw rate is 0%.\n- If board_game_expert holds a Jack, he will likely fold (60% probability) or call (40% probability). If he folds, I will win the pot. If he calls, I will raise, increasing the pot. The winning rate is 100% (as my King beats his Jack), 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 King, which is the highest rank in this game.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be half of the total pot (currently 3 chips, so 1.5 chips). If lose, the lose payoff would be half of the total pot (currently 3 chips, so 1.5 chips).\n- Plan 2: If win, the winning payoff would be half of the total pot (currently 3 chips, so 1.5 chips). If lose, the lose payoff would be half of the total pot (currently 3 chips, so 1.5 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.5 * 1.5 - 0.5 * 1.5 = 0 chips\n- Plan 2: Expected Chips Gain = 0.5 * 1.5 - 0.5 * 1.5 = 0 chips\n\nPlan Selection:\n- Both Plan 1 and Plan 2 have the same expected chips gain, so either plan could be selected. However, considering the strategy improvement, Plan 2 (Raise) might be a better choice as it could potentially bluff board_game_expert into folding and win the pot."}}
{"message": "", "40_2": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King, he will likely call (70% probability) or raise (30% probability). If he calls, I will win unless the next public card is a King. If he raises, it's likely a bluff, and I will win unless the next public card is a King. \n- If board_game_expert holds a Queen, he will likely raise (80% probability) or check (20% probability). If he raises, I will lose unless the next public card is a King. If he checks, it's likely a bluff, and I will win unless the next public card is a Queen. \n- If board_game_expert holds a Jack, he will likely check (80% probability) or raise (20% probability). If he checks, I will win unless the next public card is a Jack. If he raises, it's likely a bluff, and I will win unless the next public card is a Jack. \n\nPlan 2: Fold\n- If I fold, I will lose the current pot but save my remaining chips for future rounds. This is a safe strategy but does not maximize my potential gains.\n\nPlan 3: Check\n- If board_game_expert holds a King, he will likely check (60% probability) or raise (40% probability). If he checks, I will win unless the next public card is a King. If he raises, it's likely a bluff, and I will win unless the next public card is a King. \n- If board_game_expert holds a Queen, he will likely raise (80% probability) or check (20% probability). If he raises, I will lose unless the next public card is a King. If he checks, it's likely a bluff, and I will win unless the next public card is a Queen. \n- If board_game_expert holds a Jack, he will likely check (80% probability) or raise (20% probability). If he checks, I will win unless the next public card is a Jack. If he raises, it's likely a bluff, and I will win unless the next public card is a Jack. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (currently 8 chips). If I lose, the lose payoff would be half of the total pot.\n- Plan 2: If I fold, there is no winning payoff. The lose payoff would be the 4 chips I have already put in the pot.\n- Plan 3: If I win, the winning payoff would be half of the total pot (currently 8 chips). If I lose, the lose payoff would be half of the total pot.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning Rate * Winning Payoff - Lose Rate * Lose Payoff\n- Plan 2: Expected Chips Gain = 0 (since I will fold and not win any chips)\n- Plan 3: Expected Chips Gain = Winning Rate * Winning Payoff - Lose Rate * Lose Payoff\n\nPlan Selection:\nBased on the estimated expected chips gain, I would rank the plans as follows: Plan 1 > Plan 3 > Plan 2. Therefore, I would select Plan 1 (Raise) as it has the highest estimated expected chips gain."}}
{"message": "", "40_4": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (55% probability), he will likely raise (40% probability). If he raises, I will lose as we both have a King but he has more chips in the pot. The losing rate is 55% * 40% = 22%.\n- If board_game_expert holds a Queen (40% probability), he will likely check (70% probability). If he checks, I will win as my King is higher than his Queen. The winning rate is 40% * 70% = 28%.\n- If board_game_expert holds a Jack (30% probability), he will likely check (80% probability). If he checks, I will win as my King is higher than his Jack. The winning rate is 30% * 80% = 24%.\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of what card board_game_expert holds. The losing rate is 100%.\n\nThe number of winning and lose 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 (12 chips). If lose, the lose payoff would be half of the total pot (12 chips).\n- Plan 2: After the action, all chips in the pot: If lose, the lose payoff would be half of the total 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 = 52% * 12 - 22% * 12 = 3.6 chips\n- Plan 2: Expected Chips Gain = 0% * Winning Payoff - 100% * Losing Payoff = -12 chips\n\nPlan Selection:\n- Plan 1 (Call) has the highest estimated expected chips gain (3.6 chips), so I will choose this plan."}}
