{"message": "", "1_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a Queen:\n  - In the 1st round, GoodGuy will call with a probability of 70%. If the opponent holds a King, GoodGuy will lose with a probability of 50%. If the opponent holds a Queen or a Jack, it will be a draw with a probability of 50%.\n  - In the 2nd round, if the public card is a Queen, GoodGuy will win with a probability of 80%. If the public card is not a Queen, GoodGuy will lose with a probability of 60%.\n- If GoodGuy holds a King or a Jack, the probabilities will be similar to the above but with different percentages.\n\nPlan 2: Raise\n- If GoodGuy holds a Queen:\n  - In the 1st round, GoodGuy will raise with a probability of 30%. If the opponent holds a King, GoodGuy will lose with a probability of 50%. If the opponent holds a Queen or a Jack, it will be a draw with a probability of 50%.\n  - In the 2nd round, if the public card is a Queen, GoodGuy will win with a probability of 80%. If the public card is not a Queen, GoodGuy will lose with a probability of 60%.\n- If GoodGuy holds a King or a Jack, the probabilities will be similar to the above but with different percentages.\n\nPlan 3: Fold\n- If GoodGuy folds, he will lose the round and lose any chips he has already put in the pot.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, Chips in the pot: 4. If win, the winning payoff would be 2. If lose, the lose payoff would be 2.\n- Plan 2: After the action, Chips in the pot: 8. If win, the winning payoff would be 4. If lose, the lose payoff would be 4.\n- Plan 3: After the action, Chips in the pot: 2. If lose, the lose payoff would be 2.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.7 * 2 - 0.3 * 2 = 0.8 chips\n- Plan 2: Expected Chips Gain = 0.3 * 4 - 0.7 * 4 = -1.6 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so it should be selected."}}
{"message": "", "1_3": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (40% probability), he is likely to raise (90%) or call (10%). If he raises, I will lose (as his King pairs with the public card, while my Queen does not). If he calls, it's a draw (as neither of our cards pair with the public card). So, the winning rate is 0%, losing rate is 36% (40%*90%), and draw rate is 4% (40%*10%).\n- If GoodGuy holds a Queen (35% probability), he is likely to call (60%) or fold (40%). If he calls, it's a draw (as we both hold Queens). If he folds, I will win. So, the winning rate is 14% (35%*40%), losing rate is 0%, and draw rate is 21% (35%*60%).\n- If GoodGuy holds a Jack (25% probability), he is likely to call (50%) or fold (50%). If he calls, I will win (as my Queen is higher than his Jack). If he folds, I will also win. So, the winning rate is 25% (25%*100%), losing rate is 0%, and draw rate is 0%.\n\nPlan 1 overall winning rate is 39% (0%+14%+25%), losing rate is 36% (36%+0%+0%), and draw rate is 25% (4%+21%+0%).\n\nPlan 2: Raise\n- If GoodGuy holds a King (40% probability), he is likely to raise (90%) or call (10%). If he raises, I will lose. If he calls, it's a draw. So, the winning rate is 0%, losing rate is 36% (40%*90%), and draw rate is 4% (40%*10%).\n- If GoodGuy holds a Queen (35% probability), he is likely to call (60%) or fold (40%). If he calls, it's a draw. If he folds, I will win. So, the winning rate is 14% (35%*40%), losing rate is 0%, and draw rate is 21% (35%*60%).\n- If GoodGuy holds a Jack (25% probability), he is likely to call (50%) or fold (50%). If he calls, I will win. If he folds, I will also win. So, the winning rate is 25% (25%*100%), losing rate is 0%, and draw rate is 0%.\n\nPlan 2 overall winning rate is 39% (0%+14%+25%), losing rate is 36% (36%+0%+0%), and draw rate is 25% (4%+21%+0%).\n\nPlan 3: Fold\n- If I fold, I will lose regardless of GoodGuy's card. 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 6 chips (half of the pot). If lose, the lose payoff would be 4 chips (half of the pot).\n- Plan 2: If win, the winning payoff would be 10 chips (half of the pot). If lose, the lose payoff would be 6 chips (half of the pot).\n- Plan 3: If lose, the lose payoff would be 4 chips (half of the pot).\n\nEstimated expected chips gain for each plan:\n- Plan 1: 39%*6 - 36%*4 = 0.54 chips\n- Plan 2: 39%*10 - 36%*6 = 1.44 chips\n- Plan 3: 0%*0 - 100%*4 = -4 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest estimated expected chips gain, followed by Plan 1 (Call), and Plan 3 (Fold). Therefore, I should choose Plan 2 (Raise)."}}
{"message": "", "2_1": {"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, we both have a pair and it's a draw. If the public card is a Queen or Jack, I win as I have a higher card. So, the winning rate is 50%, the draw rate is 50%, and the losing rate is 0%.\n- If GoodGuy holds a Queen (50% probability), he will likely raise (100% probability). If the public card is a King, I win as I have a higher card. If the public card is a Queen, GoodGuy wins as he has a pair. If the public card is a Jack, I win as I have a higher card. So, the winning rate is 66.67%, the draw rate is 0%, and the losing rate is 33.33%.\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, we both have a pair and it's a draw. If the public card is a Queen or Jack, I win as I have a higher card. So, the winning rate is 50%, the draw rate is 50%, and the losing rate is 0%.\n- If GoodGuy holds a Queen (50% probability), he will likely call (100% probability). If the public card is a King, I win as I have a higher card. If the public card is a Queen, GoodGuy wins as he has a pair. If the public card is a Jack, I win as I have a higher card. So, the winning rate is 66.67%, the draw rate is 0%, and the losing rate is 33.33%.\n\nPlan 3: Fold\n- If I fold, I lose the round regardless of GoodGuy's card or the public card. So, the winning rate is 0%, the draw rate is 0%, and the losing rate is 100%.\n\nWinning/Lose Payoffs:\n- Plan 1: If I win, the pot would be 6 chips, so the winning payoff would be 3 chips. If I lose, the pot would be 6 chips, so the losing payoff would be 3 chips.\n- Plan 2: If I win, the pot would be 10 chips, so the winning payoff would be 5 chips. If I lose, the pot would be 10 chips, so the losing payoff would be 5 chips.\n- Plan 3: If I fold, I lose the round and the pot would be 4 chips, so the losing payoff would be 2 chips.\n\nExpected Chips Gain:\n- Plan 1: (50% * 3 chips) - (0% * 3 chips) = 1.5 chips\n- Plan 2: (58.33% * 5 chips) - (16.67% * 5 chips) = 2.08 chips\n- Plan 3: 0 chips - (100% * 2 chips) = -2 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I would choose this plan."}}
{"message": "", "2_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (70% probability), he will likely raise (100% probability). If he raises, I will win (0% probability), lose (100% probability), or draw (0% probability). The overall winning rate is 0%, the losing rate is 70%, and the drawing rate is 0%.\n- If GoodGuy holds a Queen (30% probability), he will likely raise (100% probability). If he raises, I will win (100% probability), lose (0% probability), or draw (0% probability). The overall winning rate is 30%, the losing rate is 0%, and the drawing rate is 0%.\n\nPlan 1 overall GoodGuy's Winning/Lose/Draw rates: The Winning rate for plan 1 is 30%, the Lose rate for plan 1 is 70%, and the Draw Rate for plan 1 is 0%.\n\nPlan 2: Fold\n- If GoodGuy holds a King (70% probability), he will likely raise (100% probability). If I fold, I will lose (100% probability). The overall losing rate is 70%.\n- If GoodGuy holds a Queen (30% probability), he will likely raise (100% probability). If I fold, I will lose (100% probability). The overall losing rate is 30%.\n\nPlan 2 overall GoodGuy's Winning/Lose/Draw rates: The Winning rate for plan 2 is 0%, the Lose rate for plan 2 is 100%, and the Draw Rate for plan 2 is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King (70% probability), he will likely raise (100% probability). If I check, I will win (0% probability), lose (100% probability), or draw (0% probability). The overall winning rate is 0%, the losing rate is 70%, and the drawing rate is 0%.\n- If GoodGuy holds a Queen (30% probability), he will likely raise (100% probability). If I check, I will win (100% probability), lose (0% probability), or draw (0% probability). The overall winning rate is 30%, the losing rate is 0%, and the drawing rate is 0%.\n\nPlan 3 overall GoodGuy's Winning/Lose/Draw rates: The Winning rate for plan 3 is 30%, the Lose rate for plan 3 is 70%, and the Draw Rate for plan 3 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 win, the winning payoff would be 0 chips. If I lose, the losing payoff would be 6 chips.\n- Plan 3: If I win, the winning payoff would be 6 chips. If I lose, the losing payoff would be 6 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 30% * 6 - 70% * 6 = -2.4 chips\n- Plan 2: Expected Chips Gain = 0% * 0 - 100% * 6 = -6 chips\n- Plan 3: Expected Chips Gain = 30% * 6 - 70% * 6 = -2.4 chips\n\nPlan Selection: The rank of estimated expected chips gains for every plan is Plan 1 = Plan 3 > Plan 2. Therefore, I should select either Plan 1 (Raise) or Plan 3 (Check) as they both have the highest estimated expected chips gain."}}
