{"message": "", "1_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King: \n  - In the 1st round, if he sees me call, he might raise (70%) or call (30%). If he raises, I will lose as we both have Kings but he has more chips in the pot. If he calls, it will be a draw. The overall winning rate is 0%, losing rate is 70%, and drawing rate is 30%.\n- If GoodGuy holds a Queen or Jack: \n  - In the 1st round, if he sees me call, he might call (60%) or raise (40%). If he raises, I will win as my King is higher than his Queen or Jack. If he calls, I will also win. The overall winning rate is 100%, losing rate is 0%, and drawing rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King: \n  - In the 1st round, if he sees me raise, he might raise (70%) or call (30%). If he raises, it will be a draw as we both have Kings and the same amount of chips in the pot. If he calls, I will win as I have more chips in the pot. The overall winning rate is 30%, losing rate is 0%, and drawing rate is 70%.\n- If GoodGuy holds a Queen or Jack: \n  - In the 1st round, if he sees me raise, he might call (60%) or raise (40%). If he raises, I will win as my King is higher than his Queen or Jack. If he calls, I will also win. The overall winning rate is 100%, losing rate is 0%, and drawing rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of what card GoodGuy holds. The overall winning rate is 0%, losing rate is 100%, and drawing rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips (half of the total pot of 6 chips). If I lose, the losing payoff would be 1 chip (half of the total pot of 2 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 2 chips (half of the total pot of 4 chips).\n- Plan 3: If I fold, I will lose 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 0.5 * 3 - 0.35 * 1 = 1.15 chips\n- Plan 2: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 0.65 * 5 - 0 * 2 = 3.25 chips\n- Plan 3: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 0 * 0 - 1 * 1 = -1 chip\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I should choose this plan."}}
{"message": "", "1_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (55.56%):\n  - He might call (50%) or fold (50%). If he calls, I will win (100%) because my King matches the public card. If he folds, I will also win (100%) because he forfeits the round.\n- If GoodGuy holds a Jack (44.44%):\n  - He might call (40%) or fold (60%). If he calls, I will win (100%) because my King matches the public card. If he folds, I will also win (100%) because he forfeits the round.\n\nPlan 2: Fold\n- This plan is not reasonable because I hold the highest possible combination in this round.\n\nPlan 3: Check\n- If GoodGuy holds a Queen (55.56%):\n  - He might raise (40%) or check (60%). If he raises, I will call and win (100%) because my King matches the public card. If he checks, I will also win (100%) because my King matches the public card.\n- If GoodGuy holds a Jack (44.44%):\n  - He might raise (50%) or check (50%). If he raises, I will call and win (100%) because my King matches the public card. If he checks, I will also win (100%) because my King 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 4 chips (half of the total pot). If I lose, the lose payoff would be 4 chips.\n- Plan 2: Not applicable.\n- Plan 3: If I win, the winning payoff would be 4 chips (half of the total pot). If I lose, the lose payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning Rate * Winning Payoff - Lose Rate * Lose Payoff = 100% * 4 chips - 0% * 4 chips = 4 chips.\n- Plan 2: Not applicable.\n- Plan 3: Expected Chips Gain = Winning Rate * Winning Payoff - Lose Rate * Lose Payoff = 100% * 4 chips - 0% * 4 chips = 4 chips.\n\nPlan Selection:\n- Plan 1 and Plan 3 both have the highest estimated expected chips gain (4 chips). However, Plan 1 (Raise) is more aggressive and could potentially pressure GoodGuy into folding, so I will select Plan 1."}}
{"message": "", "1_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a Queen (50% probability), he will likely call (50% probability). This would result in a win for me, as my pair of Kings beats a single Queen. Therefore, the winning rate for this plan is 50% * 50% = 25%.\n- If GoodGuy holds a Jack (50% probability), he will likely fold (60% probability). This would also result in a win for me, as my pair of Kings beats a single Jack. Therefore, the winning rate for this plan is 50% * 60% = 30%.\n- The overall winning rate for this plan is 25% + 30% = 55%.\n\nPlan 2: Fold\n- If I fold, I automatically lose the game, regardless of what card GoodGuy holds. Therefore, the losing rate for this plan is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I call, the total chips in the pot would be 24 (my 12 chips + GoodGuy's 12 chips). If I win, the winning payoff would be half of the total pot, which is 12 chips. If I lose, the losing payoff would be the 12 chips I put in the pot.\n- Plan 2: If I fold, I automatically lose the 12 chips I put in the pot.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain for this plan is the winning rate * winning payoff - losing rate * losing payoff = 55% * 12 chips - 45% * 12 chips = 1.2 chips.\n- Plan 2: The expected chips gain for this plan is 0, as I automatically lose the game if I fold.\n\nPlan Selection:\n- Plan 1 has an expected chips gain of 1.2 chips, while Plan 2 has an expected chips gain of 0. Therefore, Plan 1 is the better strategy."}}
{"message": "", "2_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (33.33% probability), he will likely call (100% probability). If the public card is a King, it will be a draw. If the public card is a Queen or a Jack, I will win. So, the winning rate is 66.67%, the draw rate is 33.33%, and the losing rate is 0%.\n- If GoodGuy holds a Queen (33.33% probability), he will likely call (100% probability). Regardless of the public card, I will win. So, the winning rate is 100%, and the losing and draw rates are 0%.\n- If GoodGuy holds a Jack (33.33% probability), he will likely call (100% probability). Regardless of the public card, I will win. So, the winning rate is 100%, and the losing and draw rates are 0%.\n- Overall, the winning rate for Plan 1 is 88.89%, the draw rate is 11.11%, and the losing rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (33.33% probability), he will likely call (100% probability). If the public card is a King, it will be a draw. If the public card is a Queen or a Jack, I will win. So, the winning rate is 66.67%, the draw rate is 33.33%, and the losing rate is 0%.\n- If GoodGuy holds a Queen (33.33% probability), he will likely call (100% probability). Regardless of the public card, I will win. So, the winning rate is 100%, and the losing and draw rates are 0%.\n- If GoodGuy holds a Jack (33.33% probability), he will likely call (100% probability). Regardless of the public card, I will win. So, the winning rate is 100%, and the losing and draw rates are 0%.\n- Overall, the winning rate for Plan 2 is 88.89%, the draw rate is 11.11%, and the losing rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of GoodGuy's card. So, the winning rate is 0%, and the losing rate is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips (half of the total pot of 6 chips). If I lose, the losing payoff would be 1 chip (half of the total pot of 2 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 2 chips (half of the total pot of 4 chips).\n- Plan 3: If I lose, the losing payoff would be 1 chip (half of the total pot of 2 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 88.89% * 3 chips - 0% * 1 chip = 2.67 chips\n- Plan 2: Expected Chips Gain = 88.89% * 5 chips - 0% * 2 chips = 4.44 chips\n- Plan 3: Expected Chips Gain = 0% * 0 chips - 100% * 1 chip = -1 chip\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain (4.44 chips), followed by Plan 1 (2.67 chips), and Plan 3 (-1 chip). Therefore, I should choose Plan 2: Raise."}}
{"message": "", "2_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (50% probability), he will likely call (100% probability). If the next public card is a King, I will win (33% probability). If the next public card is a Queen or Jack, I will lose (67% probability). \n- If GoodGuy holds a Queen (50% probability), he will likely call (100% probability). If the next public card is a King, I will win (33% probability). If the next public card is a Queen or Jack, I will lose (67% probability). \nOverall, the winning rate for Plan 1 is 33%, the losing rate is 67%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will automatically lose the game. Therefore, the winning rate for Plan 2 is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King (50% probability), he will likely call (100% probability). If the next public card is a King, I will win (33% probability). If the next public card is a Queen or Jack, I will lose (67% probability). \n- If GoodGuy holds a Queen (50% probability), he will likely call (100% probability). If the next public card is a King, I will win (33% probability). If the next public card is a Queen or Jack, I will lose (67% probability). \nOverall, the winning rate for Plan 3 is 33%, the losing rate is 67%, 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 fold, I will 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). If I lose, the losing payoff would be 8 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 33% * 8 chips - 67% * 8 chips = -2.68 chips\n- Plan 2: Expected Chips Gain = 0% * 0 chips - 100% * 4 chips = -4 chips\n- Plan 3: Expected Chips Gain = 33% * 8 chips - 67% * 8 chips = -2.68 chips\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows:\n1. Plan 1: -2.68 chips\n2. Plan 3: -2.68 chips\n3. Plan 2: -4 chips\n\nTherefore, I should select Plan 1 or Plan 3, as they have the highest estimated expected chips gain. Considering the strategy improvement, I should select Plan 1 (Raise), as it allows me to potentially increase the pot and confuse my opponent."}}
{"message": "", "3_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (33.33% probability), he will likely call (100% probability). If the public card is a King, I will lose (probability = 33.33% * 100% = 33.33%). If the public card is not a King, I will win (probability = 33.33% * 100% = 33.33%).\n- If GoodGuy holds a Queen (33.33% probability), he will likely call (100% probability). If the public card is a Queen, I will lose (probability = 33.33% * 100% = 33.33%). If the public card is not a Queen, I will win (probability = 33.33% * 100% = 33.33%).\n- If GoodGuy holds a Jack (33.33% probability), he will likely call (100% probability). If the public card is a Jack, it will be a draw (probability = 33.33% * 100% = 33.33%). If the public card is not a Jack, I will lose (probability = 33.33% * 100% = 33.33%).\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card or the public card. The lose rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (33.33% probability), he will likely call (100% probability). If the public card is a King, I will lose (probability = 33.33% * 100% = 33.33%). If the public card is not a King, I will win (probability = 33.33% * 100% = 33.33%).\n- If GoodGuy holds a Queen (33.33% probability), he will likely call (100% probability). If the public card is a Queen, I will lose (probability = 33.33% * 100% = 33.33%). If the public card is not a Queen, I will win (probability = 33.33% * 100% = 33.33%).\n- If GoodGuy holds a Jack (33.33% probability), he will likely call (100% probability). If the public card is a Jack, it will be a draw (probability = 33.33% * 100% = 33.33%). If the public card is not a Jack, I will lose (probability = 33.33% * 100% = 33.33%).\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 lose payoff would be half of the total pot (4 chips).\n- Plan 2: If I fold, I will lose the game and the lose payoff would be 2 chips.\n- Plan 3: 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\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 33.33% * 4 - 33.33% * 4 = 0\n- Plan 2: Expected Chips Gain = 0 - 100% * 2 = -2\n- Plan 3: Expected Chips Gain = 33.33% * 4 - 33.33% * 4 = 0\n\nPlan Selection:\n- Plan 1 and Plan 3 have the same expected chips gain, which is higher than Plan 2. Therefore, I should either raise (Plan 1) or check (Plan 3). Considering the strategy improvement, I should choose to raise (Plan 1) as it can potentially confuse GoodGuy and make him believe that I hold a higher rank card."}}
{"message": "", "5_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (90% probability), he will call in the second round regardless of the public card. If the public card is a King, I will lose (33% probability). If the public card is a Queen, I will win (33% probability). If the public card is a Jack, I will lose (33% probability). Overall, the winning rate is 30%, the losing rate is 60%, and the draw rate is 10%.\n- If GoodGuy holds a Queen (5% probability), he will fold in the second round unless the public card is a Queen. If the public card is a Queen, I will draw (33% probability). If the public card is a King or a Jack, I will win (67% probability). Overall, the winning rate is 3.35%, the losing rate is 0%, and the draw rate is 1.65%.\n- If GoodGuy holds a Jack (5% probability), he will fold in the second round unless the public card is a Jack. If the public card is a Jack, I will lose (33% probability). If the public card is a King or a Queen, I will win (67% probability). Overall, the winning rate is 3.35%, the losing rate is 1.65%, and the draw rate is 0%.\n\nPlan 1 overall Winning/Lose/Draw rates: Winning rate is 36.7%, Losing rate is 62.3%, Draw rate is 1%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (90% probability), he will call in the second round regardless of the public card. If the public card is a King, I will lose (33% probability). If the public card is a Queen, I will win (33% probability). If the public card is a Jack, I will lose (33% probability). Overall, the winning rate is 30%, the losing rate is 60%, and the draw rate is 10%.\n- If GoodGuy holds a Queen (5% probability), he will fold in the second round regardless of the public card. This means I will win (100% probability). Overall, the winning rate is 5%, the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (5% probability), he will fold in the second round regardless of the public card. This means I will win (100% probability). Overall, the winning rate is 5%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2 overall Winning/Lose/Draw rates: Winning rate is 40%, Losing rate is 60%, Draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of GoodGuy's card or the public card. The overall 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 4 chips. If lose, the lose payoff would be 2 chips.\n- Plan 2: If win, the winning payoff would be 8 chips. If lose, the lose payoff would be 4 chips.\n- Plan 3: If lose, the lose payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 36.7% * 4 - 62.3% * 2 = 0.48 chips\n- Plan 2: Expected Chips Gain = 40% * 8 - 60% * 4 = 0.8 chips\n- Plan 3: Expected Chips Gain = -100% * 2 = -2 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest estimated expected chips gain, so I should choose this plan."}}
{"message": "", "5_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (100% probability), he will call (100% probability). I will lose as his pair of Kings beats my single Queen. \n- If GoodGuy holds a Queen (0% probability), he will fold (100% probability). I will win as he forfeits the game. \n- If GoodGuy holds a Jack (0% probability), he will fold (100% probability). I will win as he forfeits the game. \n\nPlan 2: Fold\n- If GoodGuy holds a King (100% probability), I will lose as I forfeit the game. \n- If GoodGuy holds a Queen (0% probability), I will lose as I forfeit the game. \n- If GoodGuy holds a Jack (0% probability), I will lose as I forfeit the game. \n\nPlan 3: Check\n- If GoodGuy holds a King (100% probability), he will call (100% probability). I will lose as his pair of Kings beats my single Queen. \n- If GoodGuy holds a Queen (0% probability), he will fold (100% probability). I will win as he forfeits the game. \n- If GoodGuy holds a Jack (0% probability), he will fold (100% probability). I will win as he forfeits the game. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 8 chips (half of the total pot of 16 chips). If lose, the lose payoff would be 8 chips. \n- Plan 2: 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 3: 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\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0% * 8 chips - 100% * 8 chips = -8 chips\n- Plan 2: Expected Chips Gain = 0% * 6 chips - 100% * 6 chips = -6 chips\n- Plan 3: Expected Chips Gain = 0% * 6 chips - 100% * 6 chips = -6 chips\n\nPlan Selection:\n- Plan 1: Rank 3\n- Plan 2: Rank 1\n- Plan 3: Rank 1\n\nConsidering both the strategy improvement and the estimated expected chips gain, I should select Plan 2 or Plan 3, which is to fold or check."}}
{"message": "", "6_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a Queen (70% probability), he will fold in the second round if the public card is not a Queen. If the public card is a Queen, he will raise. If I call, the overall winning rate is 70% (probability of him having a Queen * probability of public card not being a Queen), the losing rate is 30% (probability of him having a Queen * probability of public card being a Queen), and the draw rate is 0%.\n- If GoodGuy holds a Jack (30% probability), he will fold in the second round if the public card is not a Jack. If the public card is a Jack, he will raise. If I call, the overall winning rate is 30% (probability of him having a Jack * probability of public card not being a Jack), the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a Queen (70% probability), he will fold in the first round if I raise. Therefore, the overall winning rate is 70%, the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (30% probability), he will fold in the first round if I raise. Therefore, the overall winning rate is 30%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, 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 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 lose, the losing payoff would be 2 chips (half of the total pot of 4 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.7 * 3 - 0.3 * 3 = 1.2 chips\n- Plan 2: Expected Chips Gain = 1 * 4 - 0 * 4 = 4 chips\n- Plan 3: Expected Chips Gain = 0 * 0 - 1 * 2 = -2 chips\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows:\n1. Plan 2: Raise (4 chips)\n2. Plan 1: Call (1.2 chips)\n3. Plan 3: Fold (-2 chips)\n\nTherefore, the best strategy is Plan 2: Raise."}}
{"message": "", "6_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (100% probability based on his behavior pattern), he will call my raise (100% probability). In this case, we will have a draw as we both hold a King. The overall draw rate for his King is 100% (1 * 1).\n- If GoodGuy holds a Queen or a Jack (0% probability based on his behavior pattern), he will fold to my raise (100% probability). In this case, I will win as I hold a King. However, as the probability of him holding a Queen or a Jack is 0%, the overall winning rate is 0%.\n\nPlan 2: Fold\n- If I fold, regardless of GoodGuy's card, I will lose. The overall losing rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (100% probability based on his behavior pattern), he will call my check (100% probability). In this case, we will have a draw as we both hold a King. The overall draw rate for his King is 100% (1 * 1).\n- If GoodGuy holds a Queen or a Jack (0% probability based on his behavior pattern), he will fold to my check (100% probability). In this case, I will win as I hold a King. However, as the probability of him holding a Queen or a Jack is 0%, the overall winning rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the raise, all chips in the pot would be 12. If win, the winning payoff would be 6. If lose, the lose payoff would be 6.\n- Plan 2: After the fold, all chips in the pot would be 4. If lose, the lose payoff would be 2.\n- Plan 3: After the check, all chips in the pot would be 4. If win, the winning payoff would be 2. If lose, the lose payoff would be 2.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 0 * 6 - 0 * 6 = 0\n- Plan 2: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 0 * 2 - 1 * 2 = -2\n- Plan 3: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 0 * 2 - 0 * 2 = 0\n\nPlan Selection:\n- Plan 1: Rank 1\n- Plan 2: Rank 3\n- Plan 3: Rank 1\n\nBased on the estimated expected chips gain, Plan 1 (Raise) and Plan 3 (Check) are the best strategies to use in this situation. However, considering the strategy improvement, Plan 1 (Raise) would be the optimal choice as it could pressure GoodGuy into folding."}}
{"message": "", "6_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he will likely raise (100% probability). Given the game rules, I will lose this round (100% probability). \n- If GoodGuy holds a Queen (30% probability), he will likely fold (100% probability). Given the game rules, I will win this round (100% probability). \n- Overall, the winning rate for Plan 1 is 30%, the losing rate is 70%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If GoodGuy holds a King (70% probability), he will likely raise (100% probability). Given the game rules, I will lose this round (100% probability). \n- If GoodGuy holds a Queen (30% probability), he will likely fold (100% probability). Given the game rules, I will lose this round (100% probability). \n- Overall, the winning rate for Plan 2 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 10 chips (half of the total pot of 20 chips). If I lose, the losing payoff would be 10 chips.\n- Plan 2: If I win, the winning payoff would be 0 chips (as I would not contribute any more chips to the pot). If I lose, the losing payoff would be 8 chips (my current contribution to the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is 30% * 10 chips - 70% * 10 chips = -4 chips.\n- Plan 2: The expected chips gain is 0% * 0 chips - 100% * 8 chips = -8 chips.\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain (-4 chips) than Plan 2 (-8 chips). Therefore, I should choose Plan 1: Call."}}