{"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 win if the public card is not a King (probability of winning = 0.8 * 0.67 = 0.536). If he calls, I will win if the public card is not a King (probability of winning = 0.2 * 0.67 = 0.134). Overall, the winning rate for this plan is 0.67.\n- If board_game_expert holds a Queen, he will likely fold (50% probability) or call (50% probability). If he folds, I will win (probability of winning = 0.5). If he calls, I will win if the public card is not a Queen (probability of winning = 0.5 * 0.67 = 0.335). Overall, the winning rate for this plan is 0.835.\n- If board_game_expert holds a Jack, he will likely fold (60% probability) or call (40% probability). If he folds, I will win (probability of winning = 0.6). If he calls, I will win if the public card is not a Jack (probability of winning = 0.4 * 0.67 = 0.268). Overall, the winning rate for this plan is 0.868.\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 win if the public card is not a King (probability of winning = 0.7 * 0.67 = 0.469). If he raises, I will win if the public card is not a King (probability of winning = 0.3 * 0.67 = 0.201). Overall, the winning rate for this plan is 0.67.\n- If board_game_expert holds a Queen, he will likely fold (50% probability) or call (50% probability). If he folds, I will win (probability of winning = 0.5). If he calls, I will win if the public card is not a Queen (probability of winning = 0.5 * 0.67 = 0.335). Overall, the winning rate for this plan is 0.835.\n- If board_game_expert holds a Jack, he will likely fold (60% probability) or call (40% probability). If he folds, I will win (probability of winning = 0.6). If he calls, I will win if the public card is not a Jack (probability of winning = 0.4 * 0.67 = 0.268). Overall, the winning rate for this plan is 0.868.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of what card board_game_expert holds. Therefore, the winning rate for this plan is 0.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (3 chips). If I lose, the lose payoff would be half of the total pot (3 chips).\n- Plan 2: If I win, the winning payoff would be half of the total pot (4 chips). If I lose, the lose payoff would be half of the total pot (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 = 0.79 * 3 - 0.21 * 3 = 1.74 chips\n- Plan 2: Expected Chips Gain = 0.79 * 4 - 0.21 * 4 = 2.32 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": "", "41_2": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (70% probability), he will likely raise (30% probability) or call (70% probability). If he raises, I will win if the public card is a King (33.33% probability), lose if the public card is a Queen or Jack (66.67% probability). If he calls, I will win if the public card is a King or Queen (66.67% probability), lose if the public card is a Jack (33.33% probability).\n- If board_game_expert holds a Queen (15% probability), he will likely check (70% probability) or call (30% probability). If he checks or calls, I will win if the public card is a King or Jack (66.67% probability), lose if the public card is a Queen (33.33% probability).\n- If board_game_expert holds a Jack (15% probability), he will likely check (80% probability) or call (20% probability). If he checks or calls, I will win if the public card is a King or Queen (66.67% probability), lose if the public card is a Jack (33.33% probability).\n- Overall, the winning rate for Plan 1 is 66.67%, the losing rate is 33.33%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose all the chips in the pot. The losing rate for Plan 2 is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (5 chips). If I lose, the losing payoff would be half of the total pot (5 chips).\n- Plan 2: If I fold, I will lose all the chips in the pot (4 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is winning rate * winning payoff - losing rate * losing payoff = 66.67% * 5 - 33.33% * 5 = 1.67 chips.\n- Plan 2: The expected chips gain is -4 chips.\n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 1 > Plan 2.\n- Therefore, I should select Plan 1: Call."}}
{"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 as my card is of the same rank. If he raises, I will still win as my card is of the same rank. Therefore, the winning rate for this plan is 100%.\n- If board_game_expert holds a Queen, he will likely check (70% probability) or call (30% probability). If he checks, I will lose as his card matches the public card. If he calls, I will still lose as his card matches the public card. Therefore, the losing rate for this plan is 100%.\n- If board_game_expert holds a Jack, he will likely check (80% probability) or call (20% probability). If he checks, I will win as my card is of higher rank. If he calls, I will still win as my card is of higher rank. Therefore, the winning rate for this plan is 100%.