{"message": "", "2_5": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (50% probability), he will likely raise (100% probability). If he raises, I will lose as we both have a King but he has more chips in the pot. The losing rate for this scenario is 50%.\n- If GoodGuy holds a Jack (50% probability), he will likely raise (100% probability). If he raises, I will win as my King is higher than his Jack. The winning rate for this scenario is 50%.\n\nPlan 2: Fold\n- If GoodGuy holds a King (50% probability), he will likely raise (100% probability). If I fold, I will lose the chips I have already put in the pot. The losing rate for this scenario is 50%.\n- If GoodGuy holds a Jack (50% probability), he will likely raise (100% probability). If I fold, I will lose the chips I have already put in the pot. The losing rate for this scenario is 50%.\n\nNumber of Winning and Lose Payoffs for Each Plan:\nPlan 1: \n- After the call action, chips in the pot would be 28. If win, the winning payoff would be 14. If lose, the lose payoff would be 14.\nPlan 2: \n- After the fold action, chips in the pot would remain 24. If lose, the lose payoff would be 14.\n\nEstimate Expected Chips Gain for Each Plan:\nPlan 1: \n- Expected chips gain = winning rate * winning payoff - losing rate * losing payoff = 50% * 14 - 50% * 14 = 0\nPlan 2: \n- Expected chips gain = - losing rate * losing payoff = - 100% * 14 = -14\n\nPlan Selection:\n- Plan 1 has an expected chips gain of 0, while Plan 2 has an expected chips gain of -14. Therefore, Plan 1 (Call) is the better strategy as it has the higher expected chips gain."}}
{"message": "", "3_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (0% probability), he will raise (0% probability). I will lose (0% probability). \n- If GoodGuy holds a Queen (50% probability), he will call (50% probability). I will draw (25% probability). \n- If GoodGuy holds a Jack (50% probability), his actions are uncertain. I will win if the public card is a Queen or King (50% probability). \n\nPlan 2: Raise\n- If GoodGuy holds a King (0% probability), he will raise (0% probability). I will lose (0% probability). \n- If GoodGuy holds a Queen (50% probability), he will call (50% probability). I will draw (25% probability). \n- If GoodGuy holds a Jack (50% probability), his actions are uncertain. I will win if the public card is a Queen or King (50% probability). \n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot (2 chips). \n\nWinning/Lose Payoff for Each Plan:\n- Plan 1: If win, the winning payoff would be 1.5 chips. If lose, the lose payoff would be 2 chips.\n- Plan 2: If win, the winning payoff would be 3 chips. If lose, the lose payoff would be 4 chips.\n- Plan 3: If lose, the lose payoff would be 2 chips.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.5 * 1.5 - 0 * 2 = 0.75 chips\n- Plan 2: Expected Chips Gain = 0.5 * 3 - 0 * 4 = 1.5 chips\n- Plan 3: Expected Chips Gain = 0 - 1 * 2 = -2 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain (1.5 chips), followed by Plan 1 (Call) with 0.75 chips, and Plan 3 (Fold) with -2 chips. Therefore, I should choose Plan 2 (Raise)."}}
{"message": "", "3_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (probability 33.33%), he will likely raise (probability 100%). In this case, I will lose as my pair of Queens is lower than his King. The overall losing rate for this card is 33.33%.\n- If GoodGuy holds a Queen (probability 33.33%), he will likely raise (probability 100%). In this case, it will be a draw as we both have a pair of Queens. The overall draw rate for this card is 33.33%.\n- If GoodGuy holds a Jack (probability 33.33%), his actions are uncertain due to lack of data. However, if he calls or raises, I will win as my pair of Queens is higher than his Jack. The overall winning rate for this card is 33.33%.\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of what card GoodGuy holds. The overall losing rate for this plan is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (probability 33.33%), he will likely raise (probability 100%). In this case, I will lose as my pair of Queens is lower than his King. The overall losing rate for this card is 33.33%.\n- If GoodGuy holds a Queen (probability 33.33%), he will likely raise (probability 100%). In this case, it will be a draw as we both have a pair of Queens. The overall draw rate for this card is 33.33%.\n- If GoodGuy holds a Jack (probability 33.33%), his actions are uncertain due to lack of data. However, if he calls or raises, I will win as my pair of Queens is higher than his Jack. The overall winning rate for this card is 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 pot (currently 8 chips), so 4 chips. If I lose, the losing payoff would be half of the pot, so 4 chips.\n- Plan 2: If I fold, I will lose the game and the losing payoff would be half of the pot, so 4 chips.\n- Plan 3: If I win, the winning payoff would be half of the pot (currently 8 chips), so 4 chips. If I lose, the losing payoff would be half of the pot, so 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 33.33% * 4 - 33.33% * 4 = 0 chips\n- Plan 2: Expected Chips Gain = 0% * Winning Payoff - 100% * Losing Payoff = 0 - 4 = -4 chips\n- Plan 3: Expected Chips Gain = 33.33% * 4 - 33.33% * 4 = 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 4. Therefore, Plan 1 or Plan 3 should be selected. Considering the strategy improvement, Plan 1 (Raise) should be selected as it is more aggressive and could potentially lead to a higher payoff in the long run."}}
{"message": "", "4_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 or Queen, I will lose. If the public card is a Jack, I will win. So, the winning rate is 33.33%, the losing rate is 66.67%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (33.33% probability), he will raise (100% probability). If the public card is a Queen or King, I will lose. If the public card is a Jack, I will win. So, the winning rate is 33.33%, the losing rate is 66.67%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (33.33% probability), he will call (100% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, it will be a draw. So, the winning rate is 0%, the losing rate is 66.67%, and the draw rate is 33.33%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (33.33% probability), he will raise (100% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, I will win. So, the winning rate is 33.33%, the losing rate is 66.67%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (33.33% probability), he will raise (100% probability). If the public card is a Queen or King, I will lose. If the public card is a Jack, I will win. So, the winning rate is 33.33%, the losing rate is 66.67%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (33.33% probability), he will call (100% probability). If the public card is a King or Queen, I will lose. If the public card is a Jack, it will be a draw. So, the winning rate is 0%, the losing rate is 66.67%, and the draw rate is 33.33%.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card. 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 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: Expected Chips Gain = 33.33% * 3 - 66.67% * 1 = 0.33 chips\n- Plan 2: Expected Chips Gain = 33.33% * 7 - 66.67% * 3 = 0.33 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 1 has a lower risk as the lose payoff is smaller. So, I will choose Plan 1: Call."}}
{"message": "", "4_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (probability 33%), he will likely raise (probability 100%). If he raises, I will lose as my Jack is lower than his King. The overall losing rate for his King is 33%.\n- If GoodGuy holds a Queen (probability 33%), he will likely call if I raise (probability 100%). If he calls, I will win as my Jack is higher than his Queen. The overall winning rate for his Queen is 33%.\n- If GoodGuy holds a Jack (probability 33%), he will likely call if I raise (probability 100%). If he calls, it will be a draw as we both hold a Jack. The overall draw rate for his Jack is 33%.\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card. The overall losing rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (probability 33%), he will likely check if I check (probability 100%). If he checks, I will lose as my Jack is lower than his King. The overall losing rate for his King is 33%.\n- If GoodGuy holds a Queen (probability 33%), he will likely check if I check (probability 100%). If he checks, I will win as my Jack is higher than his Queen. The overall winning rate for his Queen is 33%.\n- If GoodGuy holds a Jack (probability 33%), he will likely check if I check (probability 100%). If he checks, it will be a draw as we both hold a Jack. The overall draw rate for his Jack is 33%.\n\nWinning/Lose Payoffs for Each Plan:\n- Plan 1: If I win, the winning payoff would be half of the pot (6 chips). If I lose, the losing payoff would be half of the pot (6 chips).\n- Plan 2: If I fold, I will lose the game and the losing payoff would be the chips I've put into the pot (2 chips).\n- Plan 3: If I win, the winning payoff would be half of the pot (4 chips). If I lose, the losing payoff would be half of the pot (4 chips).\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 33% * 6 - 33% * 6 = 0\n- Plan 2: Expected Chips Gain = 0 * Winning Payoff - 100% * Losing Payoff = -2\n- Plan 3: Expected Chips Gain = 33% * 4 - 33% * 4 = 0\n\nPlan Selection:\n- Plan 1 and Plan 3 both have an expected chips gain of 0, which is higher than Plan 2's expected chips gain of -2. Therefore, Plan 1 (Raise) or Plan 3 (Check) should be selected. Considering the strategy improvement, Plan 1 (Raise) should be selected as it has the potential to confuse GoodGuy and make him believe that I hold a King or Queen."}}