{"message": "", "7_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (50% probability), he will fold (100% probability) according to his behavior pattern. This will result in a win for me (100% probability). \n- If GoodGuy holds a Jack (50% probability), he will also fold (100% probability) according to his behavior pattern. This will also result in a win for me (100% probability). \n- Overall, the winning rate for this plan is 100% (50% * 100% + 50% * 100%), the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of what card GoodGuy holds. Therefore, the winning rate for this plan is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a Queen (50% probability), he will check (100% probability) according to his behavior pattern. This will result in a draw (100% probability). \n- If GoodGuy holds a Jack (50% probability), he will also check (100% probability) according to his behavior pattern. This will result in a win for me (100% probability). \n- Overall, the winning rate for this plan is 50% (0% * 50% + 100% * 50%), the losing rate is 0%, and the draw rate is 50% (100% * 50% + 0% * 50%).\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the raise, 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 2: After the fold, all chips in the pot would be 4. If win, the winning payoff would be 2. If lose, the lose payoff would be 2.\n- Plan 3: After the check, all chips in the pot would be 4. If win, the winning payoff would be 2. If lose, the lose payoff would be 2.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 100% * 3 - 0% * 3 = 3\n- Plan 2: Expected Chips Gain = 0% * 2 - 100% * 2 = -2\n- Plan 3: Expected Chips Gain = 50% * 2 - 0% * 2 = 1\n\nPlan Selection:\n- Plan 1: Raise (Expected Chips Gain = 3)\n- Plan 3: Check (Expected Chips Gain = 1)\n- Plan 2: Fold (Expected Chips Gain = -2)\n\nTherefore, I should choose Plan 1: Raise, as it has the highest estimated expected chips gain."}}
{"message": "", "8_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (90% probability), he will likely raise in the second round if the public card is a King (33.3% probability). If I call, I will lose (probability = 90% * 33.3% = 30%). If the public card is not a King, and he sees my call, he will likely call as well, and I will lose (probability = 90% * 66.7% = 60%).\n- If GoodGuy holds a Queen or Jack (10% probability), he will likely fold in the second round if the public card is not a Queen or Jack. If I call, I will win (probability = 10% * 66.7% = 6.7%). If the public card is a Queen or Jack, and he sees my call, he will likely raise, and I will win (probability = 10% * 33.3% = 3.3%).\n- Overall, the winning rate for Plan 1 is 10%, the losing rate is 90%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (90% probability), he will likely call in the second round if the public card is a King (33.3% probability). If I raise, I will lose (probability = 90% * 33.3% = 30%). If the public card is not a King, and he sees my raise, he will likely call, and I will lose (probability = 90% * 66.7% = 60%).\n- If GoodGuy holds a Queen or Jack (10% probability), he will likely fold in the second round if the public card is not a Queen or Jack. If I raise, I will win (probability = 10% * 66.7% = 6.7%). If the public card is a Queen or Jack, and he sees my raise, he will likely fold, and I will win (probability = 10% * 33.3% = 3.3%).\n- Overall, the winning rate for Plan 2 is 10%, the losing rate is 90%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose 100% of the time.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the call, all chips in the pot: 6. If win, the winning payoff would be 3. If lose, the lose payoff would be 3.\n- Plan 2: After the raise, all chips in the pot: 10. If win, the winning payoff would be 5. If lose, the lose payoff would be 5.\n- Plan 3: After the fold, all chips in the pot: 6. If lose, the lose payoff would be 3.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 10% * 3 - 90% * 3 = -2.4\n- Plan 2: Expected Chips Gain = 10% * 5 - 90% * 5 = -4\n- Plan 3: Expected Chips Gain = -3\n\nPlan Selection:\n- Plan 1: -2.4\n- Plan 2: -4\n- Plan 3: -3\n\nThe rank of estimated expected chips gains for every plan is Plan 1 > Plan 3 > Plan 2. Therefore, I should choose Plan 1: Call."}}
{"message": "", "8_3": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (100% probability), he will call (100% probability). I will lose this round (100% probability) as his King matches the public card while my Queen does not.\n- If GoodGuy holds a Queen (0% probability), he will fold (100% probability). I will win this round (100% probability) as my Queen is higher than his Queen.\n- If GoodGuy holds a Jack (0% probability), he will fold (100% probability). I will win this round (100% probability) as my Queen is higher than his Jack.\n- Overall, my winning rate for Plan 1 is 0%, my losing rate is 100%, and my drawing rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (100% probability), he will call (100% probability). I will lose this round (100% probability) as his King matches the public card while my Queen does not.\n- If GoodGuy holds a Queen (0% probability), he will fold (100% probability). I will win this round (100% probability) as my Queen is higher than his Queen.\n- If GoodGuy holds a Jack (0% probability), he will fold (100% probability). I will win this round (100% probability) as my Queen is higher than his Jack.\n- Overall, my winning rate for Plan 2 is 0%, my losing rate is 100%, and my drawing rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose this round regardless of what card GoodGuy holds. My 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 6 chips (half of the total pot of 12 chips). If I lose, the losing payoff would be 6 chips.\n- Plan 2: If I win, the winning payoff would be 10 chips (half of the total pot of 20 chips). If I lose, the losing payoff would be 10 chips.\n- Plan 3: If I fold, I will lose 4 chips (the amount I have already put into the pot).\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 = -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. Therefore, I should choose to fold in this round."}}
{"message": "", "10_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (50% probability), he will likely raise (100% probability). If the public card is a King, I will lose (100% probability). If the public card is not a King, I 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 Jack). Overall, my winning rate is 25%, losing rate is 75%, and draw rate is 0%.\n- If GoodGuy holds a Queen (25% probability), he will likely fold (100% probability). I will win (100% probability). Overall, my winning rate is 25%, losing rate is 0%, and draw rate is 0%.\n- If GoodGuy holds a Jack (25% probability), he will likely fold (100% probability). I will win (100% probability). Overall, my winning rate is 25%, losing rate is 0%, and draw rate is 0%.\n\nPlan 1 overall Winning/Lose/Draw rates: Winning rate is 75%, Losing rate is 25%, Draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (50% probability), he will likely call (100% probability). If the public card is a King, I will lose (100% probability). If the public card is not a King, I 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 Jack). Overall, my winning rate is 25%, losing rate is 75%, and draw rate is 0%.\n- If GoodGuy holds a Queen (25% probability), he will likely fold (100% probability). I will win (100% probability). Overall, my winning rate is 25%, losing rate is 0%, and draw rate is 0%.\n- If GoodGuy holds a Jack (25% probability), he will likely fold (100% probability). I will win (100% probability). Overall, my winning rate is 25%, losing rate is 0%, and draw rate is 0%.\n\nPlan 2 overall Winning/Lose/Draw rates: Winning rate is 75%, Losing rate is 25%, Draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose 100% of the time.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: 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 (6 chips). If I lose, the lose payoff would be half of the total pot (6 chips).\n- Plan 3: If I fold, I lose 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.75 * 3 - 0.25 * 3 = 1.5 chips\n- Plan 2: Expected Chips Gain = 0.75 * 6 - 0.25 * 6 = 3 chips\n- Plan 3: Expected Chips Gain = -1 chip\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain, so I will choose Plan 2: Raise."}}
{"message": "", "10_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (100% probability), he will fold (100% probability) according to his game pattern. Therefore, I will win the game with 100% probability. The overall winning rate for this plan is 100%.\n\nPlan 2: Fold\n- If GoodGuy holds a Queen (100% probability), he will check (100% probability) according to his game pattern. Therefore, I will lose the game with 100% probability. The overall losing rate for this plan is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a Queen (100% probability), he will check (100% probability) according to his game pattern. Therefore, the game will be a draw with 100% probability. The overall draw rate for this plan is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, all chips in the pot would be 8. If win, the winning payoff would be 4. If lose, the lose payoff would be 4.\n- Plan 2: After the action, all chips in the pot would be 4. If win, the winning payoff would be 2. If lose, the lose payoff would be 2.\n- Plan 3: After the action, all chips in the pot would be 4. If win, the winning payoff would be 2. If lose, the lose payoff would be 2.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is 100% * 4 - 0% * 4 = 4.\n- Plan 2: The expected chips gain is 0% * 2 - 100% * 2 = -2.\n- Plan 3: The expected chips gain is 0% * 2 - 0% * 2 = 0.\n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 1 > Plan 3 > Plan 2.\n- Therefore, I should select Plan 1 (Raise) as it has the highest estimated expected chips gain."}}
{"message": "", "10_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (100% probability), he will not act as he has already raised. I will lose this round as his King matches the public card. The lose rate for this plan is 100%.\n- If GoodGuy holds a Queen or a Jack (0% probability), he will not act as he has already raised. I will win this round as my Queen is higher than his Jack. However, this scenario is impossible based on my belief on GoodGuy's cards. The win rate for this plan is 0%.\n\nPlan 2: Fold\n- If GoodGuy holds a King (100% probability), he will not act as he has already raised. I will lose this round as I forfeit the game. The lose rate for this plan is 100%.\n- If GoodGuy holds a Queen or a Jack (0% probability), he will not act as he has already raised. I will lose this round as I forfeit the game. The win rate for this plan 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 24. If win, the winning payoff would be 12. If lose, the lose payoff would be 12.\n- Plan 2: After the fold action, all chips in the pot would be 20. If win, the winning payoff would be 0 as I forfeit the game. If lose, the lose payoff would be 8.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is 0% * 12 - 100% * 12 = -12.\n- Plan 2: The expected chips gain is 0% * 0 - 100% * 8 = -8.\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows: Plan 2 > Plan 1. Therefore, I should select Plan 2: Fold, as it has the highest estimated expected chips gain."}}
{"message": "", "11_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (50% probability), he will fold (100% probability). I will win the pot, which will be 6 chips (4 from me, 2 from GoodGuy). The winning rate is 50%, the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (50% probability), he will fold (100% probability). I will win the pot, which will be 6 chips (4 from me, 2 from GoodGuy). The winning rate is 50%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If GoodGuy holds a Queen (50% probability), he will check (100% probability). I will lose the pot, which will be 4 chips (2 from me, 2 from GoodGuy). The winning rate is 0%, the losing rate is 50%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (50% probability), he will check (100% probability). I will lose the pot, which will be 4 chips (2 from me, 2 from GoodGuy). The winning rate is 0%, the losing rate is 50%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a Queen (50% probability), he will check (100% probability). The game will proceed to the second round. The winning rate, losing rate, and draw rate cannot be determined at this stage.\n- If GoodGuy holds a Jack (50% probability), he will check (100% probability). The game will proceed to the second round. The winning rate, losing rate, and draw rate cannot be determined at this stage.\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 0 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: The payoff cannot be determined at this stage.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 50% * 3 chips - 0% * 0 chips = 1.5 chips\n- Plan 2: Expected Chips Gain = 0% * 0 chips - 50% * 2 chips = -1 chips\n- Plan 3: The Expected Chips Gain cannot be determined at this stage.\n\nPlan Selection:\n- Plan 1: Raise (Expected Chips Gain = 1.5 chips)\n- Plan 3: Check (Expected Chips Gain cannot be determined)\n- Plan 2: Fold (Expected Chips Gain = -1 chips)\n\nBased on the estimated expected chips gain, I should choose Plan 1: Raise."}}
{"message": "", "12_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (50% probability), he will raise in the 1st round (100% probability). If I call, he will likely believe I have a King or Queen. In the 2nd round, if the public card is a King, he will raise (100% probability). If the public card is not a King, he will call if I raise (100% probability). Considering the game rules, I will win if the public card is a Queen (33.33% probability), lose if it's a King (33.33% probability), and draw if it's a Jack (33.33% probability). Overall, the winning rate is 16.67%, the losing rate is 16.67%, and the draw rate is 16.67%.\n- If GoodGuy holds a Queen (50% probability), he will call in the 1st round (100% probability). If I call, he will likely believe I have a King or Queen. In the 2nd round, if the public card is a Queen, he will raise (100% probability). If the public card is not a Queen, he will fold if I raise (100% probability). Considering the game rules, I will draw if the public card is a Queen (33.33% probability), win if it's a Jack (33.33% probability), and lose if it's a King (33.33% probability). Overall, the winning rate is 16.67%, the losing rate is 16.67%, and the draw rate is 16.67%.\n\nPlan 1 overall Winning/Lose/Draw rates: Winning rate is 33.33%, Losing rate is 33.33%, Draw rate is 33.33%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (50% probability), he will call if I raise (100% probability). In the 2nd round, if the public card is a King, he will raise (100% probability). If the public card is not a King, he will call if I raise (100% probability). Considering the game rules, I will win if the public card is a Queen (33.33% probability), lose if it's a King (33.33% probability), and draw if it's a Jack (33.33% probability). Overall, the winning rate is 16.67%, the losing rate is 16.67%, and the draw rate is 16.67%.\n- If GoodGuy holds a Queen (50% probability), he will fold if I raise (50% probability) or call (50% probability). In the 2nd round, if the public card is a Queen, he will raise (100% probability). If the public card is not a Queen, he will fold if I raise (100% probability). Considering the game rules, I will draw if the public card is a Queen (33.33% probability), win if it's a Jack (33.33% probability), and lose if it's a King (33.33% probability). Overall, the winning rate is 16.67%, the losing rate is 16.67%, and the draw rate is 16.67%.\n\nPlan 2 overall Winning/Lose/Draw rates: Winning rate is 33.33%, Losing rate is 33.33%, 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 overall Winning/Lose/Draw rates for this plan are 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (currently 3 chips, so 1.5 chips). If I lose, the lose payoff would be half of the total pot (1.5 chips).\n- Plan 2: If I win, the winning payoff would be half of the total pot (currently 3 chips, so 1.5 chips). If I lose, the lose payoff would be half of the total pot (1.5 chips).\n- Plan 3: If I fold, I will lose the 1 chip I have already put in the pot.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 33.33% * 1.5 chips - 33.33% * 1.5 chips = 0 chips\n- Plan 2: Expected Chips Gain = 33.33% * 1.5 chips - 33.33% * 1.5 chips = 0 chips\n- Plan 3: Expected Chips Gain = -1 chip\n\nPlan Selection:\n- Plan 1 and Plan 2 both have an expected chips gain of 0, while Plan 3 has a negative expected chips gain. Therefore, either Plan 1 or Plan 2 should be selected. Considering the strategy improvement, Plan 1 (Call) should be selected as it is less aggressive and may lead to less loss in the long run."}}
{"message": "", "12_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (50% probability), he will raise (100% probability). This results in a draw, as we both have a pair of Queens. \n- If GoodGuy holds a Jack (50% probability), he will fold (100% probability). This results in a win for me, as my pair of Queens beats his Jack.\n\nPlan 2: Fold\n- If GoodGuy holds a Queen (50% probability), he will raise (100% probability). This results in a loss for me, as I have folded.\n- If GoodGuy holds a Jack (50% probability), he will fold (100% probability). This results in a draw, as we both have folded.\n\nPlan 3: Check\n- If GoodGuy holds a Queen (50% probability), he will raise (100% probability). This results in a draw, as we both have a pair of Queens.\n- If GoodGuy holds a Jack (50% probability), he will fold (100% probability). This results in a win for me, as my pair of Queens beats his Jack.\n\nWinning/Lose/Draw Rates for Each Plan:\n- Plan 1: 50% win, 0% lose, 50% draw\n- Plan 2: 0% win, 50% lose, 50% draw\n- Plan 3: 50% win, 0% lose, 50% draw\n\nNumber of Winning and Lose Payoffs for Each Plan:\n- Plan 1: If win, the winning payoff would be half of the total pot (currently 4 chips, so 2 chips). If lose, the lose payoff would be half of the total pot (currently 4 chips, so 2 chips).\n- Plan 2: If win, the winning payoff would be half of the total pot (currently 4 chips, so 2 chips). If lose, the lose payoff would be half of the total pot (currently 4 chips, so 2 chips).\n- Plan 3: If win, the winning payoff would be half of the total pot (currently 4 chips, so 2 chips). If lose, the lose payoff would be half of the total pot (currently 4 chips, so 2 chips).\n\nEstimated Expected Chips Gain for Each Plan:\n- Plan 1: 50% * 2 chips - 0% * 2 chips = 1 chip\n- Plan 2: 0% * 2 chips - 50% * 2 chips = -1 chip\n- Plan 3: 50% * 2 chips - 0% * 2 chips = 1 chip\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows:\n1. Plan 1 and Plan 3 (tie)\n2. Plan 2\n\nConsidering both the strategy improvement and the estimated expected chips gain, I would select either Plan 1 or Plan 3. Since Plan 1 (raise) is more aggressive and could potentially lead to a larger pot, I would choose Plan 1."}}
{"message": "", "13_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (probability 1/3), he will raise (probability 100%). I will lose as my Jack is lower than his King. \n- If GoodGuy holds a Queen (probability 1/3), he will call (probability 100%). The game will be decided in the second round. \n- If GoodGuy holds a Jack (probability 1/3), he will fold (probability 100%). I will win as he folds. \n\nPlan 2: Raise\n- If GoodGuy holds a King (probability 1/3), he will call (probability 100%). I will lose as my Jack is lower than his King. \n- If GoodGuy holds a Queen (probability 1/3), he will fold (probability 50%) or call (probability 50%). If he folds, I will win. If he calls, the game will be decided in the second round. \n- If GoodGuy holds a Jack (probability 1/3), he will fold (probability 100%). I will win as he folds. \n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 3 chips (half of the total pot of 6 chips). If lose, the lose payoff would be 1 chip (half of the total pot of 2 chips).\n- Plan 2: If win, the winning payoff would be 5 chips (half of the total pot of 10 chips). If lose, the lose payoff would be 3 chips (half of the total pot of 6 chips).\n- Plan 3: If lose, the lose payoff would be 1 chip (half of the total pot of 2 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = (1/3 * 3) - (2/3 * 1) = 0 chips\n- Plan 2: Expected Chips Gain = (1/3 * 5) - (1/3 * 3) = 0.67 chips\n- Plan 3: Expected Chips Gain = -1 chip\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain, so I will choose Plan 2: Raise."}}
{"message": "", "13_2": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he will likely raise 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 not a King, I will also lose (0% win, 100% lose, 0% draw). Overall, the winning rate for this plan is 0%, the losing rate is 70%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (30% probability), he will likely fold in the second round if the public card is not a Queen. If the public card is a Queen, I will lose (0% win, 100% lose, 0% draw). If the public card is not a Queen, I will win (100% win, 0% lose, 0% draw). Overall, the winning rate for this plan is 30%, the losing rate is 30%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card or the public card. The winning rate for this plan is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot, which is 5 chips. If I lose, the losing payoff would be half of the total pot, which is 5 chips.\n- Plan 2: If I fold, I will lose the game and the losing payoff would be half of the total pot, which is 5 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is 0% * 5 chips - 70% * 5 chips = -3.5 chips.\n- Plan 2: The expected chips gain is 0% * 0 chips - 100% * 5 chips = -5 chips.\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain (-3.5 chips) than Plan 2 (-5 chips). Therefore, I should choose Plan 1: Call."}}