\n\nPlan 2: 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\nPlan 3: Check\n- If board_game_expert holds a King, he will likely raise (40% probability) or check (60% probability). If he raises, I will win as my card is of the same rank. If he checks, I will win as my card is of the same rank. Therefore, the winning rate for this plan is 100%.\n- If board_game_expert holds a Queen, he will likely raise (30% probability) or check (70% probability). If he raises, I will lose as his card matches the public card. If he checks, I will lose as his card matches the public card. Therefore, the losing rate for this plan is 100%.\n- If board_game_expert holds a Jack, he will likely raise (20% probability) or check (80% probability). If he raises, I will win as my card is of higher rank. If he checks, I will win as my card is of higher rank. Therefore, the winning rate for this plan is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 6 chips (half of the 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 = 100% * 6 chips - 100% * 6 chips = 0 chips\n- Plan 2: Expected Chips Gain = 0% * 6 chips - 100% * 6 chips = -6 chips\n- Plan 3: Expected Chips Gain = 100% * 6 chips - 100% * 6 chips = 0 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 both have an expected chips gain of 0, while Plan 2 has an expected chips loss of 6. Therefore, either Plan 1 or Plan 3 would be the best choice. Considering the strategy improvement, I would choose Plan 1 (Raise) as it is more aggressive and may put more pressure on board_game_expert."}}
{"message": "", "43_1": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King, he will likely call (80% probability) or raise (20% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I have a chance to win. The overall winning rate is approximately 31% (31% * 80%).\n- If board_game_expert holds a Queen, he will likely call (70% probability) or fold (30% probability). If the public card is a Queen, I will lose. If the public card is a King or Jack, I have a chance to win. The overall winning rate is approximately 27% (38% * 70%).\n- If board_game_expert holds a Jack, he will likely call (60% probability) or fold (40% probability). If the public card is a Jack, it's a draw. If the public card is a King or Queen, I will lose. The overall winning rate is approximately 19% (31% * 60%).\n\nPlan 2: Fold\n- If I fold, I will lose the chips in the pot. The overall winning rate is 0%.\n\nPlan 3: Check\n- If board_game_expert holds a King, he will likely check (60% probability) or call (40% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I have a chance to win. The overall winning rate is approximately 19% (31% * 60%).\n- If board_game_expert holds a Queen, he will likely check (70% probability) or call (30% probability). If the public card is a Queen, I will lose. If the public card is a King or Jack, I have a chance to win. The overall winning rate is approximately 27% (38% * 70%).\n- If board_game_expert holds a Jack, he will likely check (80% probability) or call (20% probability). If the public card is a Jack, it's a draw. If the public card is a King or Queen, I will lose. The overall winning rate is approximately 25% (31% * 80%).\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 6 chips (half of the total pot). If I lose, the losing payoff would be 6 chips.\n- Plan 2: If I fold, I will 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). If I lose, the losing payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 31% * 6 - 69% * 6 = -2.28 chips\n- Plan 2: Expected Chips Gain = 0% * 0 - 100% * 2 = -2 chips\n- Plan 3: Expected Chips Gain = 24% * 4 - 76% * 4 = -2.08 chips\n\nPlan Selection:\n- Plan 1: Rank 3\n- Plan 2: Rank 2\n- Plan 3: Rank 1\n\nBased on the estimated expected chips gain, I should choose Plan 3: Check."}}
{"message": "", "43_3": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (30% probability), he will likely call (80% probability). Given the current public card, he would win. Therefore, the winning rate for this plan is 0%, the losing rate is 24% (30% * 80%), and the draw rate is 0%.\n- If board_game_expert holds a Queen (60% probability), he will likely call (70% probability) or fold (30% probability). Given the current public card, he would win if he calls. Therefore, the winning rate for this plan is 0%, the losing rate is 42% (60% * 70%), and the draw rate is 0%.\n- If board_game_expert holds a Jack (50% probability), he will likely call (60% probability) or fold (40% probability). Given the current public card, I would win if he folds. Therefore, the winning rate for this plan is 20% (50% * 40%), the losing rate is 30% (50% * 60%), and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I automatically lose the current pot. Therefore, the winning rate for this plan is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If board_game_expert holds a King (30% probability), he will likely check (60% probability). Given the current public card, he would win. Therefore, the winning rate for this plan is 0%, the losing rate is 18% (30% * 60%), and the draw rate is 0%.\n- If board_game_expert holds a Queen (60% probability), he will likely check (70% probability). Given the current public card, he would win. Therefore, the winning rate for this plan is 0%, the losing rate is 42% (60% * 70%), and the draw rate is 0%.