{"message": "", "4_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a Queen (probability 100%), he will raise (probability 100%). Considering the game rule, I will lose (probability 100%). \n- Overall, the losing rate for his Queen is 100% (probability = his card probability * lose action probability).\n\nPlan 2: Fold\n- If GoodGuy holds a Queen (probability 100%), he will raise (probability 100%). Considering the game rule, I will lose (probability 100%). \n- Overall, the losing rate for his Queen is 100% (probability = his card probability * lose action probability).\n\nPlan 1 overall GoodGuy's Winning/Lose/Draw rates: \n- The Winning rate for plan 1 is 0%; \n- Lose rate for plan 1 is 100%; \n- Draw Rate for plan 1 is 0%.\n\nPlan 2 overall GoodGuy's Winning/Lose/Draw rates: \n- The Winning rate for plan 2 is 0%; \n- Lose rate for plan 2 is 100%; \n- Draw Rate for plan 2 is 0%.\n\nThe number of winning and lose payoffs for each plan:\nPlan1: After the action, Chips in the pot: 16. If win, the winning payoff would be 8. After the action, Chips in the pot: 16. If lose, the lose payoff would be 8.\nPlan2: After the action, Chips in the pot: 10. If win, the winning payoff would be 5. After the action, Chips in the pot: 10. If lose, the lose payoff would be 5.\n\nEstimate Expected Chips Gain for Each Plan:\nPlan 1: 0 * 8 - 1 * 8 = -8\nPlan 2: 0 * 5 - 1 * 5 = -5\n\nPlan Selection:\nPlan 2 has the highest estimated expected chips gain (-5), so I will choose Plan 2: Fold."}}
{"message": "", "5_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King, he will raise (probability 100%). I will win if the public card is a King (probability 1/3), draw if the public card is a Queen or Jack (probability 2/3). Overall, the winning rate is 33.33%, the draw rate is 66.67%, and the lose rate is 0%.\n- If GoodGuy holds a Queen, he will raise if I raise (probability 80%) or call if I call (probability 20%). I will win if the public card is a King or Queen (probability 2/3), lose if the public card is a Jack (probability 1/3). Overall, the winning rate is 66.67%, the draw rate is 0%, and the lose rate is 33.33%.\n- If GoodGuy holds a Jack, he will call if I raise (probability 70%) or raise if I call (probability 30%). I will win if the public card is a King or Jack (probability 2/3), lose if the public card is a Queen (probability 1/3). Overall, the winning rate is 66.67%, the draw rate is 0%, and the lose rate is 33.33%.\n\nPlan 2: Raise\n- If GoodGuy holds a King, he will raise (probability 100%). I will win if the public card is a King (probability 1/3), draw if the public card is a Queen or Jack (probability 2/3). Overall, the winning rate is 33.33%, the draw rate is 66.67%, and the lose rate is 0%.\n- If GoodGuy holds a Queen, he will raise if I raise (probability 80%) or call if I call (probability 20%). I will win if the public card is a King or Queen (probability 2/3), lose if the public card is a Jack (probability 1/3). Overall, the winning rate is 66.67%, the draw rate is 0%, and the lose rate is 33.33%.\n- If GoodGuy holds a Jack, he will call if I raise (probability 70%) or raise if I call (probability 30%). I will win if the public card is a King or Jack (probability 2/3), lose if the public card is a Queen (probability 1/3). Overall, the winning rate is 66.67%, the draw rate is 0%, and the lose rate is 33.33%.\n\nPlan 3: Fold\n- If I fold, I will lose the round and lose any chips I have already put in the pot. The winning rate is 0%, the draw rate is 0%, and the lose rate is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, chips in the pot: 2. If win, the winning payoff would be 1. If lose, the lose payoff would be 1.\n- Plan 2: After the action, chips in the pot: 6. If win, the winning payoff would be 3. If lose, the lose payoff would be 3.\n- Plan 3: After the action, chips in the pot: 2. If lose, the lose payoff would be 1.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.67 * 1 - 0.33 * 1 = 0.34\n- Plan 2: Expected Chips Gain = 0.67 * 3 - 0.33 * 3 = 1.02\n- Plan 3: Expected Chips Gain = 0 * 0 - 1 * 1 = -1\n\nPlan Selection:\n- Plan 2 > Plan 1 > Plan 3\n- Therefore, the best plan is to raise."}}
{"message": "", "5_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (probability 33.3%), he will raise (probability 100%). If he raises, I will win because I have a pair of Kings. The winning rate for his King is 33.3%.\n- If GoodGuy holds a Queen (probability 33.3%), he will call (probability 20%) or raise (probability 80%). If he calls or raises, I will win because I have a pair of Kings. The winning rate for his Queen is 33.3%.\n- If GoodGuy holds a Jack (probability 33.3%), he will call (probability 20%) or fold (probability 80%). If he calls, I will win because I have a pair of Kings. If he folds, I will also win because he forfeits the game. The winning rate for his Jack is 33.3%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. The losing rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (probability 33.3%), he will raise (probability 100%). If he raises, I will win because I have a pair of Kings. The winning rate for his King is 33.3%.\n- If GoodGuy holds a Queen (probability 33.3%), he will call (probability 20%) or raise (probability 80%). If he calls or raises, I will win because I have a pair of Kings. The winning rate for his Queen is 33.3%.\n- If GoodGuy holds a Jack (probability 33.3%), he will call (probability 20%) or fold (probability 80%). If he calls, I will win because I have a pair of Kings. If he folds, I will also win because he forfeits the game. The winning rate for his Jack is 33.3%.\n\nWinning/Lose Payoffs for Each Plan:\n- Plan 1: After the action, chips in the pot: 8. If win, the winning payoff would be 4. If lose, the lose payoff would be 4.\n- Plan 2: After the action, chips in the pot: 4. If lose, the lose payoff would be 2.\n- Plan 3: After the action, chips in the pot: 4. If win, the winning payoff would be 2. If lose, the lose payoff would be 2.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected chips gain = winning rate * winning payoff - losing rate * losing payoff = 100% * 4 - 0% * 4 = 4\n- Plan 2: Expected chips gain = winning rate * winning payoff - losing rate * losing payoff = 0% * 2 - 100% * 2 = -2\n- Plan 3: Expected chips gain = winning rate * winning payoff - losing rate * losing payoff = 100% * 2 - 0% * 2 = 2\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I will choose Plan 1: Raise."}}