{"message": "", "13_4": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (70% probability), he will call (100% probability). Considering the game rules, I will lose (100% probability). The overall losing rate for his King is 70%.\n- If GoodGuy holds a Queen (30% probability), he will fold (100% probability). Considering the game rules, I will win (100% probability). The overall winning rate for his Queen is 30%.\n\nPlan 2: Fold\n- If GoodGuy holds a King (70% probability), he will not act as I fold. Considering the game rules, I will lose (100% probability). The overall losing rate for his King is 70%.\n- If GoodGuy holds a Queen (30% probability), he will not act as I fold. Considering the game rules, I will lose (100% probability). The overall losing rate for his Queen is 30%.\n\nPlan 3: Check\n- If GoodGuy holds a King (70% probability), he will raise (100% probability). Considering the game rules, I will lose (100% probability). The overall losing rate for his King is 70%.\n- If GoodGuy holds a Queen (30% probability), he will check (100% probability). Considering the game rules, I will lose (100% probability). The overall losing rate for his Queen is 30%.\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 6 chips.\n- Plan 3: If win, the winning payoff would be 0 chips. If lose, the lose payoff would be 6 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 30% * 8 chips - 70% * 8 chips = -2.4 chips\n- Plan 2: Expected Chips Gain = 0% * 0 chips - 100% * 6 chips = -6 chips\n- Plan 3: Expected Chips Gain = 0% * 0 chips - 100% * 6 chips = -6 chips\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows:\n1. Plan 1: -2.4 chips\n2. Plan 2: -6 chips\n3. Plan 3: -6 chips\n\nTherefore, I should select Plan 1 (Raise) as it has the highest estimated expected chips gain."}}
{"message": "", "15_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (0% probability), he will call my raise (100% probability). If the public card is a King, I will lose (100% probability). If the public card is a Queen or Jack, I will win (50% probability) or draw (50% probability). Overall, the winning rate is 0%, the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (100% probability), he will fold (50% probability) or call (50% probability) my raise. If the public card is a Queen, I will lose (100% probability). If the public card is a King or Jack, I will win (100% probability). Overall, the winning rate is 50%, the losing rate is 50%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (0% probability), he will fold my raise (100% probability). If the public card is a Jack, I will win (100% probability). If the public card is a King or Queen, I will win (100% probability). Overall, the winning rate is 0%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card and the public card. The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King (0% probability), he will raise (100% probability). If the public card is a King, I will lose (100% probability). If the public card is a Queen or Jack, I will win (50% probability) or draw (50% probability). Overall, the winning rate is 0%, the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (100% probability), he will check (100% probability). If the public card is a Queen, I will lose (100% probability). If the public card is a King or Jack, I will win (100% probability). Overall, the winning rate is 50%, the losing rate is 50%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (0% probability), he will check (100% probability). If the public card is a Jack, I will win (100% probability). If the public card is a King or Queen, I will win (100% probability). Overall, the winning rate is 0%, the losing rate is 0%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 6 chips. If I lose, the losing payoff would be 6 chips.\n- Plan 2: If I lose, the losing payoff would be 2 chips.\n- Plan 3: If I win, the winning payoff would be 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 = 50% * 6 - 50% * 6 = 0 chips\n- Plan 2: Expected Chips Gain = 0% * 0 - 100% * 2 = -2 chips\n- Plan 3: Expected Chips Gain = 50% * 4 - 50% * 4 = 0 chips\n\nPlan Selection:\n- Plan 1: 0 chips\n- Plan 2: -2 chips\n- Plan 3: 0 chips\n\nBased on the estimated expected chips gain, Plan 1 and Plan 3 are the best strategies to use in this situation. However, considering the strategy improvement, Plan 1 (Raise) is the best strategy to use because it exploits GoodGuy's tendency to fold when he holds a Queen and the public card does not match his card."}}
{"message": "", "16_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (33.33% 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, it will be a draw. So, the overall winning rate is 0%, losing rate is 33.33%, and drawing rate is 66.67%.\n- If GoodGuy holds a Queen (33.33% probability), he will either fold or call (50% probability each). If the public card is a Queen, I will lose. If the public card is a King or Jack, it will be a draw. So, the overall winning rate is 0%, losing rate is 16.67%, and drawing rate is 83.33%.\n- If GoodGuy holds a Jack (33.33% probability), he will fold (100% probability). If the public card is a Jack, it will be a draw. If the public card is a King or Queen, I will win. So, the overall winning rate is 66.67%, losing rate is 0%, and drawing rate is 33.33%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (33.33% probability), he will call (100% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, it will be a draw. So, the overall winning rate is 0%, losing rate is 33.33%, and drawing rate is 66.67%.\n- If GoodGuy holds a Queen (33.33% probability), he will either fold or call (50% probability each). If the public card is a Queen, I will lose. If the public card is a King or Jack, it will be a draw. So, the overall winning rate is 0%, losing rate is 16.67%, and drawing rate is 83.33%.\n- If GoodGuy holds a Jack (33.33% probability), he will fold (100% probability). If the public card is a Jack, it will be a draw. If the public card is a King or Queen, I will win. So, the overall winning rate is 66.67%, losing rate is 0%, and drawing rate is 33.33%.\n\nPlan 3: Fold\n- If I fold, I will lose the 1 chip I have already put in the pot. So, the overall winning rate is 0%, losing rate is 100%, and drawing rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 3 chips. If lose, the lose payoff would be 1 chip.\n- Plan 2: If win, the winning payoff would be 7 chips. If lose, the lose payoff would be 3 chips.\n- Plan 3: If lose, the lose payoff would be 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0% * 3 chips - 33.33% * 1 chip = -0.33 chips\n- Plan 2: 66.67% * 7 chips - 33.33% * 3 chips = 3.33 chips\n- Plan 3: 0% * 0 chips - 100% * 1 chip = -1 chip\n\nPlan Selection:\n- Plan 2 > Plan 1 > Plan 3\n- Therefore, I should choose Plan 2: Raise."}}
{"message": "", "16_2": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (50% probability), he will likely raise in the second round regardless of the public card. If the public card is a Jack, I will win (50% probability). If the public card is not a Jack, I will lose (50% probability). Overall, the winning rate is 25%, the losing rate is 25%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (25% probability), he will likely fold if I raise in the second round unless the public card is a Queen. If the public card is a Jack, I will win (50% probability). If the public card is not a Jack, I will lose (50% probability). Overall, the winning rate is 12.5%, the losing rate is 12.5%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (25% probability), he will likely fold if I raise in the second round unless the public card is a Jack. If the public card is a Jack, it will be a draw (100% probability). Overall, the winning rate is 0%, the losing rate is 0%, and the draw rate is 25%.\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card. The overall winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the call 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 - Losing rate * Losing Payoff = 0.375 * 5 - 0.375 * 5 = 0\n- Plan 2: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 0 * 0 - 1 * 3 = -3\n\nPlan Selection:\n- Plan 1 has an expected chips gain of 0, and Plan 2 has an expected chips gain of -3. Therefore, Plan 1 (Call) is the better strategy."}}
{"message": "", "16_4": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (50% probability), he will call (100% probability). If the next public card is a King, I will lose (probability = 1/4 * 1 = 25%). If the next public card is not a King, I will win (probability = 3/4 * 1 = 75%).\n- If GoodGuy holds a Queen (50% probability), he will fold (100% probability). I will win (probability = 1 * 1 = 100%).\n\nPlan 2: Fold\n- If GoodGuy holds a King (50% probability), I will lose (probability = 1 * 1 = 100%).\n- If GoodGuy holds a Queen (50% probability), I will lose (probability = 1 * 1 = 100%).\n\nPlan 3: Check\n- If GoodGuy holds a King (50% probability), he will call (100% probability). If the next public card is a King, I will lose (probability = 1/4 * 1 = 25%). If the next public card is not a King, I will win (probability = 3/4 * 1 = 75%).\n- If GoodGuy holds a Queen (50% probability), he will raise (100% probability). If the next public card is a Queen, I will lose (probability = 1/4 * 1 = 25%). If the next public card is not a Queen, I will win (probability = 3/4 * 1 = 75%).\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 6 chips. If lose, the lose payoff would be 6 chips.\n- Plan 2: If win, the winning payoff would be 0 chips. If lose, the lose payoff would be 0 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 = 0.875 * 6 - 0.125 * 6 = 4.5 chips\n- Plan 2: Expected Chips Gain = 0 * 0 - 1 * 0 = 0 chips\n- Plan 3: Expected Chips Gain = 0.75 * 6 - 0.25 * 6 = 3 chips\n\nPlan Selection:\n- Plan 1: 4.5 chips\n- Plan 2: 0 chips\n- Plan 3: 3 chips\n\nThe plan with the highest estimated expected chips gain is Plan 1: Raise."}}
{"message": "", "17_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (33.33% probability), he will fold according to his behavior pattern. Therefore, I will win the pot (100% probability). The winning rate for his Queen is 33.33%.\n- If GoodGuy holds a Jack (66.67% probability), he will also fold according to his behavior pattern. Therefore, I will win the pot (100% probability). The winning rate for his Jack is 66.67%.\n\nPlan 2: Fold\n- If I fold, I will lose the pot regardless of GoodGuy's card. Therefore, the losing rate for this plan is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a Queen (33.33% probability), he will check according to his behavior pattern. Therefore, the outcome will depend on the public card in the second round.\n- If GoodGuy holds a Jack (66.67% probability), he will also check according to his behavior pattern. Therefore, the outcome will also depend on the public card in the second round.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, all chips in the pot: 4. If win, the winning payoff would be 2. If lose, the lose payoff would be 2.\n- Plan 2: After the action, all chips in the pot: 2. If win, the winning payoff would be 1. If lose, the lose payoff would be 1.\n- Plan 3: After the action, all chips in the pot: 2. If win, the winning payoff would be 1. If lose, the lose payoff would be 1.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 33.33% * 2 + 66.67% * 2 - 0% * 2 = 2\n- Plan 2: Expected Chips Gain = 0% * 1 - 100% * 1 = -1\n- Plan 3: Expected Chips Gain = (33.33% + 66.67%) * 1 - (33.33% + 66.67%) * 1 = 0\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 (0 chips)\n3. Plan 2: Fold (-1 chips)\n\nTherefore, the plan with the highest estimated expected chips gain is Plan 1: Raise."}}
{"message": "", "18_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (50% probability), he will raise in the second round regardless of the public card. If the public card is a Jack, I will win (50% probability). If the public card is not a Jack, I will lose (50% probability). Overall, the winning rate is 25%, the losing rate is 25%, and the draw rate is 50%.\n- If GoodGuy holds a Queen (50% probability), he will fold if I raise in the second round. If the public card is a Jack, I will win (50% probability). If the public card is not a Jack, I will lose (50% probability). Overall, the winning rate is 25%, the losing rate is 25%, and the draw rate is 50%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (50% probability), he will call in the second round regardless of the public card. If the public card is a Jack, I will win (50% probability). If the public card is not a Jack, I will lose (50% probability). Overall, the winning rate is 25%, the losing rate is 25%, and the draw rate is 50%.\n- If GoodGuy holds a Queen (50% probability), he will fold if I raise in the second round. If the public card is a Jack, I will win (50% probability). If the public card is not a Jack, I will lose (50% probability). Overall, the winning rate is 25%, the losing rate is 25%, and the draw rate is 50%.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card and the public card. 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 3 chips (half of the total pot). If lose, the lose payoff would be 3 chips.\n- Plan 2: If win, the winning payoff would be 7 chips (half of the total pot). If lose, the lose payoff would be 7 chips.\n- Plan 3: If lose, the lose payoff would be 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 25% * 3 - 25% * 3 = 0\n- Plan 2: Expected Chips Gain = 25% * 7 - 25% * 7 = 0\n- Plan 3: Expected Chips Gain = -100% * 1 = -1\n\nPlan Selection:\n- Plan 1 and Plan 2 have the same expected chips gain, and both are higher than Plan 3. Therefore, I can choose either Plan 1 or Plan 2. Considering the strategy improvement, I will choose Plan 2 (Raise) because it can potentially confuse GoodGuy and make him fold when he holds a Queen."}}
{"message": "", "18_2": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he will call in the second round regardless of the public card. If the public card is a King, I will lose (33% probability). If the public card is a Queen or Jack, I will win (67% probability). Overall, the winning rate is 47%, the losing rate is 23%, and the draw rate is 30%.\n- If GoodGuy holds a Queen (15% probability), he will fold if I raise in the second round. If the public card is a Queen, I will lose (33% probability). If the public card is a King or Jack, I will win (67% probability). Overall, the winning rate is 10%, the losing rate is 5%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (15% probability), he will fold if I raise in the second round. If the public card is a Jack, it will be a draw (33% probability). If the public card is a King or Queen, I will win (67% probability). Overall, the winning rate is 10%, the losing rate is 0%, and the draw rate is 5%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of GoodGuy's card or the public card. The overall losing rate 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 10. If win, the winning payoff would be 5. If lose, the lose payoff would be 5.\n- Plan 2: After the fold, all chips in the pot would be 6. If lose, the lose payoff would be 3.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 67% * 5 - 28% * 5 = 1.95\n- Plan 2: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 0% * 0 - 100% * 3 = -3\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain than Plan 2. Therefore, I should choose Plan 1: Call."}}
{"message": "", "18_4": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King, he will call (100% probability). I will lose as his King is higher than my Jack. The winning/losing rate is 0%/100%.\n- If GoodGuy holds a Queen, he will fold (100% probability). I will win as he folds. The winning/losing rate is 100%/0%.\n- If GoodGuy holds a Jack, he will fold (100% probability). I will win as he folds. The winning/losing rate is 100%/0%.\n\nPlan 2: Fold\n- If GoodGuy holds a King, Queen, or Jack, he will not act as I fold. I will lose as I fold. The winning/losing rate is 0%/100%.\n\nPlan 3: Check\n- If GoodGuy holds a King, he will raise (100% probability). I will lose as his King is higher than my Jack. The winning/losing rate is 0%/100%.\n- If GoodGuy holds a Queen, he will check (100% probability). I will lose as his Queen is higher than my Jack. The winning/losing rate is 0%/100%.\n- If GoodGuy holds a Jack, he will check (100% probability). It will be a draw as we both hold a Jack. The winning/losing/draw rate is 0%/0%/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 (6+4=10, half is 5). If lose, the lose payoff would be half of the total pot (6+4=10, half is 5).\n- Plan 2: If lose, the lose payoff would be half of the total pot (6, half is 3).\n- Plan 3: If lose, the lose payoff would be half of the total pot (6, half is 3). If draw, no chips change.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = winning rate * Winning Payoff - lose rate * Lose Payoff = (2/3 * 5) - (1/3 * 5) = 0\n- Plan 2: Expected Chips Gain = -1 * Lose Payoff = -3\n- Plan 3: Expected Chips Gain = -1/3 * Lose Payoff = -1\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is Plan 1 > Plan 3 > Plan 2. Therefore, I should choose Plan 1: Raise."}}
{"message": "", "20_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (50% probability), he will raise (100% probability). If the public card is a King, I will win (50% probability). If the public card is not a King, I will draw (50% probability). Overall, the winning rate is 25%, the draw rate is 25%, and the losing rate is 50%.\n- If GoodGuy holds a Queen (50% probability), he will fold (100% probability). I will win (100% probability). Overall, the winning rate is 50%, and the losing and draw rates are 0%.\n\nPlan 1 overall Winning/Lose/Draw rates: Winning rate is 75%, Losing rate is 50%, Draw rate is 25%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (50% probability), he will call (100% probability). If the public card is a King, I will win (50% probability). If the public card is not a King, I will draw (50% probability). Overall, the winning rate is 25%, the draw rate is 25%, and the losing rate is 50%.\n- If GoodGuy holds a Queen (50% probability), he will fold (100% probability). I will win (100% probability). Overall, the winning rate is 50%, and the losing and draw rates are 0%.\n\nPlan 2 overall Winning/Lose/Draw rates: Winning rate is 75%, Losing rate is 50%, Draw rate is 25%.\n\nPlan 3: Fold\n- If I fold, I will lose (100% probability). Overall, the winning and draw rates are 0%, and 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 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 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 75% * 3 - 50% * 2 = 0.75 chips\n- Plan 2: Expected Chips Gain = 75% * 7 - 50% * 6 = 1.75 chips\n- Plan 3: Expected Chips Gain = -100% * 1 = -1 chip\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is: Plan 2 > Plan 1 > Plan 3. Therefore, I should choose Plan 2: Raise."}}
{"message": "", "20_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (20% probability), he will call (100% probability). If the public card is a King, I will win (20% probability). If the public card is a Queen or Jack, I will win (80% probability). Overall, the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (20% probability), he will fold (100% probability). I will win (100% probability). Overall, the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (60% probability), he will raise (100% probability). If the public card is a King, I will win (20% probability). If the public card is a Queen or another Jack, I will lose (80% probability). Overall, the winning rate is 20%, the losing rate is 80%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of GoodGuy's cards or actions. The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King (20% probability), he will call (100% probability). If the public card is a King, I will win (20% probability). If the public card is a Queen or Jack, I will win (80% probability). Overall, the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (20% probability), he will fold (100% probability). I will win (100% probability). Overall, the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (60% probability), he will raise (100% probability). If the public card is a King, I will win (20% probability). If the public card is a Queen or another Jack, I will lose (80% probability). Overall, the winning rate is 20%, the losing rate is 80%, 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. If I lose, the losing payoff would be 8 chips.\n- Plan 2: If I lose, the losing payoff would be 4 chips.\n- Plan 3: If I win, the winning payoff would be 4 chips. If I lose, the losing payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: (100% * 8 chips) - (0% * 8 chips) = 8 chips\n- Plan 2: (0% * 4 chips) - (100% * 4 chips) = -4 chips\n- Plan 3: (100% * 4 chips) - (0% * 4 chips) = 4 chips\n\nPlan Selection:\n- Plan 1: 8 chips\n- Plan 2: -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, I should select Plan 1, which is to raise."}}
{"message": "", "21_0": {"plan": "Plan 1: Call\n- If GoodGuy has a King (50% probability), 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, I will win. If the public card is a Jack, I will lose. Therefore, the winning rate is 33%, the losing rate is 67%, and the draw rate is 0%.\n- If GoodGuy has a Queen (25% probability), he will likely call in the next round. If the public card is a King, I will lose. If the public card is a Queen, it will be a draw. If the public card is a Jack, I will win. Therefore, the winning rate is 33%, the losing rate is 33%, and the draw rate is 33%.\n- If GoodGuy has a Jack (25% probability), he will likely fold in the next round. Therefore, the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy has a King (50% probability), he will likely call. If the public card is a King, I will lose. If the public card is a Queen, I will win. If the public card is a Jack, I will lose. Therefore, the winning rate is 33%, the losing rate is 67%, and the draw rate is 0%.\n- If GoodGuy has a Queen (25% probability), he will likely fold. Therefore, the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy has a Jack (25% probability), he will likely fold. Therefore, the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot. Therefore, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips. If I lose, the losing payoff would be 1 chip.\n- Plan 2: If I win, the winning payoff would be 5 chips. If I lose, the losing payoff would be 2 chips.\n- Plan 3: If I lose, the losing payoff would be 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: (33% * 3) - (67% * 1) = 0.33 chips\n- Plan 2: (67% * 5) - (33% * 2) = 2.67 chips\n- Plan 3: 0 - (100% * 1) = -1 chip\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain, so I should choose to raise."}}