\n- If board_game_expert holds a Jack (50% probability), he will likely check (80% probability). Given the current public card, I would win. Therefore, the winning rate for this plan is 40% (50% * 80%), the losing rate is 0%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 6 chips (half of the total pot of 12 chips). If lose, the lose payoff would be 6 chips.\n- Plan 2: If lose, the lose payoff would be 2 chips (half of the total pot of 4 chips).\n- Plan 3: If win, the winning payoff would be 2 chips (half of the total pot of 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 = 20% * 6 chips - 96% * 6 chips = -4.56 chips\n- Plan 2: Expected Chips Gain = 0% * 0 chips - 100% * 2 chips = -2 chips\n- Plan 3: Expected Chips Gain = 40% * 2 chips - 60% * 2 chips = -0.4 chips\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows:\n1. Plan 3: Check (-0.4 chips)\n2. Plan 2: Fold (-2 chips)\n3. Plan 1: Raise (-4.56 chips)\n\nTherefore, the best plan to execute would be Plan 3: Check."}}
{"message": "", "44_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, he will likely raise (70% probability) or call (20% probability). If he raises, I will likely lose unless the public card is a Queen. If he calls, I have a chance to win if the public card is a Queen or a Jack. \n- If board_game_expert holds a Jack, he will likely call (50% probability) or fold (30% probability). If he calls, I will likely win unless the public card is a Jack. If he folds, I will win the game. \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 likely lose unless the public card is a Queen. If he raises, I have a chance to win if the public card is a Queen or a Jack. \n- If board_game_expert holds a Jack, he will likely call (40% probability) or fold (60% probability). If he calls, I will likely win unless the public card is a Jack. If he folds, I will win the game. \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 winning and lose 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, I will lose 2 chips. \n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.5 * 3 - 0.5 * 3 = 0 chips\n- Plan 2: Expected Chips Gain = 0.6 * 5 - 0.4 * 5 = 1 chip\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I will choose this plan."}}
{"message": "", "44_2": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, there is a 40% chance he will raise and a 60% chance he will call. If the public card is a King, I will lose. If the public card is a Queen or Jack, I will win unless he also holds a Queen or Jack. The overall winning rate is 30%, losing rate is 70%, and drawing rate is 0%.\n- If board_game_expert holds a Queen, there is a 70% chance he will call and a 30% chance he will fold. If the public card is a Queen, I will win. If the public card is a King or Jack, I will lose unless he also holds a King or Jack. The overall winning rate is 35%, losing rate is 65%, and drawing rate is 0%.\n- If board_game_expert holds a Jack, there is a 40% chance he will call and a 60% chance he will fold. If the public card is a Jack, I will win. If the public card is a King or Queen, I will lose unless he also holds a King or Queen. The overall winning rate is 20%, losing rate is 80%, and 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. The overall winning rate is 0%, losing rate is 100%, and drawing rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, all chips in the pot: If win, the winning payoff would be 5 chips. If lose, the lose payoff would be 5 chips.\n- Plan 2: After the action, all chips in the pot: If win, the winning payoff would be 0 chips. If lose, the lose payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is 30% * 5 chips - 70% * 5 chips = -2 chips.\n- Plan 2: The expected chips gain is 0% * 0 chips - 100% * 4 chips = -4 chips.\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain than Plan 2, so I should choose Plan 1 and call."}}
{"message": "", "44_4": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, he will likely call (80% probability) or raise (20% probability). If he calls, I will lose as his King outranks my Queen. If he raises, I will also lose. 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, he will likely call (80% probability) or fold (20% probability). If he calls, it will be a draw as we both hold Queens. If he folds, I will win. So, the winning rate is 20%, the losing rate is 0%, 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, I will win as my Queen outranks his Jack. If he folds, I will also win. So, the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If board_game_expert holds a King, he will likely call (80% probability) or raise (20% probability). Regardless of his action, I will lose as his King outranks my 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, he will likely call (80% probability) or fold (20% probability). If he calls, it will be a draw as we both hold Queens. If he folds, I will win. So, the winning rate is 20%, the losing rate is 0%, 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, I will win as my Queen outranks his Jack. If he folds, I will also win. So, the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of what card board_game_expert holds. So, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: 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 win, the winning payoff would be 12 chips (half of the total pot). If I lose, the losing payoff would be 12 chips.\n- Plan 3: If I fold, I will lose 10 chips (my contribution to the pot).\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 = 0.6 * 12 - 0.4 * 12 = 2.4 chips\n- Plan 3: Expected Chips Gain = -10 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I should choose this plan."}}