{"message": "", "6_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King: \n  - In the 1st round, GoodGuy will raise (100% probability). If I call, GoodGuy will likely believe I have a King (100% probability). \n  - In the 2nd round, if the public card is a King, GoodGuy will raise (100% probability). If I call, GoodGuy will likely believe I have a King (100% probability). \n  - Overall, the winning rate is 50% (probability of a King being the public card), the losing rate is 33.33% (probability of a Queen or Jack being the public card and the opponent having a matching card), and the draw rate is 16.67% (probability of a Queen or Jack being the public card and the opponent not having a matching card).\n- If GoodGuy holds a Queen or Jack: \n  - In the 1st round, GoodGuy will call (100% probability). If I call, GoodGuy will likely believe I have a Queen or Jack (100% probability). \n  - In the 2nd round, if the public card is a Queen or Jack, GoodGuy will raise (100% probability). If I call, GoodGuy will likely believe I have a Queen or Jack (100% probability). \n  - Overall, the winning rate is 33.33% (probability of a Queen or Jack being the public card), the losing rate is 50% (probability of a King being the public card or the opponent having a matching card), and the draw rate is 16.67% (probability of a King being the public card and the opponent not having a matching card).\n\nPlan 2: Raise\n- If GoodGuy holds a King: \n  - In the 1st round, GoodGuy will raise (100% probability). If I raise, GoodGuy will likely believe I have a King (100% probability). \n  - In the 2nd round, if the public card is a King, GoodGuy will raise (100% probability). If I raise, GoodGuy will likely believe I have a King (100% probability). \n  - Overall, the winning rate is 50% (probability of a King being the public card), the losing rate is 33.33% (probability of a Queen or Jack being the public card and the opponent having a matching card), and the draw rate is 16.67% (probability of a Queen or Jack being the public card and the opponent not having a matching card).\n- If GoodGuy holds a Queen or Jack: \n  - In the 1st round, GoodGuy will call (100% probability). If I raise, GoodGuy will likely believe I have a King (100% probability). \n  - In the 2nd round, if the public card is a Queen or Jack, GoodGuy will fold (100% probability). If I raise, GoodGuy will likely believe I have a King (100% probability). \n  - Overall, the winning rate is 66.67% (probability of a King being the public card or the opponent not having a matching card), the losing rate is 16.67% (probability of a Queen or Jack being the public card and the opponent having a matching card), and the draw rate is 16.67% (probability of a Queen or Jack being the public card and the opponent not having a matching card).\n\nPlan 3: Fold\n- If GoodGuy folds, he will lose the chips he has 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 win, the winning payoff would be 6 chips. If lose, the lose payoff would be 2 chips.\n- Plan 2: If win, the winning payoff would be 10 chips. If lose, the lose payoff would be 6 chips.\n- Plan 3: If lose, the lose payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 50% * 6 - 33.33% * 2 = 2.33 chips\n- Plan 2: Expected Chips Gain = 66.67% * 10 - 16.67% * 6 = 5.67 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so it should be selected."}}
{"message": "", "6_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (70% probability), he will call (100% probability). If I raise, the pot will be 14 chips. If I win, I will gain 7 chips. If I lose, I will lose 7 chips. The expected chips gain is 0.7 * 7 - 0.3 * 7 = 2.8 chips.\n- If GoodGuy holds a Queen (30% probability), he will raise (100% probability). If I raise, the pot will be 14 chips. If I win, I will gain 7 chips. If I lose, I will lose 7 chips. The expected chips gain is 0.3 * 7 - 0.7 * 7 = -2.8 chips.\n\nPlan 2: Fold\n- If I fold, I will lose 6 chips regardless of GoodGuy's card. The expected chips gain is -6 chips.\n\nPlan 3: Check\n- If GoodGuy holds a King (70% probability), he will call (100% probability). If I check, the pot will remain 6 chips. If I win, I will gain 3 chips. If I lose, I will lose 3 chips. The expected chips gain is 0.7 * 3 - 0.3 * 3 = 1.2 chips.\n- If GoodGuy holds a Queen (30% probability), he will raise (100% probability). If I check, the pot will be 10 chips. If I win, I will gain 5 chips. If I lose, I will lose 5 chips. The expected chips gain is 0.3 * 5 - 0.7 * 5 = -2 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: Raise."}}
{"message": "", "7_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King, he will raise the bet (probability 100%). 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 33.3%, the losing rate is 66.7%, and the draw rate is 0%.\n- If GoodGuy holds a Queen, he will raise the bet if I raise (probability 100%). If the public card is a King, I will lose. If the public card is a Queen or Jack, it will be a draw. So, the winning rate is 0%, the losing rate is 33.3%, and the draw rate is 66.7%.\n- If GoodGuy holds a Jack, he will call if I raise (probability 100%). 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 66.7%, the losing rate is 0%, and the draw rate is 33.3%.\n\nPlan 2: Raise\n- If GoodGuy holds a King, he will raise the bet (probability 100%). 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 33.3%, the losing rate is 66.7%, and the draw rate is 0%.\n- If GoodGuy holds a Queen, he will raise the bet if I raise (probability 100%). If the public card is a King, I will lose. If the public card is a Queen or Jack, it will be a draw. So, the winning rate is 0%, the losing rate is 33.3%, and the draw rate is 66.7%.\n- If GoodGuy holds a Jack, he will call if I raise (probability 100%). 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 66.7%, the losing rate is 0%, and the draw rate is 33.3%.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card or the public 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 2 chips. If lose, the lose payoff would be 1 chip.\n- Plan 2: If win, the winning payoff would be 6 chips. If lose, the lose payoff would be 2 chips.\n- Plan 3: If fold, the lose payoff would be 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 33.3% * 2 - 66.7% * 1 = -0.33 chips\n- Plan 2: Expected Chips Gain = 33.3% * 6 - 66.7% * 2 = 0 chips\n- Plan 3: Expected Chips Gain = 0% * 0 - 100% * 1 = -1 chips\n\nPlan Selection:\n- Plan 1: -0.33 chips\n- Plan 2: 0 chips\n- Plan 3: -1 chips\n\nBased on the estimated expected chips gain, Plan 2 (Raise) is the best strategy to use in this situation."}}
{"message": "", "7_2": {"plan": "Plan 1: Raise the bet\n- If GoodGuy holds a Jack, he will raise the bet (probability 100%). I will lose as he has a pair of Jacks and I only have a single Queen. The lose rate for his Jack is 50% (probability of him having a Jack * probability of losing).\n- If GoodGuy holds a Queen, he might raise the bet (probability 50%) or fold (probability 50%). I will win if he folds as I have a higher card. The win rate for his Queen is 12.5% (probability of him having a Queen * probability of winning).\n- If GoodGuy holds a King, he will fold (probability 100%). I will win as he folds. The win rate for his King is 25% (probability of him having a King * probability of winning).\n- Overall, the winning rate for plan 1 is 37.5%, the lose rate is 50%, and the draw rate is 12.5%.\n\nPlan 2: Fold the hand\n- If I fold, I will lose regardless of GoodGuy's card. The lose rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a Jack, he will raise the bet (probability 100%). I will lose as he has a pair of Jacks and I only have a single Queen. The lose rate for his Jack is 50%.\n- If GoodGuy holds a Queen, he might raise the bet (probability 50%) or check (probability 50%). I will win if he checks as I have a higher card. The win rate for his Queen is 12.5%.\n- If GoodGuy holds a King, he will check (probability 100%). I will win as I have a higher card. The win rate for his King is 25%.\n- Overall, the winning rate for plan 3 is 37.5%, the lose rate is 50%, and the draw rate is 12.5%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After raising the bet, the 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 folding, the chips in the pot would remain 8. If lose, the lose payoff would be 4.\n- Plan 3: After checking, the chips in the pot would remain 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 = 37.5% * 8 - 50% * 8 = -1\n- Plan 2: Expected Chips Gain = 0% * 4 - 100% * 4 = -4\n- Plan 3: Expected Chips Gain = 37.5% * 4 - 50% * 4 = -0.5\n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 3 > Plan 1 > Plan 2.\n- Therefore, the best strategy is to check (Plan 3), as it has the highest estimated expected chips gain."}}
{"message": "", "8_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (20% 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 lose (50% probability). Overall, the winning rate is 10%, the losing rate is 10%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (40% probability), he will call (100% probability). If the public card is a King or a Jack, I will win (66.67% probability). If the public card is a Queen, I will lose (33.33% probability). Overall, the winning rate is 26.67%, the losing rate is 13.33%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (40% probability), he will call (100% probability). If the public card is a King or a Queen, I will win (66.67% probability). If the public card is a Jack, I will lose (33.33% probability). Overall, the winning rate is 26.67%, the losing rate is 13.33%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (20% 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 lose (50% probability). Overall, the winning rate is 10%, the losing rate is 10%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (40% probability), he will call (100% probability). If the public card is a King or a Jack, I will win (66.67% probability). If the public card is a Queen, I will lose (33.33% probability). Overall, the winning rate is 26.67%, the losing rate is 13.33%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (40% probability), he will raise (100% probability). If the public card is a King or a Queen, I will win (66.67% probability). If the public card is a Jack, I will lose (33.33% probability). Overall, the winning rate is 26.67%, the losing rate is 13.33%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose 100% of the time. The losing rate is 100%, and the winning and draw rates are 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the call, chips in the pot: 4. If win, the winning payoff would be 2. If lose, the lose payoff would be 2.\n- Plan 2: After the raise, chips in the pot: 8. If win, the winning payoff would be 4. If lose, the lose payoff would be 4.\n- Plan 3: After the fold, chips in the pot: 3. If lose, the lose payoff would be 1.5.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0.6367 * 2 - 0.3633 * 2 = 0.5468\n- Plan 2: 0.6367 * 4 - 0.3633 * 4 = 1.0936\n- Plan 3: 0 - 1 * 1.5 = -1.5\n\nPlan Selection:\n- Plan 2 (Raise) has the highest estimated expected chips gain, followed by Plan 1 (Call), and Plan 3 (Fold) has the lowest estimated expected chips gain. Therefore, I should choose Plan 2 (Raise)."}}