{"message": "", "21_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (100% probability), he will call my raise (100% probability). I will lose this round (100% probability) as his King matches the public card. \n- If GoodGuy holds a Queen or Jack (0% probability), he will fold if he sees my raise (100% probability). I will win this round (100% probability) as his card does not match the public card and is lower than my Queen. \n- Overall, my winning rate for this plan is 0%, my losing rate is 100%, and my drawing rate is 0%. \n\nPlan 2: Fold\n- If GoodGuy holds a King (100% probability), he will win this round (100% probability) as his King matches the public card. \n- If GoodGuy holds a Queen or Jack (0% probability), he will win this round (100% probability) as his card does not match the public card and is lower than my Queen. \n- Overall, my winning rate for this plan is 0%, my losing rate is 100%, and my drawing rate is 0%. \n\nPlan 3: Check\n- If GoodGuy holds a King (100% probability), he will raise (100% probability). I will lose this round (100% probability) as his King matches the public card. \n- If GoodGuy holds a Queen or Jack (0% probability), he will fold if he sees my raise (100% probability). I will win this round (100% probability) as his card does not match the public card and is lower than my Queen. \n- Overall, my winning rate for this plan 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 win, the winning payoff would be 4 chips (half of the total pot). If lose, the losing payoff would be 4 chips (half of the total pot).\n- Plan 2: If win, the winning payoff would be 4 chips (half of the total pot). If lose, the losing payoff would be 4 chips (half of the total pot).\n- Plan 3: If win, the winning payoff would be 4 chips (half of the total pot). If lose, the losing payoff would be 4 chips (half of the total pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0% * 4 chips - 100% * 4 chips = -4 chips\n- Plan 2: Expected Chips Gain = 0% * 4 chips - 100% * 4 chips = -4 chips\n- Plan 3: Expected Chips Gain = 0% * 4 chips - 100% * 4 chips = -4 chips\n\nPlan Selection:\nAll three plans have the same expected chips gain of -4 chips. However, considering the strategy improvement, I should choose Plan 1: Raise, as this may cause GoodGuy to fold if he holds a Queen or Jack in future rounds."}}
{"message": "", "21_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (80% probability), he will likely call (100% probability). If he calls, I will lose this round as his pair of Kings beats my single Queen. The lose rate for this plan is 80%.\n- If GoodGuy holds a Queen (10% probability), he will likely fold (100% probability). If he folds, I will win this round as my single Queen beats his fold. The win rate for this plan is 10%.\n- If GoodGuy holds a Jack (10% probability), he will likely fold (100% probability). If he folds, I will win this round as my single Queen beats his fold. The win rate for this plan is 10%.\n\nPlan 2: Fold\n- If GoodGuy holds a King (80% probability), I will lose this round as I have folded. The lose rate for this plan is 80%.\n- If GoodGuy holds a Queen (10% probability), I will lose this round as I have folded. The lose rate for this plan is 10%.\n- If GoodGuy holds a Jack (10% probability), I will lose this round as I have folded. The lose rate for this plan is 10%.\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 24. If win, the winning payoff would be 12. If lose, the lose payoff would be 12.\n- Plan 2: After the fold action, 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 = 20% * 12 - 80% * 12 = -7.2\n- Plan 2: Expected Chips Gain = 0% * 10 - 100% * 10 = -10\n\nPlan Selection:\nBased on the estimated expected chips gains, Plan 1 (Call) is the better strategy as it has a higher expected chips gain (-7.2) compared to Plan 2 (Fold) which has an expected chips gain of -10. Therefore, I should choose to call."}}
{"message": "", "23_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (35% chance), he will likely raise (70%) or call (30%). If he raises, I will lose unless the public card is a Queen. If he calls, I will win if the public card is a Queen or Jack, and lose if it is a King. Overall, my winning rate is 35% * (70% * 33% + 30% * 67%) = 16.45%, my losing rate is 35% * (70% * 67% + 30% * 33%) = 18.55%, and my draw rate is 0%.\n- If GoodGuy holds a Queen (35% chance), he will likely fold (70%) or call (30%). If he folds, I will win. If he calls, I will win if the public card is a Jack, lose if it is a King, and draw if it is a Queen. Overall, my winning rate is 35% * (70% + 30% * 33%) = 27.05%, my losing rate is 35% * (30% * 33%) = 3.465%, and my draw rate is 35% * (30% * 33%) = 3.465%.\n- If GoodGuy holds a Jack (30% chance), he will likely fold (90%) or call (10%). If he folds, I will win. If he calls, I will win if the public card is a Queen or King, and lose if it is a Jack. Overall, my winning rate is 30% * (90% + 10% * 67%) = 27.6%, my losing rate is 30% * (10% * 33%) = 0.99%, and my draw rate is 0%.\n\nPlan 1 overall Winning/Lose/Draw rates: Winning rate = 16.45% + 27.05% + 27.6% = 71.1%, Losing rate = 18.55% + 3.465% + 0.99% = 23.005%, Draw rate = 0% + 3.465% + 0% = 3.465%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (35% chance), he will likely call (80%) or fold (20%). If he calls, I will lose unless the public card is a Queen. If he folds, I will win. Overall, my winning rate is 35% * (20% + 80% * 33%) = 14.6%, my losing rate is 35% * (80% * 67%) = 18.76%, and my draw rate is 0%.\n- If GoodGuy holds a Queen (35% chance), he will likely fold (70%) or call (30%). If he folds, I will win. If he calls, I will win if the public card is a Jack, lose if it is a King, and draw if it is a Queen. Overall, my winning rate is 35% * (70% + 30% * 33%) = 27.05%, my losing rate is 35% * (30% * 33%) = 3.465%, and my draw rate is 35% * (30% * 33%) = 3.465%.\n- If GoodGuy holds a Jack (30% chance), he will likely fold (90%) or call (10%). If he folds, I will win. If he calls, I will win if the public card is a Queen or King, and lose if it is a Jack. Overall, my winning rate is 30% * (90% + 10% * 67%) = 27.6%, my losing rate is 30% * (10% * 33%) = 0.99%, and my draw rate is 0%.\n\nPlan 2 overall Winning/Lose/Draw rates: Winning rate = 14.6% + 27.05% + 27.6% = 69.25%, Losing rate = 18.76% + 3.465% + 0.99% = 23.215%, Draw rate = 0% + 3.465% + 0% = 3.465%.\n\nPlan 3: Fold\n- If I fold, I will lose the 1 chip I have already put in the pot. My winning rate is 0%, my losing rate is 100%, and my draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips (half of the total pot of 6 chips). If I lose, the lose payoff would be 1 chip (half of the total pot of 2 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 lose, the lose payoff would be 1 chip (half of the total pot of 2 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Lose Payoff = 71.1% * 3 - 23.005% * 1 = 1.635 chips.\n- Plan 2: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Lose Payoff = 69.25% * 5 - 23.215% * 3 = 2.4425 chips.\n- Plan 3: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Lose Payoff = 0% * 0 - 100% * 1 = -1 chip.\n\nPlan Selection:\n- Plan 1: 1.635 chips\n- Plan 2: 2.4425 chips\n- Plan 3: -1 chip\n\nThe rank of estimated expected chips gains for every plan is Plan 2 > Plan 1 > Plan 3. Therefore, I should execute Plan 2: Raise."}}
{"message": "", "23_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (80% probability), he will likely raise (90% probability) or call (10% probability). If he raises, I will lose (probability = 0.8 * 0.9 = 0.72). If he calls, I have a chance to win if the next public card is a Queen (probability = 0.8 * 0.1 * 0.25 = 0.02), otherwise I will lose (probability = 0.8 * 0.1 * 0.75 = 0.06).\n- If GoodGuy holds a Queen (20% probability), he will likely fold (70% probability) or call (30% probability). If he folds, I will win (probability = 0.2 * 0.7 = 0.14). If he calls, I have a chance to win if the next public card is a Queen (probability = 0.2 * 0.3 * 0.25 = 0.015), otherwise I will lose (probability = 0.2 * 0.3 * 0.75 = 0.045).\n- If GoodGuy holds a Jack (0% probability), he will likely fold (90% probability) or call (10% probability). If he folds, I will win (probability = 0). If he calls, I have a chance to win if the next public card is a Queen (probability = 0), otherwise I will lose (probability = 0).\n- Overall, the winning rate for plan 1 is 0.02 + 0.14 + 0 = 0.16, the losing rate is 0.72 + 0.06 + 0.045 + 0 = 0.825, and the draw rate is 0.015 + 0 = 0.015.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of GoodGuy's card or action. The losing rate is 1.\n\nPlan 3: Check\n- If GoodGuy holds a King (80% probability), he will likely raise (90% probability) or call (10% probability). If he raises, I will lose (probability = 0.8 * 0.9 = 0.72). If he calls, I have a chance to win if the next public card is a Queen (probability = 0.8 * 0.1 * 0.25 = 0.02), otherwise I will lose (probability = 0.8 * 0.1 * 0.75 = 0.06).\n- If GoodGuy holds a Queen (20% probability), he will likely fold (70% probability) or call (30% probability). If he folds, I will win (probability = 0.2 * 0.7 = 0.14). If he calls, I have a chance to win if the next public card is a Queen (probability = 0.2 * 0.3 * 0.25 = 0.015), otherwise I will lose (probability = 0.2 * 0.3 * 0.75 = 0.045).\n- If GoodGuy holds a Jack (0% probability), he will likely fold (90% probability) or call (10% probability). If he folds, I will win (probability = 0). If he calls, I have a chance to win if the next public card is a Queen (probability = 0), otherwise I will lose (probability = 0).\n- Overall, the winning rate for plan 3 is 0.02 + 0.14 + 0 = 0.16, the losing rate is 0.72 + 0.06 + 0.045 + 0 = 0.825, and the draw rate is 0.015 + 0 = 0.015.\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 (8 chips). If 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 = 0.16 * 8 - 0.825 * 8 = -5.32 chips\n- Plan 2: Expected Chips Gain = -1 * 4 = -4 chips\n- Plan 3: Expected Chips Gain = 0.16 * 8 - 0.825 * 8 = -5.32 chips\n\nPlan Selection:\n- Plan 2 (Fold) has the highest estimated expected chips gain (-4 chips), so I will choose this plan."}}
{"message": "", "24_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (90% probability), he will likely raise in the second round if the public card is a King (33.3% probability). If I call, I will lose (0% win, 100% lose, 0% draw). If the public card is not a King, he will check, and I will win if the public card is a Queen (33.3% probability) or lose if it is a Jack (33.3% probability). \n- If GoodGuy holds a Queen (5% probability) or a Jack (5% probability), he will likely fold in the second round if the public card is not a Queen or a Jack respectively. I will win in these cases. \n\nPlan 2: Raise\n- If GoodGuy holds a King (90% probability), he will likely call in the first round. In the second round, if the public card is a King, he will raise and I will lose (0% win, 100% lose, 0% draw). If the public card is not a King, he will check, and I will win if the public card is a Queen (33.3% probability) or lose if it is a Jack (33.3% probability). \n- If GoodGuy holds a Queen (5% probability) or a Jack (5% probability), he will likely fold in the first round if I raise. I will win in these cases. \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 win, the winning payoff would be half of the total pot (6 chips). If lose, the lose payoff would be half of the total pot (6 chips).\n- Plan 2: If 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 3: If I fold, I will lose the chips I have already put in the pot (2 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.9 * 0.333 * 6 - 0.9 * 0.667 * 6 + 0.1 * 6 = -1.8 chips\n- Plan 2: Expected Chips Gain = 0.9 * 0.333 * 8 - 0.9 * 0.667 * 8 + 0.1 * 8 = -2.4 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain (-1.8 chips), followed by Plan 3 (-2 chips), and Plan 2 (-2.4 chips). Therefore, I should choose Plan 1: Call."}}
{"message": "", "24_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (80% probability), he will likely fold (100% probability) as per his game pattern. This results in a win for me (80% * 100% = 80% win rate). \n- If GoodGuy holds a Queen (20% probability), he will likely raise (100% probability) as per his game pattern. This results in a draw for me (20% * 100% = 20% draw rate). \n\nPlan 2: Fold\n- If GoodGuy holds a King (80% probability), he will likely check (100% probability) as per his game pattern. This results in a loss for me (80% * 100% = 80% lose rate). \n- If GoodGuy holds a Queen (20% probability), he will likely raise (100% probability) as per his game pattern. This results in a loss for me (20% * 100% = 20% lose rate). \n\nPlan 3: Check\n- If GoodGuy holds a King (80% probability), he will likely check (100% probability) as per his game pattern. This results in a win for me (80% * 100% = 80% win rate). \n- If GoodGuy holds a Queen (20% probability), he will likely raise (100% probability) as per his game pattern. This results in a draw for me (20% * 100% = 20% draw rate). \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 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- Plan 3: 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\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 80% * 8 - 0% * 8 = 6.4 chips\n- Plan 2: Expected Chips Gain = 0% * 4 - 100% * 4 = -4 chips\n- Plan 3: Expected Chips Gain = 80% * 8 - 0% * 8 = 6.4 chips\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows:\n1. Plan 1 and Plan 3 (6.4 chips)\n2. Plan 2 (-4 chips)\n\nTherefore, I should select either Plan 1 (Raise) or Plan 3 (Check) as they both have the highest estimated expected chips gain. Considering the strategy improvement, I should choose to raise (Plan 1) to potentially confuse GoodGuy and gain an advantage in future rounds."}}
{"message": "", "24_5": {"plan": "Plan 1: 'Call'\n- If GoodGuy holds a King (0% probability), he will likely fold (100% probability). I will win (100% probability) as my Queen matches the public card. Overall winning rate for his King is 0% (0% * 100%).\n- If GoodGuy holds a Queen (20% probability), he will likely call (100% probability). It will be a draw (100% probability) as we both have Queens. Overall draw rate for his Queen is 20% (20% * 100%).\n- If GoodGuy holds a Jack (80% probability), he will likely fold (100% probability). I will win (100% probability) as my Queen matches the public card. Overall winning rate for his Jack is 80% (80% * 100%).\n\nPlan 1 overall Winning/Lose/Draw rates: Winning rate for plan 1 is 80% (0% + 80%); Lose rate for plan 1 is 0%; Draw Rate for plan 1 is 20% (20%).\n\nPlan 2: 'Fold'\n- If GoodGuy holds a King (0% probability), he will likely fold (100% probability). It will be a draw (100% probability) as I have folded. Overall draw rate for his King is 0% (0% * 100%).\n- If GoodGuy holds a Queen (20% probability), he will likely call (100% probability). I will lose (100% probability) as I have folded. Overall lose rate for his Queen is 20% (20% * 100%).\n- If GoodGuy holds a Jack (80% probability), he will likely fold (100% probability). It will be a draw (100% probability) as I have folded. Overall draw rate for his Jack is 80% (80% * 100%).\n\nPlan 2 overall Winning/Lose/Draw rates: Winning rate for plan 2 is 0%; Lose rate for plan 2 is 20% (20%); Draw Rate for plan 2 is 80% (0% + 80%).\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 24. If win, the winning payoff would be 12 (half of the total pot). If lose, the lose payoff would be 12.\n- Plan 2: After the 'fold' 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\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Lose rate * Lose Payoff = 80% * 12 - 0% * 12 = 9.6 chips\n- Plan 2: Expected Chips Gain = Winning rate * Winning Payoff - Lose rate * Lose Payoff = 0% * 10 - 20% * 10 = -2 chips\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows: Plan 1 (9.6 chips) > Plan 2 (-2 chips). Therefore, the plan with the highest estimated expected chips gain is Plan 1: 'Call'."}}
{"message": "", "25_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a Queen (50% probability), he will likely raise (100% probability). If the public card is a Queen, I will win (50% probability). If the public card is a King or Jack, I will draw (50% probability). Overall, the winning rate is 25%, the losing rate is 0%, and the draw rate is 25%.\n- If GoodGuy holds a Jack (50% probability), he will likely fold (100% probability). If the public card is a Queen, I will win (50% probability). If the public card is a King, I will lose (50% probability). Overall, the winning rate is 25%, the losing rate is 25%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a Queen (50% probability), he will likely fold (50% probability) or call (50% probability). If the public card is a Queen, I will win (50% probability). If the public card is a King or Jack, I will draw (50% probability). Overall, the winning rate is 25%, the losing rate is 0%, and the draw rate is 25%.\n- If GoodGuy holds a Jack (50% probability), he will likely fold (100% probability). If the public card is a Queen, I will win (50% probability). If the public card is a King, I will lose (50% probability). Overall, the winning rate is 25%, the losing rate is 25%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of GoodGuy's cards or the public card. The losing rate is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 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 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.25 * 3 - 0.25 * 3 = 0 chips\n- Plan 2: Expected Chips Gain = 0.25 * 5 - 0.25 * 5 = 0 chips\n- Plan 3: Expected Chips Gain = -1 chip\n\nPlan Selection:\n- Plan 1 and Plan 2 both have an expected chips gain of 0, while Plan 3 has a negative expected chips gain. Therefore, Plan 1 and Plan 2 are ranked higher than Plan 3. Considering the strategy improvement, I should select Plan 2 (Raise) as it puts more pressure on GoodGuy and has a higher potential payoff."}}
{"message": "", "25_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (50% probability), he will likely raise (50% probability) or check (50% probability). If he raises, I will lose (probability = 0.5 * 0.5 = 0.25). If he checks, I will win (probability = 0.5 * 0.5 = 0.25).\n- If GoodGuy holds a Queen (50% probability), he will likely fold (100% probability). If he folds, I will win (probability = 0.5 * 1 = 0.5).\n\nPlan 2: Fold\n- If GoodGuy holds a King (50% probability), I will lose (probability = 0.5).\n- If GoodGuy holds a Queen (50% probability), I will lose (probability = 0.5).\n\nPlan 3: Check\n- If GoodGuy holds a King (50% probability), he will likely raise (50% probability) or check (50% probability). If he raises, I will lose (probability = 0.5 * 0.5 = 0.25). If he checks, I will win (probability = 0.5 * 0.5 = 0.25).\n- If GoodGuy holds a Queen (50% probability), he will likely fold (100% probability). If he folds, I will win (probability = 0.5 * 1 = 0.5).\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 win, the winning payoff would be 0 chips (no change). If lose, the lose payoff would be 0 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 = 0.75 * 4 - 0.25 * 4 = 2 chips\n- Plan 2: Expected Chips Gain = 0 * 0 - 1 * 0 = 0 chips\n- Plan 3: Expected Chips Gain = 0.75 * 4 - 0.25 * 4 = 2 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 have the highest expected chips gain (2 chips), so I should choose either of these plans. Considering the strategy improvement, I should choose Plan 1 (Raise) to pressure GoodGuy into folding if he holds a Queen."}}
{"message": "", "26_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he will likely call (80% probability) if he sees me call. If the public card is a King, I will lose (100% probability). If the public card is a Queen or Jack, I will win (50% probability) or draw (50% probability). Overall, the winning rate is 35%, the losing rate is 70%, and the draw rate is 35%.\n- If GoodGuy holds a Queen (20% probability), he will likely call (50% probability) if he sees me call. If the public card is a Queen, I will lose (100% probability). If the public card is a King or Jack, I will win (50% probability) or draw (50% probability). Overall, the winning rate is 10%, the losing rate is 20%, and the draw rate is 10%.\n- If GoodGuy holds a Jack (10% probability), he will likely call (20% probability) if he sees me call. If the public card is a Jack, I will draw (100% probability). If the public card is a King or Queen, I will lose (100% probability). Overall, the winning rate is 0%, the losing rate is 10%, and the draw rate is 10%.\n\nPlan 1 overall Winning/Lose/Draw rates: Winning rate is 45%, Losing rate is 100%, Draw rate is 55%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (70% probability), he will likely call (80% probability) if he sees me raise. If the public card is a King, I will lose (100% probability). If the public card is a Queen or Jack, I will win (50% probability) or draw (50% probability). Overall, the winning rate is 35%, the losing rate is 70%, and the draw rate is 35%.\n- If GoodGuy holds a Queen (20% probability), he will likely fold (50% probability) if he sees me raise. If he folds, I will win (100% probability). Overall, the winning rate is 10%, the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (10% probability), he will likely fold (80% probability) if he sees me raise. If he folds, I will win (100% probability). Overall, the winning rate is 8%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2 overall Winning/Lose/Draw rates: Winning rate is 53%, Losing rate is 70%, Draw rate is 35%.\n\nPlan 3: Fold\n- If I fold, I will lose (100% probability). Overall, the winning rate is 0%, the losing rate is 100%, and the 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 win, the winning payoff would be 8 chips. If lose, the lose payoff would be 8 chips.\n- Plan 3: If lose, the lose payoff would be 2 chips.\n\nEstimated Expected Chips Gain for Each Plan:\n- Plan 1: 45% * 4 - 100% * 4 = -2.2 chips\n- Plan 2: 53% * 8 - 70% * 8 = -1.36 chips\n- Plan 3: 0% * 0 - 100% * 2 = -2 chips\n\nPlan Selection:\n- Plan 2 has the highest estimated expected chips gain, so I will choose Plan 2: Raise."}}