{"message": "", "45_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 (70% probability) or raise (30% probability). If he calls, I will win (50% probability), lose (30% probability), or draw (20% probability).\n- If board_game_expert holds a Queen, he will likely call (60% probability) or raise (40% probability). If he raises, I will call (50% probability) or fold (50% probability). If he calls, I will win (60% probability), lose (20% probability), or draw (20% probability).\n- If board_game_expert holds a Jack, he will likely call (50% probability) or fold (50% probability). If he folds, I will win (100% probability). If he calls, I will win (70% probability), lose (10% probability), or draw (20% probability).\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 win (50% probability), lose (30% probability), or draw (20% probability). If he raises, I will call (70% probability) or raise (30% probability).\n- If board_game_expert holds a Queen, he will likely call (50% probability) or fold (50% probability). If he folds, I will win (100% probability). If he calls, I will win (60% probability), lose (20% probability), or draw (20% probability).\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 win (70% probability), lose (10% probability), or draw (20% probability).\n\nPlan 3: Fold\n- If I fold, I will lose (100% probability) regardless of what card board_game_expert holds.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips (half of the total pot of 6 chips). If I lose, the lose 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 lose payoff would be 4 chips.\n- Plan 3: If I fold, I will lose 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = (0.6 * 3) - (0.2 * 3) = 1.2 chips\n- Plan 2: Expected Chips Gain = (0.7 * 4) - (0.1 * 4) = 2.4 chips\n- Plan 3: Expected Chips Gain = 0 - (1 * 2) = -2 chips\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain, so I will choose Plan 2: Raise."}}
{"message": "", "45_2": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (30% probability), he will likely call (70% probability). If the public card is a King, I will win (probability = 30% * 70% = 21%). If the public card is not a King, I will lose (probability = 30% * 30% = 9%).\n- If board_game_expert holds a Queen (40% probability), he will likely fold (50% probability). If the public card is a Queen, I will lose (probability = 40% * 50% = 20%). If the public card is not a Queen, I will win (probability = 40% * 50% = 20%).\n- If board_game_expert holds a Jack (30% probability), he will likely fold (60% probability). If the public card is a Jack, I will win (probability = 30% * 60% = 18%). If the public card is not a Jack, I will win (probability = 30% * 40% = 12%).\n\nPlan 2: Fold\n- If I fold, I will lose the pot regardless of what card board_game_expert holds or what the public card is. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the call 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 fold 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 = (21% + 20% + 18%) * 5 - (9% + 20% + 12%) * 5 = 2.95 - 2.05 = 0.9\n- Plan 2: Expected Chips Gain = 0 - 100% * 3 = -3\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain than Plan 2. Therefore, I should choose Plan 1: Call."}}
{"message": "", "45_4": {"plan": "Plan 1: Call\n- If board_game_expert holds a King, he will likely raise (40% probability). If he raises, I will lose as we both have a King but he has put more chips into the pot. He may also check (60% probability), in which case it will be a draw as we both have a King. \n- If board_game_expert holds a Queen, he will likely check (70% probability) or fold (30% probability). If he checks or folds, I will win as my King is higher than his Queen. \n- If board_game_expert holds a Jack, he will likely check (80% probability) or fold (20% probability). If he checks or folds, I will win as my King is higher than his Jack. \n\nPlan 2: Raise\n- If board_game_expert holds a King, he will likely raise (40% probability). If he raises, I will lose as we both have a King but he has put more chips into the pot. He may also check (60% probability), in which case it will be a draw as we both have a King. \n- If board_game_expert holds a Queen, he will likely fold (30% probability) or check (70% probability). If he folds, I will win as my King is higher than his Queen. If he checks, it will be a draw as we both have put the same amount of chips into the pot. \n- If board_game_expert holds a Jack, he will likely fold (20% probability) or check (80% probability). If he folds, I will win as my King is higher than his Jack. If he checks, it will be a draw as we both have put the same amount of chips into the pot. \n\nPlan 3: Fold\n- If I fold, I will lose any chips I have put into the pot. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 8 chips (half of the total pot of 16 chips). If I lose, the lose payoff would be 10 chips (the amount I have put into 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 lose payoff would be 14 chips (the amount I have put into the pot). \n- Plan 3: If I fold, the lose payoff would be 10 chips (the amount I have put into the pot). \n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.7 * 8 - 0.3 * 10 = 2.6 chips\n- Plan 2: Expected Chips Gain = 0.5 * 12 - 0.5 * 14 = -1 chip\n- Plan 3: Expected Chips Gain = -10 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I should choose to call."}}
{"message": "", "46_1": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King (25% probability), he will likely call (70% probability). If the public card is a Queen, I will lose. If the public card is a King or Jack, I will win. Overall winning rate is 17.5%, losing rate is 7.5%, and draw rate is 0%.\n- If board_game_expert holds a Jack (75% probability), he will likely call (60% probability) or fold (40% probability). If the public card is a Queen or King, I will win. If the public card is a Jack, I will lose. Overall winning rate is 45%, losing rate is 30%, and draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of board_game_expert's card. Overall 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 (25% probability), he will check (100% probability). If the public card is a Queen, I will lose. If the public card is a King or Jack, I will win. Overall winning rate is 25%, losing rate is 0%, and draw rate is 0%.\n- If board_game_expert holds a Jack (75% probability), he will check (100% probability). If the public card is a Queen or King, I will win. If the public card is a Jack, I will lose. Overall winning rate is 50%, losing rate is 25%, and draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, all chips in the pot: If win, the winning payoff would be 6 chips. If lose, the lose payoff would be 6 chips.\n- Plan 2: After the action, all chips in the pot: If lose, the lose payoff would be 2 chips.\n- Plan 3: After the action, all chips in the pot: If win, the winning payoff would be 2 chips. If lose, the lose payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.625 chips\n- Plan 2: Expected Chips Gain = -2 chips\n- Plan 3: Expected Chips Gain = 0.5 chips\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows: Plan 1 > Plan 3 > Plan 2. Therefore, the best strategy is to raise (Plan 1), as it has the highest estimated expected chips gain."}}
{"message": "", "47_0": {"plan": "Plan 1: Call\n- If board_game_expert holds King: He will likely raise (40% probability) or call (60% 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 20%, losing rate is 60%, and drawing rate is 20%.\n- If board_game_expert holds Queen: He will likely call (70% probability) or fold (30% probability). If he calls, I will draw regardless of the public card. If he folds, I will win. The overall winning rate is 30%, losing rate is 0%, and drawing rate is 70%.\n- If board_game_expert holds Jack: He will likely fold (60% probability) or call (40% probability). If he folds, I will win. If he calls, I will win if the public card is a Queen or Jack, and lose if it's a King. The overall winning rate is 80%, losing rate is 20%, and drawing rate is 0%.\n\nPlan 2: Raise\n- If board_game_expert holds King: He will likely call (70% probability) or raise (30% probability). If he calls or raises, I will lose unless the public card is a Queen. The overall winning rate is 10%, losing rate is 90%, and drawing rate is 0%.\n- If board_game_expert holds Queen: He will likely call (70% probability) or fold (30% probability). If he calls, I will draw regardless of the public card. If he folds, I will win. The overall winning rate is 30%, losing rate is 0%, and drawing rate is 70%.\n- If board_game_expert holds Jack: He will likely fold (60% probability) or call (40% probability). If he folds, I will win. If he calls, I will win if the public card is a Queen or Jack, and lose if it's a King. The overall winning rate is 80%, losing rate is 20%, and drawing rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of what card board_game_expert holds. The overall winning rate is 0%, losing rate is 100%, and drawing rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If 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 gain = 0.43 chips\n- Plan 2: Expected gain = 0.2 chips\n- Plan 3: Expected gain = -2 chips\n\nPlan Selection:\nBased on the estimated expected chips gains, Plan 1 (Call) is the best strategy to follow in this situation."}}