{"message": "", "8_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (50% probability), he will raise (100% probability). Since we both have a pair of Kings, it will be a draw. The pot will be 16 chips (4 chips from the first round, 8 chips from my raise, and 4 chips from GoodGuy's raise). The winning payoff would be 8 chips, and the losing payoff would also be 8 chips. \n- If GoodGuy holds a Queen (25% probability), he will fold (100% probability). I will win the round and the pot will be 12 chips (4 chips from the first round and 8 chips from my raise). The winning payoff would be 6 chips.\n- If GoodGuy holds a Jack (25% probability), he will raise (100% probability). I will win the round and the pot will be 16 chips (4 chips from the first round, 8 chips from my raise, and 4 chips from GoodGuy's raise). The winning payoff would be 8 chips.\n\nPlan 2: Fold\n- If I fold, I will lose the round regardless of GoodGuy's card. The pot will be 8 chips (4 chips from the first round and 4 chips from GoodGuy's call). The losing payoff would be 4 chips.\n\nPlan 3: Check\n- If GoodGuy holds a King (50% probability), he will raise (100% probability). Since we both have a pair of Kings, it will be a draw. The pot will be 12 chips (4 chips from the first round and 8 chips from GoodGuy's raise). The winning payoff would be 6 chips, and the losing payoff would also be 6 chips. \n- If GoodGuy holds a Queen (25% probability), he will fold (100% probability). I will win the round and the pot will be 8 chips (4 chips from the first round and 4 chips from GoodGuy's call). The winning payoff would be 4 chips.\n- If GoodGuy holds a Jack (25% probability), he will raise (100% probability). I will win the round and the pot will be 12 chips (4 chips from the first round and 8 chips from GoodGuy's raise). The winning payoff would be 6 chips.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: (0.5 * 8 + 0.25 * 6 + 0.25 * 8) - 0 * 8 = 7.5 chips\n- Plan 2: 0 - 1 * 4 = -4 chips\n- Plan 3: (0.5 * 6 + 0.25 * 4 + 0.25 * 6) - 0 * 6 = 5.5 chips\n\nPlan Selection:\nBased on the expected chips gain, the ranking of the plans is as follows:\n1. Plan 1: Raise\n2. Plan 3: Check\n3. Plan 2: Fold\n\nTherefore, the best strategy for this turn is to raise."}}
{"message": "", "9_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (33.33% probability), he will likely raise in the next round (100% probability). If the public card is a King, I will lose (100% probability). If the public card is a Queen or Jack, I have a 50% chance of winning (if the public card matches my card) and a 50% chance of losing (if the public card matches GoodGuy's card).\n- If GoodGuy holds a Queen (33.33% probability), he will likely call in the next round (100% probability). If the public card is a Queen, I will lose (100% probability). If the public card is a King or Jack, I have a 50% chance of winning (if the public card matches my card) and a 50% chance of losing (if the public card matches GoodGuy's card).\n- If GoodGuy holds a Jack (33.33% probability), he will likely call in the next round (100% probability). If the public card is a Jack, it will be a draw (100% probability). If the public card is a King or Queen, I have a 50% chance of winning (if the public card matches my card) and a 50% chance of losing (if the public card matches GoodGuy's card).\n\nPlan 2: Raise\n- If GoodGuy holds a King (33.33% probability), he will likely call in the next round (100% probability). If the public card is a King, I will lose (100% probability). If the public card is a Queen or Jack, I have a 50% chance of winning (if the public card matches my card) and a 50% chance of losing (if the public card matches GoodGuy's card).\n- If GoodGuy holds a Queen (33.33% probability), he will likely fold in the next round (100% probability), and I will win (100% probability).\n- If GoodGuy holds a Jack (33.33% probability), he will likely fold in the next round (100% probability), and I will win (100% probability).\n\nPlan 3: Fold\n- If I fold, I will lose the round and lose any chips I have already put in the pot (100% probability).\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 2 chips. If I lose, the lose payoff would be 1 chip.\n- Plan 2: If I win, the winning payoff would be 6 chips. If I lose, the lose payoff would be 4 chips.\n- Plan 3: If I fold, the lose payoff would be 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.33 * 2 - 0.67 * 1 = -0.01 chips\n- Plan 2: Expected Chips Gain = 0.67 * 6 - 0.33 * 4 = 2.34 chips\n- Plan 3: Expected Chips Gain = -1 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I should choose this plan."}}
{"message": "", "9_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (70% probability), he will likely call (100% probability). In this case, I will lose as his King matches the public card. \n- If GoodGuy holds a Queen (30% probability), he will likely fold (100% probability). In this case, I will win as my Jack is higher than his Queen. \n- Overall, the winning rate for this plan is 30% (probability of GoodGuy holding a Queen * probability of him folding), the losing rate is 70% (probability of GoodGuy holding a King * probability of him calling), and the draw rate is 0%. \n- After the action, if I win, the chips in the pot would be 16 (4 chips from me, 4 chips from GoodGuy, 4 chips from my raise, 4 chips from GoodGuy's call). The winning payoff would be 8 chips. If I lose, the chips in the pot would be 16, and the losing payoff would be 8 chips. \n- The expected chips gain for this plan is 30% * 8 chips - 70% * 8 chips = -2.4 chips.\n\nPlan 2: Fold\n- If I fold, I will lose the 4 chips I have already put in the pot. \n- The expected chips gain for this plan is -4 chips.\n\nPlan 3: Check\n- If GoodGuy holds a King (70% probability), he will likely raise (100% probability). In this case, I will lose as his King matches the public card. \n- If GoodGuy holds a Queen (30% probability), he will likely check (100% probability). In this case, I will win as my Jack is higher than his Queen. \n- Overall, the winning rate for this plan is 30% (probability of GoodGuy holding a Queen * probability of him checking), the losing rate is 70% (probability of GoodGuy holding a King * probability of him raising), and the draw rate is 0%. \n- After the action, if I win, the chips in the pot would be 8 (4 chips from me, 4 chips from GoodGuy). The winning payoff would be 4 chips. If I lose, the chips in the pot would be 12 (4 chips from me, 4 chips from GoodGuy, 4 chips from GoodGuy's raise), and the losing payoff would be 6 chips. \n- The expected chips gain for this plan is 30% * 4 chips - 70% * 6 chips = -3.2 chips.\n\nPlan Selection:\n- Plan 1: -2.4 chips\n- Plan 2: -4 chips\n- Plan 3: -3.2 chips\n\nBased on the expected chips gain, Plan 1 (Raise) is the best strategy to follow."}}