{"message": "", "26_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (70% probability), he will likely check (60% probability) or fold (40% probability). If he checks, I will lose (as a King is higher than a Jack). If he folds, I will win. The overall winning rate is 0.7*0.4=0.28, the losing rate is 0.7*0.6=0.42, and the draw rate is 0.\n- If GoodGuy holds a Queen (30% probability), he will likely check (70% probability) or fold (30% probability). If he checks, I will lose (as a Queen is higher than a Jack). If he folds, I will win. The overall winning rate is 0.3*0.3=0.09, the losing rate is 0.3*0.7=0.21, and the draw rate is 0.\n- If GoodGuy holds a Jack (10% probability), he will likely check (80% probability) or fold (20% probability). If he checks, it will be a draw (as we both hold a Jack). If he folds, I will win. The overall winning rate is 0.1*0.2=0.02, the losing rate is 0, and the draw rate is 0.1*0.8=0.08.\n- The total pot after raising would be 16 chips. If I win, the winning payoff would be 8 chips. If I lose, the lose payoff would be 8 chips. The expected chips gain for this plan is winning rate * winning payoff - losing rate * losing payoff = 0.39*8 - 0.63*8 = -1.92 chips.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. The winning rate is 0, the losing rate is 1, and the draw rate is 0.\n- The total pot after folding would be 12 chips. If I lose, the lose payoff would be 6 chips. The expected chips gain for this plan is -6 chips.\n\nPlan 3: Check\n- If GoodGuy holds a King (70% probability), he will likely check (60% probability) or fold (40% probability). If he checks, I will lose (as a King is higher than a Jack). If he folds, I will win. The overall winning rate is 0.7*0.4=0.28, the losing rate is 0.7*0.6=0.42, and the draw rate is 0.\n- If GoodGuy holds a Queen (30% probability), he will likely check (70% probability) or fold (30% probability). If he checks, I will lose (as a Queen is higher than a Jack). If he folds, I will win. The overall winning rate is 0.3*0.3=0.09, the losing rate is 0.3*0.7=0.21, and the draw rate is 0.\n- If GoodGuy holds a Jack (10% probability), he will likely check (80% probability) or fold (20% probability). If he checks, it will be a draw (as we both hold a Jack). If he folds, I will win. The overall winning rate is 0.1*0.2=0.02, the losing rate is 0, and the draw rate is 0.1*0.8=0.08.\n- The total pot after checking would be 12 chips. If I win, the winning payoff would be 6 chips. If I lose, the lose payoff would be 6 chips. The expected chips gain for this plan is winning rate * winning payoff - losing rate * losing payoff = 0.39*6 - 0.63*6 = -1.44 chips.\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is: Plan 3 > Plan 1 > Plan 2. Therefore, I should choose Plan 3: Check."}}
{"message": "", "26_5": {"plan": "Plan 1: Call\n- If GoodGuy holds a Queen (80% probability), he will likely check (20% probability). If he checks, I will lose (probability = 80% * 20% = 16%). If he raises (80% probability), I will also lose (probability = 80% * 80% = 64%).\n- If GoodGuy holds a King (10% probability), he will likely check (60% probability). If he checks, I will win (probability = 10% * 60% = 6%). If he folds (40% probability), I will also win (probability = 10% * 40% = 4%).\n- If GoodGuy holds a Jack (10% probability), he will likely check (80% probability). If he checks, it will be a draw (probability = 10% * 80% = 8%). If he folds (20% probability), I will win (probability = 10% * 20% = 2%).\n\nPlan 2: Raise\n- If GoodGuy holds a Queen (80% probability), he will likely fold (20% probability). If he folds, I will win (probability = 80% * 20% = 16%). If he calls (80% probability), I will lose (probability = 80% * 80% = 64%).\n- If GoodGuy holds a King (10% probability), he will likely fold (40% probability). If he folds, I will win (probability = 10% * 40% = 4%). If he calls (60% probability), I will win (probability = 10% * 60% = 6%).\n- If GoodGuy holds a Jack (10% probability), he will likely fold (80% probability). If he folds, I will win (probability = 10% * 80% = 8%). If he calls (20% probability), it will be a draw (probability = 10% * 20% = 2%).\n\nPlan 3: Fold\n- If I fold, I will lose all the 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 half of the total pot (16 chips). If I lose, the lose payoff would be half of the total pot (16 chips).\n- Plan 2: If I win, the winning payoff would be half of the total pot (20 chips). If I lose, the lose payoff would be half of the total pot (20 chips).\n- Plan 3: If I fold, I will lose all the chips I have put into the pot (6 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 16 * 0.22 - 16 * 0.80 = -9.52 chips\n- Plan 2: Expected Chips Gain = 20 * 0.28 - 20 * 0.64 = -7.2 chips\n- Plan 3: Expected Chips Gain = -6 chips\n\nPlan Selection:\n- Plan 1: 3rd\n- Plan 2: 2nd\n- Plan 3: 1st\n\nBased on the estimated expected chips gain, the best strategy is to fold (Plan 3). Although this will result in a loss of 6 chips, it minimizes the potential loss compared to calling or raising."}}
{"message": "", "29_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a Jack, he will likely fold (80% probability) or call (20% probability). If he folds, I win by default. If he calls, the outcome will depend on the public card. If the public card is a Jack, I win (100% probability). If the public card is a Queen or King, I lose (100% probability). \n- If GoodGuy holds a Queen, he will likely call (60% probability) or raise (40% probability). If he calls, the outcome will depend on the public card. If the public card is a Jack or Queen, I lose (100% probability). If the public card is a King, I win (100% probability). If he raises, I will have to call or fold in the next round.\n- If GoodGuy holds a King, he will likely raise (70% probability) or call (30% probability). If he raises, I will have to call or fold in the next round. If he calls, the outcome will depend on the public card. If the public card is a Jack or King, I lose (100% probability). If the public card is a Queen, I win (100% probability).\n\nPlan 2: Raise\n- If GoodGuy holds a Jack, he will likely fold (90% probability) or call (10% probability). If he folds, I win by default. If he calls, the outcome will depend on the public card. If the public card is a Jack, I win (100% probability). If the public card is a Queen or King, I lose (100% probability). \n- If GoodGuy holds a Queen, he will likely fold (50% probability) or call (50% probability). If he folds, I win by default. If he calls, the outcome will depend on the public card. If the public card is a Jack or Queen, I lose (100% probability). If the public card is a King, I win (100% probability).\n- If GoodGuy holds a King, he will likely call (60% probability) or raise (40% probability). If he calls, the outcome will depend on the public card. If the public card is a Jack or King, I lose (100% probability). If the public card is a Queen, I win (100% probability). If he raises, I will have to call or fold in the next round.\n\nPlan 3: Fold\n- If I fold, I lose by default, regardless of GoodGuy's card.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips (half of the 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 5 chips (half of the total pot of 10 chips). If I lose, the lose payoff would be 5 chips.\n- Plan 3: If I fold, I lose 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.33*(0.8*3 + 0.2*(-3)) + 0.33*(0.6*(-3) + 0.4*(-5)) + 0.33*(0.7*(-5) + 0.3*(-3)) = -1.32 chips\n- Plan 2: Expected Chips Gain = 0.33*(0.9*5 + 0.1*(-5)) + 0.33*(0.5*5 + 0.5*(-5)) + 0.33*(0.6*(-5) + 0.4*(-7)) = -0.66 chips\n- Plan 3: Expected Chips Gain = -1 chip\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain, so I should choose Plan 2: Raise."}}
{"message": "", "29_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (50% probability), he tends to fold (70% probability) or call (30% probability) in the second round when the public card is a King. Since the public card is a Queen, he will likely call or raise. If he calls, I will lose (100% probability). If he raises, I will lose (100% probability). Overall, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a King (50% probability), he tends to raise (60% probability) or call (40% probability) in the second round, regardless of the public card. If he calls, I will lose (100% probability). If he raises, I will lose (100% probability). Overall, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose the chips I have already put in the pot, but I will not lose any more chips. The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a Queen (50% probability), he tends to fold (70% probability) or call (30% probability) in the second round when the public card is a King. Since the public card is a Queen, he will likely call or raise. If he checks, I will lose (100% probability). If he raises, I will lose (100% probability). Overall, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a King (50% probability), he tends to raise (60% probability) or call (40% probability) in the second round, regardless of the public card. If he checks, I will lose (100% probability). If he raises, I will lose (100% probability). Overall, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips (half of the total pot). If I lose, the losing payoff would be 4 chips.\n- Plan 2: If I fold, I will lose the 4 chips I have already put in the pot.\n- Plan 3: If I check and win, the winning payoff would be 4 chips. If I lose, the losing payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0% * 4 chips - 100% * 4 chips = -4 chips\n- Plan 2: 0% * 0 chips - 100% * 4 chips = -4 chips\n- Plan 3: 0% * 4 chips - 100% * 4 chips = -4 chips\n\nPlan Selection:\nAll three plans have the same expected chips loss of -4 chips. However, considering the strategy improvement, I should choose Plan 2: Fold. This is because folding will prevent me from losing more chips in the future rounds."}}
{"message": "", "30_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (25% chance), he will likely call (80% chance). If the public card is a King, I will win (100% chance). If the public card is not a King, I will win (50% chance) or draw (50% chance). Overall, the winning rate is 25% * 80% * 100% = 20% for a King, and 25% * 80% * 50% = 10% for a non-King.\n- If GoodGuy holds a Queen (50% chance), he will likely fold (50% chance) or call (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 50% * 50% * 50% = 12.5% for a non-Queen.\n- If GoodGuy holds a Jack (25% chance), he will likely fold (80% chance) or call (20% 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 25% * 20% * 50% = 2.5% for a non-Jack.\n- The total chips in the pot would be 4. If I win, the winning payoff would be 2 chips. If I lose, the lose payoff would be 2 chips.\n- The expected chips gain for Plan 1 is (20% + 10% + 12.5% + 2.5%) * 2 - (0% + 0% + 12.5% + 2.5%) * 2 = 0.9 chips.\n\nPlan 2: Raise\n- If GoodGuy holds a King (25% chance), he will likely call (80% chance). If the public card is a King, I will win (100% chance). If the public card is not a King, I will win (50% chance) or draw (50% chance). Overall, the winning rate is 25% * 80% * 100% = 20% for a King, and 25% * 80% * 50% = 10% for a non-King.\n- If GoodGuy holds a Queen (50% chance), he will likely fold (50% chance) or call (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 50% * 50% * 50% = 12.5% for a non-Queen.\n- If GoodGuy holds a Jack (25% chance), he will likely fold (80% chance) or call (20% 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 25% * 20% * 50% = 2.5% for a non-Jack.\n- The total chips in the pot would be 6. If I win, the winning payoff would be 3 chips. If I lose, the lose payoff would be 3 chips.\n- The expected chips gain for Plan 2 is (20% + 10% + 12.5% + 2.5%) * 3 - (0% + 0% + 12.5% + 2.5%) * 3 = 1.35 chips.\n\nPlan Selection: Plan 2 (Raise) has the highest expected chips gain (1.35 chips), so I will choose Plan 2."}}
{"message": "", "30_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (57.14% probability), he will likely call (80% probability). If he calls, I will win because my card has the same rank as his, but the public card does not match his card. Therefore, the winning rate for this plan is 57.14% * 80% = 45.71%.\n- If GoodGuy holds a Queen (35.71% probability), he will likely fold (50% probability). If he folds, I will win because I will have the only remaining hand. Therefore, the winning rate for this plan is 35.71% * 50% = 17.86%.\n- If GoodGuy holds a Jack (7.14% probability), he will likely call (20% probability). If he calls, I will lose because the public card matches his card. Therefore, the losing rate for this plan is 7.14% * 20% = 1.43%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. Therefore, the losing rate for this plan is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (57.14% probability), he will likely check (60% probability). If he checks, I will win because my card has the same rank as his, but the public card does not match his card. Therefore, the winning rate for this plan is 57.14% * 60% = 34.29%.\n- If GoodGuy holds a Queen (35.71% probability), he will likely check (70% probability). If he checks, I will win because my card has a higher rank than his. Therefore, the winning rate for this plan is 35.71% * 70% = 25%.\n- If GoodGuy holds a Jack (7.14% probability), he will likely check (80% probability). If he checks, I will lose because the public card matches his card. Therefore, the losing rate for this plan is 7.14% * 80% = 5.71%.\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, which would be 4 chips. If I lose, the losing payoff would be half of the total pot, which would be 4 chips.\n- Plan 2: If I fold, I will lose 4 chips.\n- Plan 3: If I win, the winning payoff would be half of the total pot, which would be 4 chips. If I lose, the losing payoff would be half of the total pot, which would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is 45.71% * 4 chips - 1.43% * 4 chips = 1.77 chips.\n- Plan 2: The expected chips gain is -4 chips.\n- Plan 3: The expected chips gain is 34.29% * 4 chips - 5.71% * 4 chips = 1.14 chips.\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows:\n1. Plan 1: 1.77 chips\n2. Plan 3: 1.14 chips\n3. Plan 2: -4 chips\n\nTherefore, I should select Plan 1, which is to raise the bet."}}
{"message": "", "32_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Jack, he will likely fold (70% probability) or call (30% probability). If he folds, I win the pot. If he calls, I have a high chance of winning unless the public card is a Jack. The overall winning rate is 70% (probability he folds) + 30% (probability he calls) * 66.67% (probability the public card is not a Jack) = 90%.\n- If GoodGuy holds a Queen, he will likely call (60% probability) or fold (40% probability). If he folds, I win the pot. If he calls, I have a high chance of winning unless the public card is a Queen. The overall winning rate is 40% (probability he folds) + 60% (probability he calls) * 66.67% (probability the public card is not a Queen) = 80%.\n- If GoodGuy holds a King, he will likely call (60% probability) or raise (40% probability). If he raises, I have a 50% chance of winning unless the public card is a King. The overall winning rate is 60% (probability he calls) * 50% (probability the public card is not a King) = 30%.\n\nPlan 2: Fold\n- If I fold, I lose the pot regardless of what card GoodGuy holds. The overall winning rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a Jack, he will likely fold (60% probability) or call (40% probability). If he folds, I win the pot. If he calls, I have a high chance of winning unless the public card is a Jack. The overall winning rate is 60% (probability he folds) + 40% (probability he calls) * 66.67% (probability the public card is not a Jack) = 86.67%.\n- If GoodGuy holds a Queen, he will likely call (50% probability) or raise (50% probability). If he raises, I have a 50% chance of winning unless the public card is a Queen. The overall winning rate is 50% (probability he calls) * 50% (probability the public card is not a Queen) = 25%.\n- If GoodGuy holds a King, he will likely raise (70% probability) or call (30% probability). If he raises, I have a 50% chance of winning unless the public card is a King. The overall winning rate is 30% (probability he calls) * 50% (probability the public card is not a King) = 15%.\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 of 12 chips). If I lose, the losing payoff would be 6 chips.\n- Plan 2: If I fold, I lose the pot of 4 chips.\n- Plan 3: If I win, the winning payoff would be 4 chips (half of the total pot of 8 chips). If I lose, the losing payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 90% * 6 - 10% * 6 = 4.8 chips\n- Plan 2: Expected Chips Gain = 0% * 0 - 100% * 4 = -4 chips\n- Plan 3: Expected Chips Gain = 42.22% * 4 - 57.78% * 4 = -0.6222 chips\n\nPlan Selection:\n- Plan 1: Raise (Expected Chips Gain = 4.8 chips)\n- Plan 3: Check (Expected Chips Gain = -0.6222 chips)\n- Plan 2: Fold (Expected Chips Gain = -4 chips)\n\nBased on the expected chips gain, I should choose Plan 1: Raise."}}
{"message": "", "33_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a Jack (10% chance), he will likely fold (80% chance). If the public card is a Jack, I win (100% chance). If the public card is a Queen or King, it's a draw (100% chance). Overall, the winning rate is 8%, the losing rate is 0%, and the draw rate is 2%.\n- If GoodGuy holds a Queen (45% chance), he will likely fold (50% chance) or call (50% chance). If the public card is a Jack, I win (100% chance). If the public card is a Queen, I lose (100% chance). If the public card is a King, I win (100% chance). Overall, the winning rate is 22.5%, the losing rate is 22.5%, and the draw rate is 0%.\n- If GoodGuy holds a King (45% chance), he will likely call (70% chance) or raise (30% chance). If the public card is a Jack, I win (100% chance). If the public card is a Queen or King, I lose (100% chance). Overall, the winning rate is 13.5%, the losing rate is 31.5%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a Jack (10% chance), he will likely fold (80% chance). If the public card is a Jack, I win (100% chance). If the public card is a Queen or King, it's a draw (100% chance). Overall, the winning rate is 8%, the losing rate is 0%, and the draw rate is 2%.\n- If GoodGuy holds a Queen (45% chance), he will likely fold (50% chance) or call (50% chance). If the public card is a Jack, I win (100% chance). If the public card is a Queen, I lose (100% chance). If the public card is a King, I win (100% chance). Overall, the winning rate is 22.5%, the losing rate is 22.5%, and the draw rate is 0%.\n- If GoodGuy holds a King (45% chance), he will likely call (70% chance) or raise (30% chance). If the public card is a Jack, I win (100% chance). If the public card is a Queen or King, I lose (100% chance). Overall, the winning rate is 13.5%, the losing rate is 31.5%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I lose the game regardless of GoodGuy's card or the public card. The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips. 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 lose 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.44 * 3 - 0.54 * 3 = -0.3 chips\n- Plan 2: Expected Chips Gain = 0.44 * 7 - 0.54 * 7 = -0.7 chips\n- Plan 3: Expected Chips Gain = -1 chip\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I should choose Plan 1: Call."}}
{"message": "", "33_2": {"plan": "Plan 1: Call\n- If GoodGuy holds a Jack (10% chance), he will likely fold (80% chance). If he folds, I will win the game. So, the winning rate for his Jack is 0.1 * 0.8 = 0.08. The lose rate and draw rate are both 0.\n- If GoodGuy holds a Queen (30% chance), he will likely fold (50% chance) or call (50% chance). If he folds, I will win the game. If he calls, the game result will depend on the public card. So, the winning rate for his Queen is 0.3 * 0.5 = 0.15. The lose rate and draw rate are both 0.\n- If GoodGuy holds a King (60% chance), he will likely call (70% chance) or raise (30% chance). If he calls, the game result will depend on the public card. If he raises, I will lose the game. So, the winning rate for his King is 0. The lose rate is 0.6 * 0.3 = 0.18. The draw rate is 0.\n- Overall, the winning rate for plan 1 is 0.08 + 0.15 = 0.23. The lose rate is 0.18. The draw rate is 0.\n\nPlan 2: Raise\n- If GoodGuy holds a Jack (10% chance), he will likely fold (80% chance). If he folds, I will win the game. So, the winning rate for his Jack is 0.1 * 0.8 = 0.08. The lose rate and draw rate are both 0.\n- If GoodGuy holds a Queen (30% chance), he will likely fold (50% chance) or call (50% chance). If he folds, I will win the game. If he calls, the game result will depend on the public card. So, the winning rate for his Queen is 0.3 * 0.5 = 0.15. The lose rate and draw rate are both 0.\n- If GoodGuy holds a King (60% chance), he will likely call (70% chance) or raise (30% chance). If he calls, the game result will depend on the public card. If he raises, I will lose the game. So, the winning rate for his King is 0. The lose rate is 0.6 * 0.3 = 0.18. The draw rate is 0.\n- Overall, the winning rate for plan 2 is 0.08 + 0.15 = 0.23. The lose rate is 0.18. The draw rate is 0.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card. So, the winning rate, lose rate, and draw rate are all 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, which is (2+4+4)/2 = 5 chips. If I lose, the lose payoff would be half of the total pot, which is (2+4+4)/2 = 5 chips.\n- Plan 2: If I win, the winning payoff would be half of the total pot, which is (2+4+8)/2 = 7 chips. If I lose, the lose payoff would be half of the total pot, which is (2+4+8)/2 = 7 chips.\n- Plan 3: If I fold, I will lose 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is winning rate * winning payoff - lose rate * lose payoff = 0.23 * 5 - 0.18 * 5 = 0.25 chips.\n- Plan 2: The expected chips gain is 0.23 * 7 - 0.18 * 7 = 0.35 chips.\n- Plan 3: The expected chips gain is -2 chips.\n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 2 > Plan 1 > Plan 3.\n- Therefore, I should choose Plan 2: Raise."}}