{"message": "", "47_2": {"plan": "Plan 1: Raise\n- If board_game_expert holds a Queen (60% probability), he would call (50% probability) or raise (50% probability). If he calls, I would win as my Queen is higher than his Queen. If he raises, I would still win as my Queen is higher than his Queen. Therefore, the winning rate for this plan is 60%.\n- If board_game_expert holds a Jack (40% probability), he would fold (70% probability) or call (30% probability). If he folds, I would win. If he calls, I would still win as my Queen is higher than his Jack. Therefore, the winning rate for this plan is 40%.\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 Queen (60% probability), he would check (70% probability) or raise (30% probability). If he checks, I would win as my Queen is higher than his Queen. If he raises, I would still win as my Queen is higher than his Queen. Therefore, the winning rate for this plan is 60%.\n- If board_game_expert holds a Jack (40% probability), he would check (80% probability) or raise (20% probability). If he checks, I would win as my Queen is higher than his Jack. If he raises, I would still win as my Queen is higher than his Jack. Therefore, the winning rate for this plan is 40%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (4 chips). If I lose, the losing payoff would be half of the total pot (4 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 (4 chips). 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 = 60% * 4 chips - 40% * 4 chips = 0.8 chips\n- Plan 2: Expected Chips Gain = 0% * 4 chips - 100% * 4 chips = -4 chips\n- Plan 3: Expected Chips Gain = 60% * 4 chips - 40% * 4 chips = 0.8 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 have the highest expected chips gain (0.8 chips), while Plan 2 has the lowest expected chips gain (-4 chips). Therefore, I should either raise (Plan 1) or check (Plan 3) to maximize my expected chips gain. Considering the strategy improvement, I should raise (Plan 1) to pressure the opponent."}}
{"message": "", "49_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a King (10% probability), he will likely call (60% probability) or raise (40% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. The overall winning rate is 10% * 40% = 4%, the losing rate is 10% * 60% = 6%, and the draw rate is 0%.\n- If board_game_expert holds a Queen (50% probability), he will likely call (60% probability) or fold (40% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I will win. The overall winning rate is 50% * 60% = 30%, the losing rate is 50% * 40% = 20%, and the draw rate is 0%.\n- If board_game_expert holds a Jack (40% probability), he will likely fold (60% probability) or call (40% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, it will be a draw. The overall winning rate is 0%, the losing rate is 40% * 40% = 16%, and the draw rate is 40% * 60% = 24%.\n\nPlan 1 overall GoodGuy's Winning/Lose/Draw rates: Winning rate = 34%, Losing rate = 42%, Draw rate = 24%.\n\nPlan 2: Raise\n- If board_game_expert holds a King (10% probability), he will likely call (60% probability) or raise (40% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. The overall winning rate is 10% * 40% = 4%, the losing rate is 10% * 60% = 6%, and the draw rate is 0%.\n- If board_game_expert holds a Queen (50% probability), he will likely fold (40% probability) or call (60% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I will win. The overall winning rate is 50% * 40% = 20%, the losing rate is 50% * 60% = 30%, and the draw rate is 0%.\n- If board_game_expert holds a Jack (40% probability), he will likely fold (60% probability) or call (40% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, it will be a draw. The overall winning rate is 0%, the losing rate is 40% * 40% = 16%, and the draw rate is 40% * 60% = 24%.\n\nPlan 2 overall GoodGuy's Winning/Lose/Draw rates: Winning rate = 24%, Losing rate = 52%, Draw rate = 24%.\n\nPlan 3: Fold\n- If I fold, I will lose the 2 chips I have put in the pot. The overall winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 3 chips. If lose, the lose payoff would be 2 chips.\n- Plan 2: If win, the winning payoff would be 7 chips. If lose, the lose payoff would be 6 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 = 34% * 3 - 42% * 2 = 0.02 chips\n- Plan 2: Expected Chips Gain = 24% * 7 - 52% * 6 = -1.68 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I should choose to call."}}