{"message": "", "10_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (33.3% probability), he will likely raise (100% probability). If the public card is a King, I will win (100% probability). If the public card is not a King, I will lose (100% probability). Overall, the winning rate is 33.3%, the losing rate is 33.3%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (33.3% probability), he will likely raise (100% probability). If the public card is a Queen, I will lose (100% probability). If the public card is not a Queen, I will win (100% probability). Overall, the winning rate is 33.3%, the losing rate is 33.3%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (33.3% probability), he will likely call (100% probability). If the public card is a Jack, I will lose (100% probability). If the public card is not a Jack, I will win (100% probability). Overall, the winning rate is 33.3%, the losing rate is 33.3%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose the round regardless of GoodGuy's card. The losing rate is 100%, and the winning and draw rates are 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King (33.3% probability), he will likely raise (100% probability). If the public card is a King, I will win (100% probability). If the public card is not a King, I will lose (100% probability). Overall, the winning rate is 33.3%, the losing rate is 33.3%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (33.3% probability), he will likely raise (100% probability). If the public card is a Queen, I will lose (100% probability). If the public card is not a Queen, I will win (100% probability). Overall, the winning rate is 33.3%, the losing rate is 33.3%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (33.3% probability), he will likely call (100% probability). If the public card is a Jack, I will lose (100% probability). If the public card is not a Jack, I will win (100% probability). Overall, the winning rate is 33.3%, the losing rate is 33.3%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If 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: (33.3% * 6) - (33.3% * 6) = 0 chips\n- Plan 2: 0 - (100% * 2) = -2 chips\n- Plan 3: (33.3% * 4) - (33.3% * 4) = 0 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 both have an expected chips gain of 0, which is higher than Plan 2's expected chips gain of -2. Therefore, I should choose either Plan 1 or Plan 3. Considering the strategy improvement, I should choose Plan 1 (Raise) as it is more aggressive and may lead to higher gains in the long run."}}
{"message": "", "10_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (100% probability based on my belief), he will likely fold if I raise (100% probability based on his behavior pattern). This means I will win the pot, which is currently 8 chips (4 from me and 4 from GoodGuy). The winning payoff would be half of the pot, which is 4 chips. If I win, my total chips would increase to 56 (52 + 4).\n- If GoodGuy holds a Jack (0% probability based on my belief), he will likely fold if I raise (100% probability based on his behavior pattern). This means I will win the pot, which is currently 8 chips (4 from me and 4 from GoodGuy). The winning payoff would be half of the pot, which is 4 chips. If I win, my total chips would increase to 56 (52 + 4).\n- Overall, the expected chips gain for Plan 1 is (1.00 * 4) - (0.00 * 4) = 4 chips.\n\nPlan 2: Fold\n- If I fold, I will lose the pot, which is currently 8 chips (4 from me and 4 from GoodGuy). The losing payoff would be half of the pot, which is 4 chips. If I lose, my total chips would decrease to 48 (52 - 4).\n- The expected chips gain for Plan 2 is (0.00 * 4) - (1.00 * 4) = -4 chips.\n\nPlan 3: Check\n- If GoodGuy holds a Queen (100% probability based on my belief), he will likely fold if I check (0% probability based on his behavior pattern). This means I will win the pot, which is currently 8 chips (4 from me and 4 from GoodGuy). The winning payoff would be half of the pot, which is 4 chips. If I win, my total chips would increase to 56 (52 + 4).\n- If GoodGuy holds a Jack (0% probability based on my belief), he will likely fold if I check (0% probability based on his behavior pattern). This means I will win the pot, which is currently 8 chips (4 from me and 4 from GoodGuy). The winning payoff would be half of the pot, which is 4 chips. If I win, my total chips would increase to 56 (52 + 4).\n- Overall, the expected chips gain for Plan 3 is (1.00 * 4) - (0.00 * 4) = 4 chips.\n\nPlan Selection:\n- Plan 1: Expected chips gain = 4 chips\n- Plan 2: Expected chips gain = -4 chips\n- Plan 3: Expected chips gain = 4 chips\n\nBased on the expected chips gain, Plan 1 (Raise) and Plan 3 (Check) are the best strategies. However, considering the strategy improvement, Plan 1 (Raise) is the best strategy as it puts more pressure on GoodGuy and increases the chances of him folding. Therefore, I will choose Plan 1 (Raise)."}}
{"message": "", "11_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (40% chance), he will likely raise (70% chance). If he raises, I will lose as my Queen is lower than his King. Therefore, the losing rate for this plan is 40% * 70% = 28%. If he calls (30% chance), it will be a draw as we both have the same amount of chips in the pot. Therefore, the draw rate for this plan is 40% * 30% = 12%.\n- If GoodGuy holds a Queen (30% chance), he will likely call (60% chance). If he calls, it will be a draw as we both have the same amount of chips in the pot. Therefore, the draw rate for this plan is 30% * 60% = 18%. If he raises (40% chance), I will win as my Queen is higher than his Jack. Therefore, the winning rate for this plan is 30% * 40% = 12%.\n- If GoodGuy holds a Jack (30% chance), he will likely call (70% chance). If he calls, I will win as my Queen is higher than his Jack. Therefore, the winning rate for this plan is 30% * 70% = 21%. If he folds (30% chance), I will also win as he forfeits the game. Therefore, the winning rate for this plan is 30% * 30% = 9%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (40% chance), he will likely raise (70% chance). If he raises, I will lose as my Queen is lower than his King. Therefore, the losing rate for this plan is 40% * 70% = 28%. If he calls (30% chance), it will be a draw as we both have the same amount of chips in the pot. Therefore, the draw rate for this plan is 40% * 30% = 12%.\n- If GoodGuy holds a Queen (30% chance), he will likely raise (40% chance). If he raises, it will be a draw as we both have the same amount of chips in the pot. Therefore, the draw rate for this plan is 30% * 40% = 12%. If he calls (60% chance), I will win as my Queen is higher than his Jack. Therefore, the winning rate for this plan is 30% * 60% = 18%.\n- If GoodGuy holds a Jack (30% chance), he will likely fold (30% chance). If he folds, I will win as he forfeits the game. Therefore, the winning rate for this plan is 30% * 30% = 9%. If he calls (70% chance), I will win as my Queen is higher than his Jack. Therefore, the winning rate for this plan is 30% * 70% = 21%.\n\nPlan 3: Fold\n- If I fold, I will lose 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: After the action, Chips in the pot: 3. If win, the winning payoff would be 1.5 chips. If lose, the lose payoff would be 1.5 chips.\n- Plan 2: After the action, Chips in the pot: 5. If win, the winning payoff would be 2.5 chips. If lose, the lose payoff would be 2.5 chips.\n- Plan 3: After the action, Chips in the pot: 1. If lose, the lose payoff would be 0.5 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Lose Payoff = 42% * 1.5 - 28% * 1.5 = 0.21 chips\n- Plan 2: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Lose Payoff = 48% * 2.5 - 28% * 2.5 = 0.5 chips\n- Plan 3: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Lose Payoff = 0% * 0 - 100% * 0.5 = -0.5 chips\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain, so I will choose Plan 2: Raise."}}
{"message": "", "11_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (10% probability), he will likely raise (90%). If he raises, I will lose as his pair of Kings beats my single Queen. The lose rate is 90%.\n- If GoodGuy holds a Queen (50% probability), he will likely call (50%) or fold (50%). If he calls, I will win as my Queen beats his Queen due to player order. If he folds, I will also win. The win rate is 100%.\n- If GoodGuy holds a Jack (40% probability), he will likely call (40%) or fold (60%). If he calls, I will win as my Queen beats his Jack. If he folds, I will also win. The win rate is 100%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of GoodGuy's card. The lose rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (10% probability), he will likely raise (90%). If he raises, I will lose as his pair of Kings beats my single Queen. The lose rate is 90%.\n- If GoodGuy holds a Queen (50% probability), he will likely call (50%) or fold (50%). If he calls, I will win as my Queen beats his Queen due to player order. If he folds, I will also win. The win rate is 100%.\n- If GoodGuy holds a Jack (40% probability), he will likely call (40%) or fold (60%). If he calls, I will win as my Queen beats his Jack. If he folds, I will also win. The win rate is 100%.\n\nWinning/Lose Payoffs:\n- Plan 1: If I win, the pot will be 8 chips, so the winning payoff will be 4 chips. If I lose, I will lose 4 chips.\n- Plan 2: If I fold, I will lose 4 chips.\n- Plan 3: If I win, the pot will be 8 chips, so the winning payoff will be 4 chips. If I lose, I will lose 4 chips.\n\nExpected Chips Gain:\n- Plan 1: (100% * 4 chips) - (10% * 4 chips) = 3.6 chips\n- Plan 2: 0 - (100% * 4 chips) = -4 chips\n- Plan 3: (100% * 4 chips) - (10% * 4 chips) = 3.6 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 both have the highest expected chips gain of 3.6 chips, while Plan 2 has the lowest expected chips gain of -4 chips. Therefore, I should either raise (Plan 1) or check (Plan 3). Considering the strategy improvement, I should choose Plan 1: Raise, as it is more aggressive and can potentially lead to higher winnings in the long run."}}