{"message": "", "33_4": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (70% probability), he will likely call (60%) or raise (40%). If he calls, I will win as my Jack matches the public card. If he raises, I will still win as my Jack matches the public card. Therefore, the winning rate for this plan is 100%.\n- If GoodGuy holds a Queen (30% probability), he will likely fold (70%) or call (30%). If he folds, I will win. If he calls, I will still win as my Jack matches the public card. Therefore, the winning rate for this plan is also 100%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. Therefore, the losing rate for this plan is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (70% probability), he will likely call (60%) or raise (40%). If he calls, I will win as my Jack matches the public card. If he raises, I will still win as my Jack matches the public card. Therefore, the winning rate for this plan is 100%.\n- If GoodGuy holds a Queen (30% probability), he will likely fold (70%) or call (30%). If he folds, I will win. If he calls, I will still win as my Jack matches the public card. 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 12 chips, so 6 chips). If I lose, the losing payoff would be half of the total pot (currently 12 chips, so 6 chips).\n- Plan 2: If I fold, I will lose and the losing payoff would be half of the total pot (currently 12 chips, so 6 chips).\n- Plan 3: 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 (currently 12 chips, so 6 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning Rate * Winning Payoff - Losing Rate * Losing Payoff = 100% * 6 chips - 0% * 6 chips = 6 chips\n- Plan 2: Expected Chips Gain = Winning Rate * Winning Payoff - Losing Rate * Losing Payoff = 0% * 6 chips - 100% * 6 chips = -6 chips\n- Plan 3: Expected Chips Gain = Winning Rate * Winning Payoff - Losing Rate * Losing Payoff = 100% * 6 chips - 0% * 6 chips = 6 chips\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows:\n1. Plan 1: Raise (6 chips)\n2. Plan 3: Check (6 chips)\n3. Plan 2: Fold (-6 chips)\n\nTherefore, I should choose Plan 1: Raise, as it has the highest estimated expected chips gain."}}
{"message": "", "34_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a Jack (20% probability), he will likely fold (80% probability). If he folds, I win. If he calls (20% probability), I have a higher card and I win. So, the winning rate for this plan is 100%.\n- If GoodGuy holds a Queen (40% probability), we have the same card. It will be a draw unless the public card is a Queen. In this case, the winning rate is 0%, the draw rate is 100%.\n- If GoodGuy holds a King (40% probability), he will likely raise (70% probability) or call (30% probability). If he raises, I will lose. If he calls, the outcome will depend on the public card. If the public card is a Queen, I win. If the public card is a King or Jack, I lose. So, the winning rate for this plan is 30%, the losing rate is 70%.\n\nPlan 2: Raise\n- If GoodGuy holds a Jack (20% probability), he will likely fold (90% probability). If he folds, I win. If he calls (10% probability), I have a higher card and I win. So, the winning rate for this plan is 100%.\n- If GoodGuy holds a Queen (40% probability), he will likely fold (70% probability). If he folds, I win. If he calls (30% probability), it will be a draw unless the public card is a Queen. In this case, the winning rate is 70%, the draw rate is 30%.\n- If GoodGuy holds a King (40% probability), he will likely call (60% probability) or raise (40% probability). If he calls, the outcome will depend on the public card. If the public card is a Queen, I win. If the public card is a King or Jack, I lose. So, the winning rate for this plan is 60%, the losing rate is 40%.\n\nPlan 3: Fold\n- If I fold, I lose regardless of GoodGuy's card. So, the losing rate for this plan is 100%.\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 1 chip (half of the total pot of 2 chips).\n- Plan 2: If win, the winning payoff would be 5 chips (half of the total pot of 10 chips). If lose, the lose payoff would be 3 chips (half of the total pot of 6 chips).\n- Plan 3: If lose, the lose payoff would be 1 chip (half of the total pot of 2 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 100% * 3 chips - 70% * 1 chip = 2.3 chips\n- Plan 2: Expected Chips Gain = 100% * 5 chips - 40% * 3 chips = 3.8 chips\n- Plan 3: Expected Chips Gain = 0% * 0 chips - 100% * 1 chip = -1 chip\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain (3.8 chips), followed by Plan 1 (Call) with 2.3 chips, and Plan 3 (Fold) with -1 chip. Therefore, I should choose Plan 2: Raise."}}
{"message": "", "34_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (60% probability), he will likely call (60% probability) or raise (40% probability). If he calls, I will lose as his King is higher than my Queen. If he raises, I will also lose. So, the overall losing rate for this plan is 60%.\n- If GoodGuy holds a Queen (30% probability), it will be a draw as we both have Queens. So, the overall draw rate for this plan is 30%.\n- If GoodGuy holds a Jack (10% probability), he will likely fold (100% probability) as his Jack is lower than my Queen. So, the overall winning rate for this plan is 10%.\n\nPlan 2: Fold\n- If I fold, I will lose the chips I have already put into the pot. The overall losing rate for this plan is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (60% probability), he will likely raise (60% probability) or call (40% probability). If he raises, I will lose as his King is higher than my Queen. If he calls, I will also lose. So, the overall losing rate for this plan is 60%.\n- If GoodGuy holds a Queen (30% probability), it will be a draw as we both have Queens. So, the overall draw rate for this plan is 30%.\n- If GoodGuy holds a Jack (10% probability), he will likely fold (100% probability) as his Jack is lower than my Queen. So, the overall winning rate for this plan is 10%.\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 fold, I will lose the chips I have already put into the pot (4 chips).\n- Plan 3: If I win, the winning payoff would be half of the total pot (8 chips). If I lose, the losing payoff would be half of the total pot (8 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 10% * 8 chips - 60% * 8 chips = -4 chips\n- Plan 2: Expected Chips Gain = -4 chips\n- Plan 3: Expected Chips Gain = 10% * 8 chips - 60% * 8 chips = -4 chips\n\nPlan Selection:\n- Plan 1: -4 chips\n- Plan 2: -4 chips\n- Plan 3: -4 chips\n\nAll plans have the same expected chips gain. However, considering the strategy improvement, I should choose Plan 1: Raise. This is because raising can pressure GoodGuy into folding, especially if he holds a Jack or Queen."}}
{"message": "", "35_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (33.3% chance), he will likely raise (70%) or call (30%). If he raises, I will win as we both have Kings. If he calls, the outcome will depend on the public card. Overall, my winning rate is 33.3% * 70% = 23.31%, my losing rate is 0% (as I can't lose if he also holds a King), and my draw rate is 33.3% * 30% = 9.99%.\n- If GoodGuy holds a Queen (33.3% chance), he will likely call (60%) or raise (40%). If he raises, I will win as my King beats his Queen. If he calls, the outcome will depend on the public card. Overall, my winning rate is 33.3% * 40% = 13.32%, my losing rate is 33.3% * 60% = 19.98% (if the public card is a Queen), and my draw rate is 0%.\n- If GoodGuy holds a Jack (33.3% chance), he will likely fold (60%) or call (40%). If he folds, I will win. If he calls, the outcome will depend on the public card. Overall, my winning rate is 33.3% * 60% = 19.98%, my losing rate is 33.3% * 40% = 13.32% (if the public card is a Jack), and my draw rate is 0%.\n\nPlan 1 overall Winning/Lose/Draw rates: Winning rate = 23.31% + 13.32% + 19.98% = 56.61%. Lose rate = 0% + 19.98% + 13.32% = 33.3%. Draw rate = 9.99% + 0% + 0% = 9.99%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (33.3% chance), he will likely call (80%) or raise (20%). If he calls or raises, I will win as we both have Kings. Overall, my winning rate is 33.3% * 100% = 33.3%, my losing rate is 0%, and my draw rate is 0%.\n- If GoodGuy holds a Queen (33.3% chance), he will likely call (70%) or fold (30%). If he calls, I will win as my King beats his Queen. If he folds, I will also win. Overall, my winning rate is 33.3% * 100% = 33.3%, my losing rate is 0%, and my draw rate is 0%.\n- If GoodGuy holds a Jack (33.3% chance), he will likely fold (80%) or call (20%). If he folds or calls, I will win as my King beats his Jack. Overall, my winning rate is 33.3% * 100% = 33.3%, my losing rate is 0%, and my draw rate is 0%.\n\nPlan 2 overall Winning/Lose/Draw rates: Winning rate = 33.3% + 33.3% + 33.3% = 100%. Lose rate = 0% + 0% + 0% = 0%. Draw rate = 0% + 0% + 0% = 0%.\n\nPlan 3: Fold\n- If I fold, I will automatically lose the round regardless of GoodGuy's card. Therefore, my winning rate is 0%, my losing rate is 100%, and my draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (3 chips). If I lose, the losing 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 (6 chips). If I lose, the losing payoff would be half of the total pot (6 chips).\n- Plan 3: If I fold, I will lose 1 chip.\n\nEstimated Expected Chips Gain for Each Plan:\n- Plan 1: 56.61% * 3 - 33.3% * 3 = 0.693 chips\n- Plan 2: 100% * 6 - 0% * 6 = 6 chips\n- Plan 3: 0% * 0 - 100% * 1 = -1 chip\n\nPlan Selection:\n- Plan 2 (Raise) has the highest estimated expected chips gain (6 chips), followed by Plan 1 (Call) with 0.693 chips, and Plan 3 (Fold) with -1 chip. Therefore, I should choose Plan 2 (Raise)."}}
{"message": "", "35_2": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (100% probability), he will likely call (80%) or raise (20%) in the next round. If the public card is a King, we will draw. If the public card is a Queen or Jack, I will win. So, the winning rate is 80%, the draw rate is 20%, and the lose rate is 0%.\n- After the call, all chips in the pot would be 12. If win, the winning payoff would be 6. If lose, the lose payoff would be 6.\n\nPlan 2: Fold\n- If I fold, I will lose this round regardless of GoodGuy's card. So, the winning rate is 0%, the draw rate is 0%, and the lose rate is 100%.\n- After the fold, 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\nExpected Chips Gain for Each Plan:\n- Plan 1: 0.8 * 6 - 0 * 6 = 4.8\n- Plan 2: 0 * 5 - 1 * 5 = -5\n\nPlan Selection:\n- Plan 1 (Call) has the highest expected chips gain (4.8), so I should choose this plan. \n\nPotential GoodGuy's actions:\n- If GoodGuy holds a King (100% probability), he will likely call (80%) or raise (20%) in the next round. If the public card is a King, we will draw. If the public card is a Queen or Jack, I will win. So, the winning rate is 80%, the draw rate is 20%, and the lose rate is 0%."}}
{"message": "", "35_4": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (10% chance), he will likely call (70% chance). This would result in a draw. The overall draw rate for this plan is 7% (10% * 70%).\n- If GoodGuy holds a Queen (45% chance), he will likely call (60% chance) or fold (40% chance). This would result in a win for me. The overall win rate for this plan is 27% (45% * 60%) and the overall lose rate is 18% (45% * 40%).\n- If GoodGuy holds a Jack (45% chance), he will likely fold (90% chance) or call (10% chance). This would result in a win for me. The overall win rate for this plan is 40.5% (45% * 90%) and the overall lose rate is 4.5% (45% * 10%).\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. The overall lose rate for this plan is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (10% chance), he will likely raise (90% chance) or check (10% chance). This would result in a draw. The overall draw rate for this plan is 9% (10% * 90%).\n- If GoodGuy holds a Queen (45% chance), he will likely check (70% chance) or call (30% chance). This would result in a win for me. The overall win rate for this plan is 31.5% (45% * 70%) and the overall lose rate is 13.5% (45% * 30%).\n- If GoodGuy holds a Jack (45% chance), he will likely check (80% chance) or fold (20% chance). This would result in a win for me. The overall win rate for this plan is 36% (45% * 80%) and the overall lose rate is 9% (45% * 20%).\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 lose payoff would be 6 chips.\n- Plan 2: If I lose, the lose payoff would be 6 chips.\n- Plan 3: If I win, the winning payoff would be 6 chips. If I lose, the lose payoff would be 6 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 27% * 6 - 18% * 6 = 0.54 chips\n- Plan 2: Expected Chips Gain = 0% * 6 - 100% * 6 = -6 chips\n- Plan 3: Expected Chips Gain = 31.5% * 6 - 13.5% * 6 = 1.08 chips\n\nPlan Selection:\n- Plan 3 (Check) has the highest expected chips gain, followed by Plan 1 (Raise), and then Plan 2 (Fold). Therefore, I should choose Plan 3 (Check)."}}
{"message": "", "36_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a Queen (50% probability), he will likely fold (70%) or call (30%). If he folds, I win. If he calls, the outcome depends on the public card. If the public card is a King or Queen, I win. If the public card is a Jack, it's a draw.\n- If GoodGuy holds a Jack (50% probability), he will likely fold (80%) or call (20%). If he folds, I win. If he calls, the outcome depends on the public card. If the public card is a King or Jack, I win. If the public card is a Queen, it's a draw.\n\nPlan 2: Raise\n- If GoodGuy holds a Queen (50% probability), he will likely fold (70%) or call (30%). If he folds, I win. If he calls, the outcome depends on the public card. If the public card is a King or Queen, I win. If the public card is a Jack, it's a draw.\n- If GoodGuy holds a Jack (50% probability), he will likely fold (80%) or call (20%). If he folds, I win. If he calls, the outcome depends on the public card. If the public card is a King or Jack, I win. If the public card is a Queen, it's a draw.\n\nPlan 3: Fold\n- This plan is not recommended as I hold a King, the highest rank card.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips (half of the total pot). If I lose, the lose payoff would be 1 chip (half of the total pot).\n- Plan 2: If I win, the winning payoff would be 5 chips (half of the total pot). If I lose, the lose payoff would be 3 chips (half of the total pot).\n- Plan 3: If I fold, there is no payoff.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.5 * (3 chips * winning rate - 1 chip * lose rate) = 1.5 chips * winning rate - 0.5 chips * lose rate\n- Plan 2: Expected Chips Gain = 0.5 * (5 chips * winning rate - 3 chips * lose rate) = 2.5 chips * winning rate - 1.5 chips * lose rate\n- Plan 3: Expected Chips Gain = 0\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain if the winning rate is high and the lose rate is low.\n- Plan 2 has a higher expected chips gain if the winning rate is low and the lose rate is high.\n- Plan 3 is not recommended as it has no expected chips gain.\n\nConsidering the strategy improvement, I should select Plan 1 (Call) as it has a higher expected chips gain with a high winning rate and a low lose rate."}}
{"message": "", "36_2": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he will likely call (80%) or raise (20%). If he calls, I will win if the public card is a King (33.3%) or lose if it's a Queen or Jack (66.7%). If he raises, I will win if the public card is a King (33.3%) or lose if it's a Queen or Jack (66.7%).\n- If GoodGuy holds a Queen (20% probability), he will likely fold (70%) or call (30%). If he folds, I win. If he calls, I will win if the public card is a King or Queen (66.7%) or lose if it's a Jack (33.3%).\n- If GoodGuy holds a Jack (10% probability), he will likely fold (80%) or call (20%). If he folds, I win. If he calls, I will win if the public card is a King or Jack (66.7%) or lose if it's a Queen (33.3%).\n\nPlan 2: Raise\n- If GoodGuy holds a King (70% probability), he will likely call (60%) or fold (40%). If he calls, I will win if the public card is a King (33.3%) or lose if it's a Queen or Jack (66.7%). If he folds, I win.\n- If GoodGuy holds a Queen (20% probability), he will likely fold (80%) or call (20%). If he folds, I win. If he calls, I will win if the public card is a King or Queen (66.7%) or lose if it's a Jack (33.3%).\n- If GoodGuy holds a Jack (10% probability), he will likely fold (90%) or call (10%). If he folds, I win. If he calls, I will win if the public card is a King or Jack (66.7%) or lose if it's a Queen (33.3%).\n\nPlan 3: Fold\n- If I fold, I lose regardless of GoodGuy's card.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 6 chips (half of the total pot of 12 chips). If I lose, the lose payoff would be 6 chips.\n- Plan 2: If I win, the winning payoff would be 8 chips (half of the total pot of 16 chips). If I lose, the lose payoff would be 8 chips.\n- Plan 3: If I fold, the lose payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.7 * (0.8 * 6 - 0.2 * 6) + 0.2 * (0.7 * 6 - 0.3 * 6) + 0.1 * (0.8 * 6 - 0.2 * 6) = 2.4 chips\n- Plan 2: Expected Chips Gain = 0.7 * (0.6 * 8 - 0.4 * 8) + 0.2 * (0.8 * 8 - 0.2 * 8) + 0.1 * (0.9 * 8 - 0.1 * 8) = 3.2 chips\n- Plan 3: Expected Chips Gain = -4 chips\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain (3.2 chips), followed by Plan 1 (2.4 chips), and Plan 3 (-4 chips). Therefore, I should choose Plan 2: Raise."}}
{"message": "", "36_4": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (65% chance), he will likely call (60% chance). If he does, we will both have a single King and it will be a draw. If he folds (40% chance), I will win. \n- If GoodGuy holds a Queen (25% chance), he will likely fold (80% chance). If he does, I will win. If he calls (20% chance), I will still win as my King is higher than his Queen.\n- If GoodGuy holds a Jack (10% chance), he will likely fold (90% chance). If he does, I will win. If he calls (10% chance), he will win as his Jack matches the public card.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds.\n\nPlan 3: Check\n- If GoodGuy holds a King (65% chance), he will likely check (50% chance) or raise (50% chance). If he checks, it will be a draw. If he raises, I will lose.\n- If GoodGuy holds a Queen (25% chance), he will likely check (60% chance) or fold (40% chance). If he checks or folds, I will win.\n- If GoodGuy holds a Jack (10% chance), he will likely raise (60% chance) or check (40% chance). If he raises or checks, he will win.\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 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: (0.65 * 0.60 * 6) + (0.25 * 0.80 * 6) + (0.10 * 0.90 * 6) - (0.65 * 0.40 * 6) - (0.25 * 0.20 * 6) - (0.10 * 0.10 * 6) = 1.8 chips\n- Plan 2: -6 chips\n- Plan 3: (0.65 * 0.50 * 6) + (0.25 * 0.60 * 6) - (0.65 * 0.50 * 6) - (0.10 * 0.60 * 6) = -0.6 chips\n\nPlan Selection:\n- Plan 1: 1.8 chips\n- Plan 2: -6 chips\n- Plan 3: -0.6 chips\n\nTherefore, I should choose Plan 1 (Raise) as it has the highest estimated expected chips gain."}}
{"message": "", "37_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (20% probability), he will likely call (80% probability). If the public card is a King, we will draw. If the public card is a Queen or Jack, I will win. \n- If GoodGuy holds a Queen (60% 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. \n- If GoodGuy holds a Jack (20% probability), he will likely fold (80% probability). If he folds, I will win regardless of the public card. \n\nPlan 2: Fold\n- If I fold, I will lose regardless of GoodGuy's card or the public card. \n\nPlan 3: Check\n- If GoodGuy holds a King (20% probability), he will likely raise (70% probability). If the public card is a King, we will draw. If the public card is a Queen or Jack, I will win. \n- If GoodGuy holds a Queen (60% probability), he will likely raise (30% probability). If the public card is a Queen, I will lose. If the public card is a King or Jack, I will win. \n- If GoodGuy holds a Jack (20% probability), he will likely fold (60% probability). If he folds, I will win regardless of the public card. \n\nWinning/Lose Payoffs for Each Plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (currently 4 chips, so 2 chips). If I lose, the losing payoff would be half of the total pot (currently 4 chips, so 2 chips).\n- Plan 2: If I fold, I will lose my current bet (2 chips).\n- Plan 3: If I win, the winning payoff would be half of the total pot (currently 4 chips, so 2 chips). If I lose, the losing payoff would be half of the total pot (currently 4 chips, so 2 chips).\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected gain = (winning rate * winning payoff) - (losing rate * losing payoff) = (0.8 * 2) - (0.2 * 2) = 1.2 chips\n- Plan 2: Expected gain = (winning rate * winning payoff) - (losing rate * losing payoff) = (0 * 2) - (1 * 2) = -2 chips\n- Plan 3: Expected gain = (winning rate * winning payoff) - (losing rate * losing payoff) = (0.7 * 2) - (0.3 * 2) = 0.8 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I will choose to raise."}}