{"message": "", "49_2": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King, he will likely call (70% probability) or raise (30% probability). If he calls, I will lose as his King beats my Jack. If he raises, I will also lose. Therefore, my winning rate is 0%, my losing rate is 100%, and my drawing 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 win as my Jack beats his Queen. If he folds, I will also win. Therefore, my winning rate is 100%, my losing rate is 0%, and my drawing 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, it will be a draw. Therefore, my winning rate is 80%, my losing rate is 0%, and my drawing rate is 20%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card board_game_expert holds. Therefore, my winning rate is 0%, my losing rate is 100%, and my drawing rate is 0%.\n\nPlan 3: Check\n- If board_game_expert holds a King, he will likely call (70% probability) or raise (30% probability). If he calls, I will lose as his King beats my Jack. If he raises, I will also lose. Therefore, my winning rate is 0%, my losing rate is 100%, and my drawing 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 win as my Jack beats his Queen. If he folds, I will also win. Therefore, my winning rate is 100%, my losing rate is 0%, and my drawing 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, it will be a draw. Therefore, my winning rate is 80%, my losing rate is 0%, and my drawing rate is 20%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips (half of the total pot of 8 chips). If I lose, the losing payoff would be 4 chips.\n- Plan 2: If I fold, I will lose 2 chips (the amount I have already put 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 * 4 - 0.5 * 4 = 0\n- Plan 2: Expected Chips Gain = 0 - 1 * 2 = -2\n- Plan 3: Expected Chips Gain = 0.5 * 2 - 0.5 * 2 = 0\n\nPlan Selection:\n- Plan 1 and Plan 3 both have an expected chips gain of 0, while Plan 2 has a negative expected chips gain. Therefore, I should either raise (Plan 1) or check (Plan 3). Considering the strategy improvement, I should choose to raise (Plan 1) to pressure board_game_expert into folding."}}
{"message": "", "50_0": {"plan": "Plan 1: Call\n- If board_game_expert holds a Queen (50% probability), he will likely raise (40%) or call (60%). If he raises, I will have a 50% chance of winning if the public card is a Queen, and a 50% chance of losing if the public card is a King or Jack. If he calls, I will have a 33.3% chance of winning if the public card is a Queen, and a 66.7% chance of losing if the public card is a King or Jack. \n- If board_game_expert holds a Jack (50% probability), he will likely raise (30%) or call (70%). If he raises, I will have a 66.7% chance of winning if the public card is a Queen or Jack, and a 33.3% chance of losing if the public card is a King. If he calls, I will have a 66.7% chance of winning if the public card is a Queen or Jack, and a 33.3% chance of losing if the public card is a King. \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, I will have a 50% chance of winning if the public card is a Queen, and a 50% chance of losing if the public card is a King or Jack. If he folds, I will win the game. \n- If board_game_expert holds a Jack (50% probability), he will likely call (60%) or fold (40%). If he calls, I will have a 66.7% chance of winning if the public card is a Queen or Jack, and a 33.3% chance of losing if the public card is a King. If he folds, I will win the game. \n\nPlan 3: Fold\n- If I fold, I will lose the game. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips (half of the 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) - 0.5*(2*0.5 + 2*0.5) = 0.5 chips\n- Plan 2: Expected Chips Gain = 0.5*(4*0.7 + 3*0.3) - 0.5*(3*0.6 + 2*0.4) = 0.5 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- Plan 1 and Plan 2 both have the highest expected chips gain of 0.5 chips, so I can choose either of these plans. However, considering the strategy improvement, Plan 2 (Raise) is more aggressive and can potentially make board_game_expert fold, so I will choose Plan 2."}}
{"message": "", "50_2": {"plan": "Plan 1: Raise\n- If board_game_expert holds a King, he would likely call (40%) or check (60%). If he calls, I would likely win as my Queen is higher than the public Jack. If he checks, I would also likely win. \n- If board_game_expert holds a Queen, he would likely call (30%) or check (70%). If he calls, it would be a draw as we both hold Queens. If he checks, it would also be a draw. \n- If board_game_expert holds a Jack, he would likely fold (20%) or check (80%). If he folds, I would win. If he checks, I would win as my Queen is higher than his Jack. \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 likely lose as his King is higher than my Queen. If he checks, I would likely win as my Queen is higher than the public Jack. \n- If board_game_expert holds a Queen, he would likely raise (30%) or check (70%). If he raises, it would be a draw as we both hold Queens. If he checks, it would also be a draw. \n- If board_game_expert holds a Jack, he would likely raise (20%) or check (80%). If he raises, I would win as my Queen is higher than his Jack. If he checks, I would also win. \n\nWinning/Lose 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\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected gain = 0.7 * 8 - 0.3 * 8 = 2.8 chips\n- Plan 2: Expected gain = -4 chips (as I would lose the chips I have already put in the pot)\n- Plan 3: Expected gain = 0.7 * 8 - 0.3 * 8 = 2.8 chips\n\nPlan Selection:\nBased on the expected chips gain, Plan 1 (Raise) and Plan 3 (Check) are the best strategies to follow. However, considering the strategy improvement, Plan 1 (Raise) would be the optimal choice as it puts more pressure on board_game_expert and potentially makes him fold."}}