{"message": "", "12_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (0% probability as I hold a Jack), he would likely raise (80% probability) or call (20% probability). However, since I hold a Jack, the probability of winning is 0%.\n- If GoodGuy holds a Queen (50% probability), he would likely call (70% probability) or fold (30% probability). If he calls, I have a 50% chance of winning if the public card is a Jack. If he folds, I win the pot.\n- If GoodGuy holds a Jack (50% probability), he would likely call (60% probability) or fold (40% probability). If he calls, it's a draw if the public card is a Jack. If he folds, I win the pot.\n\nPlan 2: Fold\n- If I fold, I lose the pot regardless of GoodGuy's cards or actions.\n\nPlan 3: Check\n- If GoodGuy holds a King (0% probability as I hold a Jack), he would likely raise (80% probability) or call (20% probability). However, since I hold a Jack, the probability of winning is 0%.\n- If GoodGuy holds a Queen (50% probability), he would likely call (70% probability) or fold (30% probability). If he calls, I have a 50% chance of winning if the public card is a Jack. If he folds, I win the pot.\n- If GoodGuy holds a Jack (50% probability), he would likely call (60% probability) or fold (40% probability). If he calls, it's a draw if the public card is a Jack. If he folds, I win the pot.\n\nWinning/Lose Payoffs for Each Plan:\n- Plan 1: If I win, the winning payoff would be half of the pot (currently 4 chips, so 2 chips). If I lose, the losing payoff would be half of the pot (2 chips).\n- Plan 2: If I fold, I lose the pot (2 chips).\n- Plan 3: If I win, the winning payoff would be half of the pot (2 chips). If I lose, the losing payoff would be half of the pot (2 chips).\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected gain = 0.5 * (winning rate * 2 chips - losing rate * 2 chips) = 0.5 * (0.5 * 2 - 0.5 * 2) = 0 chips\n- Plan 2: Expected gain = -2 chips (as I would lose the pot)\n- Plan 3: Expected gain = 0.5 * (winning rate * 2 chips - losing rate * 2 chips) = 0.5 * (0.5 * 2 - 0.5 * 2) = 0 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 have the same expected chips gain (0 chips), while Plan 2 has a negative expected gain (-2 chips). Therefore, I should either raise (Plan 1) or check (Plan 3). Considering the strategy improvement, I should be more cautious when I have weaker hands and consider folding more often. Therefore, I would choose Plan 3: Check."}}
{"message": "", "12_3": {"plan": "Plan 1: Call\n- If GoodGuy holds a Jack (60% probability), he is likely to fold (80% probability) or call (20% probability). If he folds, I will win the pot (6 chips). If he calls, we will draw and split the pot (6 chips). \n- If GoodGuy holds a Queen (40% probability), he is likely to raise (80% probability) or call (20% probability). If he raises, I will lose the pot (6 chips). If he calls, I will lose the pot (6 chips). \n- Overall, the winning rate for plan 1 is 60% * 80% = 48%, the losing rate is 40% * 100% = 40%, and the draw rate is 60% * 20% = 12%.\n\nPlan 2: Raise\n- If GoodGuy holds a Jack (60% probability), he is likely to fold (80% probability) or call (20% probability). If he folds, I will win the pot (10 chips). If he calls, we will draw and split the pot (10 chips). \n- If GoodGuy holds a Queen (40% probability), he is likely to raise (80% probability) or call (20% probability). If he raises, I will lose the pot (10 chips). If he calls, I will lose the pot (10 chips). \n- Overall, the winning rate for plan 2 is 60% * 80% = 48%, the losing rate is 40% * 100% = 40%, and the draw rate is 60% * 20% = 12%.\n\nPlan 3: Fold\n- If I fold, I will lose the pot (6 chips) regardless of what GoodGuy holds or does. The losing rate for plan 3 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 3 chips.\n- Plan 2: If win, the winning payoff would be 5 chips. If lose, the lose payoff would be 5 chips.\n- Plan 3: If lose, the lose payoff would be 3 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 48% * 3 chips - 40% * 3 chips = 0.24 chips\n- Plan 2: 48% * 5 chips - 40% * 5 chips = 0.4 chips\n- Plan 3: -100% * 3 chips = -3 chips\n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 2 > Plan 1 > Plan 3.\n- Therefore, the plan with the highest estimated expected chips gain is Plan 2: Raise."}}
{"message": "", "13_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (probability 0.33), he will raise (probability 0.8) or call (probability 0.2). If he raises, I will lose (probability 1) because my Jack is lower than his King. If he calls, I will win (probability 0.33) if the public card is a Jack, lose (probability 0.33) if the public card is a King, and draw (probability 0.33) if the public card is a Queen.\n- If GoodGuy holds a Queen (probability 0.33), he will raise (probability 0.3) or call (probability 0.7). If he raises, I will lose (probability 1) because my Jack is lower than his Queen. If he calls, I will win (probability 0.33) if the public card is a Jack, lose (probability 0.33) if the public card is a Queen, and draw (probability 0.33) if the public card is a King.\n- If GoodGuy holds a Jack (probability 0.33), he will call (probability 0.6) or fold (probability 0.4). If he calls, I will draw (probability 1) because we both hold a Jack. If he folds, I will win (probability 1).\n- Overall, the winning rate for plan 1 is 0.33, the losing rate is 0.33, and the drawing rate is 0.33.\n\nPlan 2: Raise\n- If GoodGuy holds a King (probability 0.33), he will raise (probability 0.8) or call (probability 0.2). If he raises, I will lose (probability 1) because my Jack is lower than his King. If he calls, I will win (probability 0.33) if the public card is a Jack, lose (probability 0.33) if the public card is a King, and draw (probability 0.33) if the public card is a Queen.\n- If GoodGuy holds a Queen (probability 0.33), he will call (probability 0.7) or fold (probability 0.3). If he calls, I will win (probability 0.33) if the public card is a Jack, lose (probability 0.33) if the public card is a Queen, and draw (probability 0.33) if the public card is a King. If he folds, I will win (probability 1).\n- If GoodGuy holds a Jack (probability 0.33), he will fold (probability 0.6) or call (probability 0.4). If he folds, I will win (probability 1). If he calls, I will draw (probability 1) because we both hold a Jack.\n- Overall, the winning rate for plan 2 is 0.44, the losing rate is 0.22, and the drawing rate is 0.33.\n\nPlan 3: Fold\n- If I fold, I will lose (probability 1) because I forfeit the game.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 6 chips. If I lose, the losing payoff would be 2 chips.\n- Plan 2: If I win, the winning payoff would be 8 chips. If I lose, the losing payoff would be 4 chips.\n- Plan 3: If I lose, the losing payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0.33 * 6 - 0.33 * 2 = 1.32 chips\n- Plan 2: 0.44 * 8 - 0.22 * 4 = 2.64 chips\n- Plan 3: -2 chips\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain, so I will choose Plan 2: Raise."}}
{"message": "", "13_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (50% probability), he will likely call (60% probability). If he calls, I will win because my Jack is lower than his King. The winning rate for this scenario is 30% (50% * 60%).\n- If GoodGuy holds a Queen (50% probability), he will likely fold (50% probability). If he folds, I will win because he forfeits the game. The winning rate for this scenario is 25% (50% * 50%).\n\nPlan 2: Fold\n- If GoodGuy holds a King (50% probability), he will win because I forfeit the game. The losing rate for this scenario is 50%.\n- If GoodGuy holds a Queen (50% probability), he will win because I forfeit the game. The losing rate for this scenario is 50%.\n\nPlan 3: Check\n- If GoodGuy holds a King (50% probability), he will likely call (60% probability). If he calls, I will lose because my Jack is lower than his King. The losing rate for this scenario is 30% (50% * 60%).\n- If GoodGuy holds a Queen (50% probability), he will likely fold (50% probability). If he folds, I will win because he forfeits the game. The winning rate for this scenario is 25% (50% * 50%).\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 6 chips (half of the pot). If I lose, the lose payoff would be 6 chips.\n- Plan 2: If I win, the winning payoff would be 6 chips. If I lose, the lose payoff would be 6 chips.\n- Plan 3: If I win, the winning payoff would be 6 chips. If I lose, the lose payoff would be 6 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.55 * 6 - 0.45 * 6 = 0.6 chips\n- Plan 2: Expected Chips Gain = 0 * 6 - 1 * 6 = -6 chips\n- Plan 3: Expected Chips Gain = 0.25 * 6 - 0.75 * 6 = -3 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I will choose Plan 1: Raise."}}