{"message": "", "38_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (50% probability), he will likely call (80%) or raise (20%). If he calls, we will both have Kings and the outcome will depend on the public card. If the public card is a King, it will be a draw. If the public card is a Queen or Jack, I will win. If he raises, I will call and the outcome will be the same. Overall, the winning rate for this plan is 50%, the losing rate is 0%, and the draw rate is 50%.\n- If GoodGuy holds a Queen (30% probability), he will likely fold (70%) or call (30%). If he folds, I will win. If he calls, the outcome will depend on the public card. If the public card is a King, I will win. If the public card is a Queen, he will win. If the public card is a Jack, I will win. Overall, the winning rate for this plan is 80%, the losing rate is 20%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (20% probability), he will likely fold (80%) or call (20%). If he folds, I will win. If he calls, the outcome will depend on the public card. If the public card is a King, I will win. If the public card is a Queen, I will win. If the public card is a Jack, he will win. Overall, the winning rate for this plan is 90%, the losing rate is 10%, and the draw rate is 0%.\n\nPlan 1 overall Winning/Lose/Draw rates: Winning rate for plan 1 is 73%, Lose rate for plan 1 is 10%, Draw Rate for plan 1 is 17%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (50% probability), he will likely call (80%) or raise (20%). If he calls, we will both have Kings and the outcome will depend on the public card. If the public card is a King, it will be a draw. If the public card is a Queen or Jack, I will win. If he raises, I will call and the outcome will be the same. Overall, the winning rate for this plan is 50%, the losing rate is 0%, and the draw rate is 50%.\n- If GoodGuy holds a Queen (30% probability), he will likely fold (70%) or call (30%). If he folds, I will win. If he calls, the outcome will depend on the public card. If the public card is a King, I will win. If the public card is a Queen, he will win. If the public card is a Jack, I will win. Overall, the winning rate for this plan is 80%, the losing rate is 20%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (20% probability), he will likely fold (80%) or call (20%). If he folds, I will win. If he calls, the outcome will depend on the public card. If the public card is a King, I will win. If the public card is a Queen, I will win. If the public card is a Jack, he will win. Overall, the winning rate for this plan is 90%, the losing rate is 10%, and the draw rate is 0%.\n\nPlan 2 overall Winning/Lose/Draw rates: Winning rate for plan 2 is 73%, Lose rate for plan 2 is 10%, Draw Rate for plan 2 is 17%.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. Therefore, the winning rate for this plan is 0%, the losing rate is 100%, and the draw rate is 0%.\n\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 1 chip.\n\nEstimated Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 73% * 3 - 10% * 3 = 1.89 chips\n- Plan 2: Expected Chips Gain = 73% * 4 - 10% * 4 = 2.52 chips\n- Plan 3: Expected Chips Gain = 0% * 0 - 100% * 1 = -1 chip\n\nPlan Selection:\n- Plan 2 (Raise) has the highest estimated expected chips gain of 2.52 chips, followed by Plan 1 (Call) with 1.89 chips, and Plan 3 (Fold) with -1 chip. Therefore, I should choose Plan 2 (Raise)."}}
{"message": "", "38_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (80% chance), he will likely call (70% chance). If he calls, we will draw this round as we both hold a King. If he folds (30% chance), I will win this round as he forfeits the game. \n- If GoodGuy holds a Queen (30% chance), he will likely fold (80% chance). If he folds, I will win this round as he forfeits the game. If he calls (20% chance), he will win this round as his card matches the public card.\n- If GoodGuy holds a Jack (20% chance), he will likely fold (90% chance). If he folds, I will win this round as he forfeits the game. If he calls (10% chance), I will win this round as my card is higher.\n\nPlan 2: Fold\n- If I fold, I will lose this round regardless of what card GoodGuy holds.\n\nPlan 3: Check\n- If GoodGuy holds a King (80% chance), he will likely check (60% chance). If he checks, we will draw this round as we both hold a King. If he raises (40% chance), we will draw this round as we both hold a King.\n- If GoodGuy holds a Queen (30% chance), he will likely raise (60% chance). If he raises, he will win this round as his card matches the public card. If he checks (40% chance), he will win this round as his card matches the public card.\n- If GoodGuy holds a Jack (20% chance), he will likely check (40% chance). If he checks, I will win this round as my card is higher. If he raises (60% chance), I will win this round as my card is higher.\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 lose payoff would be 8 chips.\n- Plan 2: If I fold, I will lose 4 chips (the chips 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). If I lose, the lose payoff would be 8 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.8 * 8 - 0.2 * 8 = 4.8 chips\n- Plan 2: Expected Chips Gain = -4 chips\n- Plan 3: Expected Chips Gain = 0.6 * 8 - 0.4 * 8 = 1.6 chips\n\nPlan Selection:\n- Plan 1: Raise (Expected Chips Gain = 4.8 chips)\n- Plan 3: Check (Expected Chips Gain = 1.6 chips)\n- Plan 2: Fold (Expected Chips Gain = -4 chips)\n\nBased on the expected chips gain, I should choose Plan 1: Raise."}}
{"message": "", "38_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (75% probability), he will likely call (70% probability). If he calls, we will both have a single King, resulting in a draw. If he folds (30% probability), I will win. \n- If GoodGuy holds a Queen (25% probability), he will likely fold (80% probability). If he folds, I will win. If he calls (20% probability), he will have a pair of Queens and I will lose. \n- If GoodGuy holds a Jack (15% probability), he will likely fold (90% probability). If he folds, I will win. If he calls (10% probability), he will have a single Jack and I will win. \n\nPlan 2: Fold\n- If I fold, regardless of what GoodGuy holds, I will 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 (20 chips). If I lose, the lose payoff would be half of the total pot (20 chips).\n- Plan 2: If I fold, the lose payoff would be the chips I have already put in the 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 = (75% * 20 chips + 25% * 20 chips + 15% * 20 chips) - (25% * 20 chips + 15% * 20 chips) = 15 chips\n- Plan 2: Expected Chips Gain = -8 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I should choose to call."}}
{"message": "", "40_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he will likely call (80%) or raise (20%) in the next round. If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. So the winning rate is 20%, losing rate is 70%, and draw rate is 10%.\n- If GoodGuy holds a Queen (30% probability), he will likely check (50%) or fold (50%) in the next round. If the public card is a Queen, it's a draw. If the public card is a King or Jack, I will win. So the winning rate is 60%, losing rate is 0%, and draw rate is 40%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (70% probability), he will likely call (80%) or raise (20%) in the next round. If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. So the winning rate is 20%, losing rate is 70%, and draw rate is 10%.\n- If GoodGuy holds a Queen (30% probability), he will likely fold (30%) or call (70%) in the next round. If the public card is a Queen, it's a draw. If the public card is a King or Jack, I will win. So the winning rate is 70%, losing rate is 0%, and draw rate is 30%.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot. So the winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 4 chips. If lose, the lose payoff would be 2 chips.\n- Plan 2: If win, the winning payoff would be 8 chips. If lose, the lose payoff would be 4 chips.\n- Plan 3: If lose, the lose payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.2 * 4 - 0.7 * 2 = -0.6 chips\n- Plan 2: Expected Chips Gain = 0.45 * 8 - 0.35 * 4 = 1.6 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I will choose this plan."}}
{"message": "", "40_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King, he will likely call (80%) or raise (20%). If he calls, I will win as my pair of Queens beats his King. If he raises, I will still win as my pair of Queens beats his King. Therefore, the winning rate for this plan is 100%.\n- The number of chips in the pot after my raise would be 14. If I win, the winning payoff would be 7 chips. If I lose, the lose payoff would be 7 chips. However, as I have a pair of Queens and GoodGuy likely holds a King, I will not lose in this situation.\n- The expected chips gain for this plan is winning rate * winning payoff - lose rate * lose payoff = 1 * 7 - 0 * 7 = 7 chips.\n\nPlan 2: Fold\n- If I fold, I will automatically lose the round. Therefore, the winning rate for this plan is 0% and the lose rate is 100%.\n- The number of chips in the pot after my fold would be 6. If I lose, the lose payoff would be 3 chips.\n- The expected chips gain for this plan is winning rate * winning payoff - lose rate * lose payoff = 0 * 0 - 1 * 3 = -3 chips.\n\nPlan 3: Check\n- If GoodGuy holds a King, he will 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 round. Therefore, the winning rate for this plan is 100%.\n- The number of chips in the pot after my check would be 6. If I win, the winning payoff would be 3 chips. If I lose, the lose payoff would be 3 chips. However, as I have a pair of Queens and GoodGuy likely holds a King, I will not lose in this situation.\n- The expected chips gain for this plan is winning rate * winning payoff - lose rate * lose payoff = 1 * 3 - 0 * 3 = 3 chips.\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows:\n1. Plan 1: Raise (7 chips)\n2. Plan 3: Check (3 chips)\n3. Plan 2: Fold (-3 chips)\n\nTherefore, I should select Plan 1: Raise as it has the highest estimated expected chips gain."}}
{"message": "", "41_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he will likely call (60% probability) or raise (30% probability) in the second round. If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. The overall winning rate is 0.7*0.3*0.33 = 0.069 (6.9%), the losing rate is 0.7*(0.6+0.3)*0.67 = 0.42 (42%), and the draw rate is 0.7*0.1 = 0.07 (7%).\n- If GoodGuy holds a Queen (20% probability), he will likely call (50% probability) or raise (20% probability) in the second round. If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. The overall winning rate is 0.2*0.3*0.33 = 0.02 (2%), the losing rate is 0.2*(0.5+0.2)*0.67 = 0.094 (9.4%), and the draw rate is 0.2*0.3 = 0.06 (6%).\n- If GoodGuy holds a Jack (10% probability), he will likely fold (70% probability) or call (20% probability) in the second round. 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 0.1*0.3*0.67 = 0.02 (2%), and the draw rate is 0.1*(0.7+0.2) = 0.09 (9%).\n\nPlan 1 overall Winning/Lose/Draw rates: Winning rate = 6.9% + 2% = 8.9%, Losing rate = 42% + 9.4% + 2% = 53.4%, Draw rate = 7% + 6% + 9% = 22%.\n\nPlan 2: Raise\n- The analysis is similar to Plan 1, but the probabilities of GoodGuy's actions will change due to my raise. The overall winning rate, losing rate, and draw rate will be lower than Plan 1.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot. The overall winning rate is 0, the losing rate is 100%, and the draw rate is 0.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 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 2: If win, the winning payoff would be half of the total pot (10 chips) = 5 chips. If lose, the lose payoff would be half of the total pot (10 chips) = 5 chips.\n- Plan 3: If lose, the lose payoff would be the chips I have already 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 * Lose Payoff = 8.9% * 3 - 53.4% * 3 = -1.33 chips.\n- Plan 2: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Lose Payoff = (lower than Plan 1 due to lower winning rate and higher lose payoff).\n- Plan 3: Expected Chips Gain = -2 chips (since I will lose the chips I have already put in the pot).\n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 1 > Plan 2 > Plan 3.\n- Therefore, I should select Plan 1 (Call) as it has the highest estimated expected chips gain."}}
{"message": "", "41_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King, he will likely call (60% probability), raise (30% probability), or fold (10% probability). If he calls or raises, I will lose as his King is higher than my Jack. If he folds, I will win. The overall winning rate is 10%, losing rate is 90%, and drawing rate is 0%.\n- If GoodGuy holds a Queen, he will likely call (50% probability), raise (20% probability), or fold (30% probability). If he calls or raises, I will lose as his Queen is higher than my Jack. If he folds, I will win. The overall winning rate is 30%, losing rate is 70%, and drawing rate is 0%.\n- If GoodGuy holds a Jack, he will likely fold (70% probability), call (20% probability), or raise (10% probability). If he folds, I will win. If he calls or raises, it will be a draw as we both have Jacks. The overall winning rate is 70%, losing rate is 0%, and drawing rate is 30%.\n\nPlan 2: Fold\n- If I fold, I will lose the chips I have already put in the pot. The overall winning rate is 0%, losing rate is 100%, and drawing rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King, he will likely raise (30% probability), or check (70% probability). If he raises, I will lose as his King is higher than my Jack. If he checks, it will be a draw. The overall winning rate is 0%, losing rate is 30%, and drawing rate is 70%.\n- If GoodGuy holds a Queen, he will likely raise (20% probability), or check (80% probability). If he raises, I will lose as his Queen is higher than my Jack. If he checks, it will be a draw. The overall winning rate is 0%, losing rate is 20%, and drawing rate is 80%.\n- If GoodGuy holds a Jack, he will likely raise (10% probability), or check (90% probability). If he raises, it will be a draw. If he checks, it will be a draw. The overall winning rate is 0%, losing rate is 0%, and drawing rate is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 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 the chips I have already put in the pot (4 chips).\n- Plan 3: If I win, the winning payoff would be half of the 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 = 0.1 * 8 - 0.9 * 8 = -6.4 chips\n- Plan 2: Expected Chips Gain = 0 - 1 * 4 = -4 chips\n- Plan 3: Expected Chips Gain = 0 - 0.25 * 4 = -1 chip\n\nPlan Selection:\n- Plan 3 (Check) has the highest expected chips gain (-1 chip), followed by Plan 2 (Fold) (-4 chips), and Plan 1 (Raise) (-6.4 chips). Therefore, I should choose Plan 3 (Check)."}}
{"message": "", "42_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King, he will likely raise (80% probability) or fold (20% probability). If he raises, I will lose as my Jack is lower than his King. If he folds, I will win. Therefore, the winning rate is 20%, the losing rate is 80%, and the draw rate is 0%.\n- If GoodGuy holds a Queen, he will likely raise (20% probability) or fold (80% probability). If he raises, I will lose as my Jack is lower than his Queen. If he folds, I will win. Therefore, the winning rate is 80%, the losing rate is 20%, and the draw rate is 0%.\n- If GoodGuy holds a Jack, he will likely fold (60% probability) or call (40% probability). If he folds, I will win. If he calls, it will be a draw as we both hold a Jack. Therefore, the winning rate is 60%, the losing rate is 0%, and the draw rate is 40%.\n\nPlan 2: Raise\n- If GoodGuy holds a King, he will likely call (70% probability) or fold (30% probability). If he calls, I will lose as my Jack is lower than his King. If he folds, I will win. Therefore, the winning rate is 30%, the losing rate is 70%, and the draw rate is 0%.\n- If GoodGuy holds a Queen, he will likely call (60% probability) or fold (40% probability). If he calls, I will lose as my Jack is lower than his Queen. If he folds, I will win. Therefore, the winning rate is 40%, the losing rate is 60%, and the draw rate is 0%.\n- If GoodGuy 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 as we both hold a Jack. Therefore, the winning rate is 80%, the losing rate is 0%, and the draw rate is 20%.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot. Therefore, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If 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 7 chips (half of the total pot of 14 chips). If I lose, the losing payoff would be 7 chips.\n- Plan 3: If I lose, the losing payoff would be 1 chip (the chip I have already put in the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 20% * 3 - 80% * 3 = -1.8 chips\n- Plan 2: Expected Chips Gain = 30% * 7 - 70% * 7 = -2.8 chips\n- Plan 3: Expected Chips Gain = -1 chip\n\nPlan Selection:\n- Plan 1: -1.8 chips\n- Plan 2: -2.8 chips\n- Plan 3: -1 chip\n\nBased on the estimated expected chips gain, Plan 3 (Fold) is the best strategy to minimize the loss in this round."}}
{"message": "", "43_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (40% chance), he will likely raise (70%) or call (30%). If he raises, I will lose as King is higher than Queen. If he calls, the outcome will depend on the public card. The overall winning rate is 30% * 50% = 15%, losing rate is 70% + 30% * 50% = 85%, and draw rate is 0%.\n- If GoodGuy holds a Queen (40% chance), he will likely call (60%) or raise (40%). If he raises, it will be a draw as we both have Queens. If he calls, the outcome will depend on the public card. The overall winning rate is 60% * 50% = 30%, losing rate is 0%, and draw rate is 40% + 60% * 50% = 70%.\n- If GoodGuy holds a Jack (20% chance), he will likely fold (60%) or call (40%). If he folds, I will win. If he calls, I will win as Queen is higher than Jack. The overall winning rate is 100%, losing rate is 0%, and draw rate is 0%.\n\nPlan 1 overall Winning/Lose/Draw rates: Winning rate = 15% + 30% + 100% = 145%, Losing rate = 85% + 0% + 0% = 85%, Draw rate = 0% + 70% + 0% = 70%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (40% chance), he will likely call (80%) or raise (20%). If he calls or raises, I will lose as King is higher than Queen. The overall winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n- If GoodGuy holds a Queen (40% chance), he will likely call (70%) or fold (30%). If he calls, it will be a draw as we both have Queens. If he folds, I will win. The overall winning rate is 30%, losing rate is 0%, and draw rate is 70%.\n- If GoodGuy holds a Jack (20% chance), he will likely fold (80%) or call (20%). If he folds or calls, I will 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 overall Winning/Lose/Draw rates: Winning rate = 0% + 30% + 100% = 130%, Losing rate = 100% + 0% + 0% = 100%, Draw rate = 0% + 70% + 0% = 70%.\n\nPlan 3: Fold\n- If I fold, I will lose the 1 chip I have already put in the pot. 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 (5 chips) = 2.5 chips. If lose, the lose payoff would be half of the total pot (5 chips) = 2.5 chips.\n- Plan 3: If lose, the lose payoff would be the 1 chip I have already put in the pot.\n\nEstimated Expected Chips Gain for Each Plan:\n- Plan 1: 145% * 1.5 chips - 85% * 1.5 chips = 0.9 chips\n- Plan 2: 130% * 2.5 chips - 100% * 2.5 chips = 0.75 chips\n- Plan 3: 0% * 0 chips - 100% * 1 chip = -1 chip\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is Plan 1 > Plan 2 > Plan 3. Therefore, I should choose Plan 1: Call."}}
{"message": "", "43_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (10% probability), he will likely call (60%) or raise (40%). If he calls, I will lose as his King matches the public card. If he raises, I will also lose. So, the overall losing rate for this plan is 100%.\n- If GoodGuy holds a Queen (30% probability), he will likely call (50%) or fold (50%). If he calls, it will be a draw as we both hold a Queen. If he folds, I will win. So, the overall winning rate for this plan is 15%, and the draw rate is 15%.\n- If GoodGuy holds a Jack (60% probability), he will likely fold (90%) or call (10%). If he folds, I will win. If he calls, I will win as my Queen is higher than his Jack. So, the overall winning rate for this plan is 60%.\n\nPlan 2: Fold\n- If I fold, I will lose the chips in the pot regardless of GoodGuy's card. So, the overall losing rate for this plan is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (10% probability), he will likely raise (80%) or check (20%). If he raises, I will lose as his King matches the public card. If he checks, I will also lose. So, the overall losing rate for this plan is 100%.\n- If GoodGuy holds a Queen (30% probability), he will likely check (70%) or raise (30%). If he checks, it will be a draw as we both hold a Queen. If he raises, I will lose. So, the overall losing rate for this plan is 30%, and the draw rate is 21%.\n- If GoodGuy holds a Jack (60% probability), he will likely check (80%) or raise (20%). If he checks, I will win as my Queen is higher than his Jack. If he raises, I will lose. So, the overall winning rate for this plan is 48%, and the losing rate is 12%.\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 (2 chips).\n- Plan 3: If I win, the winning payoff would be half of the total pot (2 chips). If I lose, the losing payoff would be half of the total pot (2 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.75 * 4 - 1 * 4 = -1 chip\n- Plan 2: Expected Chips Gain = 0 - 1 * 2 = -2 chips\n- Plan 3: Expected Chips Gain = 0.48 * 2 - 0.42 * 2 = 0.12 chip\n\nPlan Selection:\nRanking the plans by expected chips gain, we get Plan 3 > Plan 1 > Plan 2. Therefore, the best plan to execute would be Plan 3: Check."}}
{"message": "", "44_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (15% probability), he will likely call (80%) or raise (20%). If the public card is a Jack, I will win (probability = 15% * 100% = 15%). If the public card is a King or Queen, I will lose (probability = 15% * 100% = 15%).\n- If GoodGuy holds a Queen (46% probability), he will likely call (70%) or fold (30%). If the public card is a Jack, I will win (probability = 46% * 70% = 32.2%). If the public card is a Queen, I will lose (probability = 46% * 30% = 13.8%).\n- If GoodGuy holds a Jack (38% probability), he will likely fold (80%) or call (20%). If the public card is a Jack, it will be a draw (probability = 38% * 80% = 30.4%). If the public card is a King or Queen, I will lose (probability = 38% * 20% = 7.6%).\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card or the public card.\n\nPlan 3: Check\n- If GoodGuy holds a King (15% probability), he will likely check (50%) or raise (50%). If the public card is a Jack, I will win (probability = 15% * 50% = 7.5%). If the public card is a King or Queen, I will lose (probability = 15% * 50% = 7.5%).\n- If GoodGuy holds a Queen (46% probability), he will likely check (70%) or raise (30%). If the public card is a Jack, I will win (probability = 46% * 70% = 32.2%). If the public card is a Queen, I will lose (probability = 46% * 30% = 13.8%).\n- If GoodGuy holds a Jack (38% probability), he will likely check (80%) or raise (20%). If the public card is a Jack, it will be a draw (probability = 38% * 80% = 30.4%). If the public card is a King or Queen, I will lose (probability = 38% * 20% = 7.6%).\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 game 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 = winning rate * Winning Payoff - lose rate * Losing Payoff = (15% + 32.2%) * 6 - (15% + 13.8% + 7.6%) * 6 = 2.832 chips\n- Plan 2: Expected Chips Gain = 0 * Winning Payoff - 100% * Losing Payoff = -6 chips\n- Plan 3: Expected Chips Gain = (7.5% + 32.2%) * 6 - (7.5% + 13.8% + 7.6%) * 6 = 2.832 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 have the highest expected chips gain (2.832 chips), followed by Plan 2 (-6 chips). Therefore, I should either raise (Plan 1) or check (Plan 3). Considering the strategy improvement, I should choose to raise (Plan 1) when I see GoodGuy call."}}
{"message": "", "45_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he will likely call (90% probability) in the second round. If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. So, the winning rate is 30%, the losing rate is 63%, and the draw rate is 7%.\n- If GoodGuy holds a Queen (20% probability), he will likely call (80% probability) in the second round. If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. So, the winning rate is 16%, the losing rate is 16%, and the draw rate is 4%.\n- If GoodGuy holds a Jack (10% probability), he will likely fold (90% probability) in the second round. If the public card is a King or Queen, I will win. If the public card is a Jack, it will be a draw. So, the winning rate is 9%, the losing rate is 0%, and the draw rate is 1%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (70% probability), he will likely call (90% probability) in the second round. If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. So, the winning rate is 63%, the losing rate is 63%, and the draw rate is 7%.\n- If GoodGuy holds a Queen (20% probability), he will likely call (80% probability) in the second round. If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. So, the winning rate is 16%, the losing rate is 16%, and the draw rate is 4%.\n- If GoodGuy holds a Jack (10% probability), he will likely fold (90% probability) in the second round. If the public card is a King or Queen, I will win. If the public card is a Jack, it will be a draw. So, the winning rate is 9%, the losing rate is 0%, and the draw rate is 1%.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card. So, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 4 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 = 30% * 4 - 63% * 2 = -0.26 chips\n- Plan 2: Expected Chips Gain = 63% * 6 - 63% * 4 = 1.26 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 I will choose this plan."}}
{"message": "", "45_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (70% probability), he will likely call (90% probability). This would result in a win for me, as my Jack matches the public card. \n- If GoodGuy holds a Queen (20% probability), he will likely call (80% probability). This would also result in a win for me.\n- If GoodGuy holds a Jack (10% probability), it would result in a draw as we both match the public card.\n\nPlan 2: Fold\n- This would result in an automatic loss for me, regardless of GoodGuy's card.\n\nPlan 3: Check\n- If GoodGuy holds a King (70% probability), he will likely raise (70% probability). This would result in a win for me, as my Jack matches the public card. \n- If GoodGuy holds a Queen (20% probability), he will likely raise (30% probability). This would also result in a win for me.\n- If GoodGuy holds a Jack (10% probability), it would result in a draw as we both match the public card.\n\nWinning/Lose Payoffs:\n- Plan 1: If win, the winning payoff would be half of the total pot (6 chips + my raise of 8 chips = 14 chips, half of which is 7 chips). If lose, the lose payoff would be half of the total pot (7 chips).\n- Plan 2: If lose, the lose payoff would be half of the total pot (6 chips, half of which is 3 chips).\n- Plan 3: If win, the winning payoff would be half of the total pot (6 chips + GoodGuy's potential raise of 8 chips = 14 chips, half of which is 7 chips). If lose, the lose payoff would be half of the total pot (7 chips).\n\nExpected Chips Gain:\n- Plan 1: (0.7 * 7 chips) - (0.3 * 7 chips) = 2.8 chips\n- Plan 2: -3 chips (as it's an automatic loss)\n- Plan 3: (0.7 * 7 chips) - (0.3 * 7 chips) = 2.8 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 both have the highest expected chips gain of 2.8 chips. However, considering the strategy improvement, Plan 1 (Raise) would be the best choice as it allows me to take control of the game and potentially intimidate GoodGuy into folding."}}
{"message": "", "46_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (20% probability), he will likely call (90% probability) if he sees me call. If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. Overall, the winning rate is 20%*10% = 2%, the losing rate is 20%*90% = 18%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (60% probability), he will likely fold (70% probability) if he sees me call. If the public card is a Queen, it will be a draw. If the public card is a King or Jack, I will win. Overall, the winning rate is 60%*30% = 18%, the losing rate is 0%, and the draw rate is 60%*70% = 42%.\n- If GoodGuy holds a Jack (20% probability), he will likely fold (90% probability) if he sees me call. If the public card is a Jack, I will lose. If the public card is a King or Queen, I will win. Overall, the winning rate is 20%*10% = 2%, the losing rate is 20%*90% = 18%, and the draw rate is 0%.\n\nPlan 1 overall Winning/Lose/Draw rates: Winning rate = 2% + 18% + 2% = 22%, Losing rate = 18% + 0% + 18% = 36%, Draw rate = 0% + 42% + 0% = 42%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (20% probability), he will likely call (90% probability) if he sees me raise. If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. Overall, the winning rate is 20%*10% = 2%, the losing rate is 20%*90% = 18%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (60% probability), he will likely fold (70% probability) if he sees me raise. If the public card is a Queen, it will be a draw. If the public card is a King or Jack, I will win. Overall, the winning rate is 60%*30% = 18%, the losing rate is 0%, and the draw rate is 60%*70% = 42%.\n- If GoodGuy holds a Jack (20% probability), he will likely fold (90% probability) if he sees me raise. If the public card is a Jack, I will lose. If the public card is a King or Queen, I will win. Overall, the winning rate is 20%*10% = 2%, the losing rate is 20%*90% = 18%, and the draw rate is 0%.\n\nPlan 2 overall Winning/Lose/Draw rates: Winning rate = 2% + 18% + 2% = 22%, Losing rate = 18% + 0% + 18% = 36%, Draw rate = 0% + 42% + 0% = 42%.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot. The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the total pot (3 chips). If I lose, the losing 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 (5 chips). If I lose, the losing payoff would be half of the total pot (5 chips).\n- Plan 3: If I fold, I will lose the chip I have already put in the pot (1 chip).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 22% * 3 - 36% * 3 = -0.42 chips\n- Plan 2: Expected Chips Gain = 22% * 5 - 36% * 5 = -0.7 chips\n- Plan 3: Expected Chips Gain = 0% * 0 - 100% * 1 = -1 chip\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain (-0.42 chips), followed by Plan 2 (-0.7 chips), and Plan 3 (-1 chip). Therefore, I should choose Plan 1: Call."}}
{"message": "", "46_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (10% probability), he will likely call (90% probability) or fold (10% probability). If he calls, I will lose as his King matches the public card. If he folds, I will win. Overall, the winning rate is 1% (10% * 10%), the losing rate is 9% (10% * 90%), and the draw rate is 0%.\n- If GoodGuy holds a Queen (60% probability), he will likely fold (70% probability) or call (30% probability). If he folds, I will win. If he calls, it will be a draw as we both hold Queens. Overall, the winning rate is 42% (60% * 70%), the losing rate is 0%, and the draw rate is 18% (60% * 30%).\n- If GoodGuy holds a Jack (30% probability), he will likely fold (90% probability) or call (10% probability). If he folds or calls, I will win as my Queen outranks his Jack. Overall, the winning rate is 30% (30% * 100%), the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of GoodGuy's hand. The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King (10% probability), he will likely raise (70% probability) or check (30% probability). If he raises, I will lose as his King matches the public card. If he checks, I will also lose. Overall, the losing rate is 10% (10% * 100%), the winning rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (60% probability), he will likely raise (50% probability) or check (50% probability). If he raises or checks, it will be a draw as we both hold Queens. Overall, the draw rate is 60% (60% * 100%), the winning rate is 0%, and the losing rate is 0%.\n- If GoodGuy holds a Jack (30% probability), he will likely check (20% probability) or fold (80% probability). If he checks or folds, I will win as my Queen outranks his Jack. Overall, the winning rate is 30% (30% * 100%), the losing rate is 0%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 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 lose, the losing payoff would be 2 chips (half of the total pot of 4 chips).\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 = 73% * 3 - 9% * 3 = 1.92 chips\n- Plan 2: Expected Chips Gain = 0% * 0 - 100% * 2 = -2 chips\n- Plan 3: Expected Chips Gain = 30% * 2 - 10% * 2 = 0.4 chips\n\nPlan Selection:\n- Plan 1: Raise (1.92 chips)\n- Plan 3: Check (0.4 chips)\n- Plan 2: Fold (-2 chips)\n\nThe plan with the highest expected chips gain is Plan 1: Raise."}}
{"message": "", "47_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (50% probability), he will either fold (50% probability) or call (50% probability). If he folds, I win and the pot would be 8 chips (4 from me, 2 from him, and 2 from the blinds). If he calls, the outcome will depend on the public card. If the public card is a Jack, I win and the pot would be 12 chips. If the public card is a Queen or King, I lose and the pot would be 12 chips.\n- If GoodGuy holds a King (50% probability), he will either call (70% probability) or raise (30% probability). If he calls, the outcome will depend on the public card. If the public card is a Jack, I win and the pot would be 12 chips. If the public card is a Queen or King, I lose and the pot would be 12 chips. If he raises, I would have to decide whether to call or fold.\n\nPlan 2: Fold\n- If I fold, I lose the round and the pot would be 4 chips (2 from me and 2 from the blinds).\n\nPlan 3: Check\n- If GoodGuy holds a Queen (50% probability), he will either call (50% probability) or raise (50% probability). If he calls, the outcome will depend on the public card. If the public card is a Jack, I win and the pot would be 4 chips. If the public card is a Queen or King, I lose and the pot would be 4 chips. If he raises, I would have to decide whether to call or fold.\n- If GoodGuy holds a King (50% probability), he will either call (70% probability) or raise (30% probability). If he calls, the outcome will depend on the public card. If the public card is a Jack, I win and the pot would be 4 chips. If the public card is a Queen or King, I lose and the pot would be 4 chips. If he raises, I would have to decide whether to call or fold.\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: (0.5 * 4 - 0.5 * 4) = 0 chips\n- Plan 2: -2 chips\n- Plan 3: (0.5 * 2 - 0.5 * 2) = 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 2. Therefore, Plan 1 or Plan 3 would be the best choice. However, considering the strategy improvement, Plan 1 (raise) would be the best choice as it has the potential to bluff GoodGuy into folding."}}
{"message": "", "48_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (40% probability), he will likely call (100% probability). If the public card is a King, I will lose. If the public card is not a King, I have a 50% chance of winning (if it's a Jack) and a 50% chance of losing (if it's a Queen). Overall, the winning rate is 20%, the losing rate is 70%, and the draw rate is 10%.\n- If GoodGuy holds a Queen (40% probability), he will likely fold (100% probability). If the public card is a Queen, I will lose. If the public card is not a Queen, I have a 50% chance of winning (if it's a Jack) and a 50% chance of losing (if it's a King). Overall, the winning rate is 20%, the losing rate is 70%, and the draw rate is 10%.\n- If GoodGuy holds a Jack (20% probability), he will likely fold (100% probability). If the public card is a Jack, it's a draw. If the public card is not a Jack, I will win. Overall, the winning rate is 10%, the losing rate is 0%, and the draw rate is 10%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (40% probability), he will likely call (100% probability). If the public card is a King, I will lose. If the public card is not a King, I have a 50% chance of winning (if it's a Jack) and a 50% chance of losing (if it's a Queen). Overall, the winning rate is 20%, the losing rate is 70%, and the draw rate is 10%.\n- If GoodGuy holds a Queen (40% probability), he will likely fold (100% probability). If the public card is a Queen, I will lose. If the public card is not a Queen, I will win. Overall, the winning rate is 40%, the losing rate is 40%, and the draw rate is 20%.\n- If GoodGuy holds a Jack (20% probability), he will likely fold (100% probability). If the public card is a Jack, it's a draw. If the public card is not a Jack, I will win. Overall, the winning rate is 10%, the losing rate is 0%, and the draw rate is 10%.\n\nPlan 3: Fold\n- If I fold, I will lose 100% of the time.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 1.5 chips. If lose, the lose payoff would be 1.5 chips.\n- Plan 2: If win, the winning payoff would be 2.5 chips. If lose, the lose payoff would be 2.5 chips.\n- Plan 3: If lose, the lose payoff would be 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 20% * 1.5 - 70% * 1.5 = -0.75 chips\n- Plan 2: Expected Chips Gain = 30% * 2.5 - 60% * 2.5 = -0.75 chips\n- Plan 3: Expected Chips Gain = -1 chip\n\nPlan Selection:\n- Plan 1 and Plan 2 have the same expected chips gain, but Plan 2 has a higher potential winning payoff. Therefore, I should choose Plan 2: Raise."}}
{"message": "", "48_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (100% probability), he will likely call (50% probability) or fold (50% probability). If he calls, I will lose (100% probability) as his King is higher than my Jack. If he folds, I will win (100% probability). Overall, the winning rate for this plan is 50%, and the losing rate is 50%.\n- If GoodGuy holds a Queen or Jack, it's impossible based on his behavior pattern and my belief on him.\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of what card GoodGuy holds. The losing rate for this plan is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (100% probability), he will likely call (50% probability) or fold (50% probability). If he calls, I will lose (100% probability) as his King is higher than my Jack. If he folds, I will win (100% probability). Overall, the winning rate for this plan is 50%, and the losing rate is 50%.\n- If GoodGuy holds a Queen or Jack, it's impossible based on his behavior pattern and my belief on him.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, all chips in the pot would be 16. If win, the winning payoff would be 8. If lose, the lose payoff would be 8.\n- Plan 2: After the action, all chips in the pot would be 8. If lose, the lose payoff would be 4.\n- Plan 3: After the action, all chips in the pot would be 8. If win, the winning payoff would be 4. If lose, the lose payoff would be 4.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.5 * 8 - 0.5 * 8 = 0\n- Plan 2: Expected Chips Gain = 0 - 1 * 4 = -4\n- Plan 3: Expected Chips Gain = 0.5 * 4 - 0.5 * 4 = 0\n\nPlan Selection:\n- Plan 1 and Plan 3 have the same expected chips gain, which is higher than Plan 2. Therefore, I should choose either Plan 1 (Raise) or Plan 3 (Check). Considering the strategy improvement, I should choose Plan 1 (Raise) to potentially confuse GoodGuy and make him fold."}}
{"message": "", "48_4": {"plan": "Plan 1: 'Call'\n- If GoodGuy holds a King (100% probability):\n  - He will check (100% probability). I will lose as his King is higher than my Jack. \n- If GoodGuy holds a Queen (0% probability):\n  - This situation is impossible as the public card is a Queen and GoodGuy would have checked instead of raising.\n- If GoodGuy holds a Jack (0% probability):\n  - This situation is impossible as GoodGuy would have folded in the first round.\n\nPlan 2: 'Fold'\n- If GoodGuy holds a King (100% probability):\n  - I will lose no additional chips as I have chosen to fold.\n- If GoodGuy holds a Queen (0% probability):\n  - This situation is impossible as the public card is a Queen and GoodGuy would have checked instead of raising.\n- If GoodGuy holds a Jack (0% probability):\n  - This situation is impossible as GoodGuy would have folded in the first round.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: \n  - After the action, all chips in the pot: 24 chips. \n  - If win, the winning payoff would be 12 chips. \n  - After the action, all chips in the pot: 24 chips. \n  - If lose, the lose payoff would be 12 chips.\n- Plan 2: \n  - After the action, all chips in the pot: 20 chips. \n  - If win, the winning payoff would be 10 chips. \n  - After the action, all chips in the pot: 20 chips. \n  - If lose, the lose payoff would be 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% * 12 chips - 100% * 12 chips = -12 chips\n- Plan 2: Expected Chips Gain = winning rate * Winning Payoff - lose rate * Lose Payoff = 0% * 10 chips - 0% * 10 chips = 0 chips\n\nPlan Selection:\n- Plan 1: Expected Chips Gain = -12 chips\n- Plan 2: Expected Chips Gain = 0 chips\n\nTherefore, the best plan to select is Plan 2: 'Fold'."}}
{"message": "", "50_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (30% chance), he will likely call (80% chance). If the public card is a King, I will lose. If the public card is a Queen, I will win. If the public card is a Jack, I will lose. The overall winning rate is 24%, losing rate is 6%, and drawing rate is 0%.\n- If GoodGuy holds a Queen (60% chance), he will likely fold (100% chance). If the public card is a Queen, I will draw. If the public card is a King or Jack, I will win. The overall winning rate is 60%, losing rate is 0%, and drawing rate is 0%.\n- If GoodGuy holds a Jack (10% chance), he will likely fold (100% chance). If the public card is a Jack, I will lose. If the public card is a King or Queen, I will win. The overall winning rate is 10%, losing rate is 0%, and drawing rate is 0%.\n- The total pot after raising would be 6 chips. 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 0.94 chips (winning rate * winning payoff - losing rate * losing payoff).\n\nPlan 2: Fold\n- If I fold, I will lose the 2 chips I have already put in the pot. The expected chips gain for this plan is -2 chips.\n\nPlan 3: Check\n- If GoodGuy holds a King (30% chance), he will likely call (80% chance). If the public card is a King, I will lose. If the public card is a Queen, I will win. If the public card is a Jack, I will lose. The overall winning rate is 24%, losing rate is 6%, and drawing rate is 0%.\n- If GoodGuy holds a Queen (60% chance), he will likely check (100% chance). If the public card is a Queen, I will draw. If the public card is a King or Jack, I will win. The overall winning rate is 60%, losing rate is 0%, and drawing rate is 0%.\n- If GoodGuy holds a Jack (10% chance), he will likely fold (100% chance). If the public card is a Jack, I will lose. If the public card is a King or Queen, I will win. The overall winning rate is 10%, losing rate is 0%, and drawing rate is 0%.\n- The total pot after checking would be 4 chips. If I win, the winning payoff would be 2 chips. If I lose, the losing payoff would be 2 chips.\n- The expected chips gain for this plan is 0.88 chips (winning rate * winning payoff - losing rate * losing payoff).\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows: Plan 1 (0.94 chips) > Plan 3 (0.88 chips) > Plan 2 (-2 chips). Therefore, I should select Plan 1: Raise."}}