{"message": "", "14_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. If the public card is a Queen or Jack, it will be a draw. \n- If GoodGuy holds a Queen (30% probability), he will likely raise if I raise (80% probability) and call if I call (20% probability). If the public card is a Queen, I will lose. If the public card is a King or Jack, it will be a draw. \n- If GoodGuy holds a Jack (20% probability), he will likely call if I raise (60% probability) and raise if I call (40% probability). If the public card is a Jack, I will win. If the public card is a King or Queen, it will be a draw. \n\nPlan 2: Raise\n- If GoodGuy holds a King (50% probability), he will likely 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. \n- If GoodGuy holds a Queen (30% probability), he will likely raise if I raise (80% probability) and call if I call (20% probability). If the public card is a Queen, I will lose. If the public card is a King or Jack, it will be a draw. \n- If GoodGuy holds a Jack (20% probability), he will likely call if I raise (60% probability) and raise if I call (40% probability). If the public card is a Jack, I will win. If the public card is a King or Queen, it will be a draw. \n\nPlan 3: Fold\n- If I fold, I will lose the 2 chips I have already put in the pot. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips (half of the 6 chips in the pot). If I lose, the lose payoff would be 2 chips (half of the 4 chips in the pot).\n- Plan 2: If I win, the winning payoff would be 5 chips (half of the 10 chips in the pot). If I lose, the lose payoff would be 4 chips (half of the 8 chips in the pot).\n- Plan 3: If I fold, I will lose the 2 chips I have already put in the pot. \n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.2 * 3 - 0.8 * 2 = -1.2 chips\n- Plan 2: Expected Chips Gain = 0.2 * 5 - 0.8 * 4 = -2.6 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain (-1.2 chips), followed by Plan 3 (-2 chips), and Plan 2 (-2.6 chips). Therefore, I should choose Plan 1: Call."}}
{"message": "", "14_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (40% probability), he will likely call (100% probability). If this happens, I will lose as his King is higher than my Jack. \n- If GoodGuy holds a Queen (0% probability), he will not be in this situation as he would have raised in the previous round.\n- If GoodGuy holds a Jack (60% probability), he will likely call (60% probability) or fold (40% probability). If he calls, it will be a draw as we both have a Jack. If he folds, I will win.\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 (40% probability), he will likely check (100% probability). If this happens, I will lose as his King is higher than my Jack. \n- If GoodGuy holds a Queen (0% probability), he will not be in this situation as he would have raised in the previous round.\n- If GoodGuy holds a Jack (60% probability), he will likely check (60% probability) or raise (40% probability). If he checks, it will be a draw as we both have a Jack. If he raises, I will lose.\n\nWinning/Lose Payoff for Each Plan:\n- Plan 1: If I win, the pot will be 8 chips, so my winning payoff will be 4 chips. If I lose, I will lose 4 chips.\n- Plan 2: If I fold, I will lose 2 chips.\n- Plan 3: If I win, the pot will be 4 chips, so my winning payoff will be 2 chips. If I lose, I will lose 2 chips.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: (0.6 * 4 - 0.4 * 4) = 0.8 chips\n- Plan 2: -2 chips\n- Plan 3: (0.6 * 2 - 0.4 * 2) = 0.4 chips\n\nPlan Selection:\nBased on the expected chips gain, Plan 1 (Raise) is the best strategy to use in this situation."}}
{"message": "", "14_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a Queen (80% probability), he will likely raise (80% probability). If he raises, I will lose as his pair of Queens is higher than my single Jack. The overall losing rate for this scenario is 0.8 * 0.8 = 0.64.\n- If GoodGuy holds a Jack (20% probability), he will likely raise (60% probability) or fold (40% probability). If he raises, it will be a draw as we both have a single Jack. If he folds, I will win. The overall winning rate for this scenario is 0.2 * 0.4 = 0.08, and the draw rate is 0.2 * 0.6 = 0.12.\n\nPlan 2: Fold\n- If GoodGuy holds a Queen (80% probability), I will lose regardless of his action. The overall losing rate for this scenario is 0.8.\n- If GoodGuy holds a Jack (20% probability), I will lose regardless of his action. The overall losing rate for this scenario is 0.2.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the pot, which is (6+10+4)/2 = 10 chips. If I lose, the losing payoff would be the chips I have put into the pot, which is 6 chips.\n- Plan 2: If I fold, I will lose the chips I have put into the pot, which is 6 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is the winning rate * winning payoff - losing rate * losing payoff = 0.08 * 10 - 0.64 * 6 = -3.2 chips.\n- Plan 2: The expected chips gain is -6 chips as I will lose the chips I have put into the pot.\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain (-3.2 chips) than Plan 2 (-6 chips). Therefore, I should choose Plan 1: Call. However, both plans result in a loss of chips, so I should also consider improving my strategy in the future games."}}
{"message": "", "15_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (probability 1/3), he will likely raise (80%) or call (20%). If he raises, I will lose as my Queen is lower than his King. If he calls, it will be a draw as we both have the same amount of chips in the pot. The overall winning rate for this plan is 0%, the losing rate is 80% (1/3 * 80%), and the draw rate is 20% (1/3 * 20%).\n- If GoodGuy holds a Queen (probability 1/3), he will likely raise (60%) or call (40%). If he raises or calls, it will be a draw as we both have the same card and the same amount of chips in the pot. The overall winning rate for this plan is 0%, the losing rate is 0%, and the draw rate is 100% (1/3 * 100%).\n- If GoodGuy holds a Jack (probability 1/3), he will likely call (70%) or raise (30%). If he calls or raises, I will win as my Queen is higher than his Jack. The overall winning rate for this plan is 100% (1/3 * 100%), the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (probability 1/3), he will likely raise (80%) or call (20%). If he raises or calls, I will lose as my Queen is lower than his King. The overall winning rate for this plan is 0%, the losing rate is 100% (1/3 * 100%), and the draw rate is 0%.\n- If GoodGuy holds a Queen (probability 1/3), he will likely raise (60%) or call (40%). If he raises or calls, it will be a draw as we both have the same card and the same amount of chips in the pot. The overall winning rate for this plan is 0%, the losing rate is 0%, and the draw rate is 100% (1/3 * 100%).\n- If GoodGuy holds a Jack (probability 1/3), he will likely call (70%) or raise (30%). If he calls, I will win as my Queen is higher than his Jack. If he raises, it will be a draw as we both have the same amount of chips in the pot. The overall winning rate for this plan is 70% (1/3 * 70%), the losing rate is 0%, and the draw rate is 30% (1/3 * 30%).\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot. The overall winning rate for this 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 pot (3 chips). If I lose, the losing payoff would be half of the pot (3 chips).\n- Plan 2: If I win, the winning payoff would be half of the pot (4 chips). If I lose, the losing payoff would be half of the pot (4 chips).\n- Plan 3: If I lose, the losing 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 * Losing Payoff = 0% * 3 chips - 80% * 3 chips = -2.4 chips\n- Plan 2: Expected Chips Gain = winning rate * Winning Payoff - losing rate * Losing Payoff = 70% * 4 chips - 100% * 4 chips = -1.2 chips\n- Plan 3: Expected Chips Gain = winning rate * Winning Payoff - losing rate * Losing Payoff = 0% * 0 chips - 100% * 2 chips = -2 chips\n\nPlan Selection:\n- Plan 1: -2.4 chips\n- Plan 2: -1.2 chips\n- Plan 3: -2 chips\n\nBased on the estimated expected chips gain, Plan 2 (Raise) is the best strategy to use in this situation."}}
{"message": "", "15_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Jack (80% probability), he will likely fold (50%) or call (30%). If he folds, I win the pot. If he calls, I still win because my pair of Queens beats his Jack. So, the winning rate for this plan is 100%.\n- If GoodGuy holds a King (20% probability), he will likely raise (60%) or call (40%). If he raises, I will call and lose because his pair of Kings beats my pair of Queens. If he calls, I still lose. So, the losing rate for this plan is 100%.\n\nPlan 2: Fold\n- If I fold, I automatically lose the pot. So, the losing rate for this plan is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a Jack (80% probability), he will likely fold (50%) or call (30%). If he folds, I win the pot. If he calls, I still win because my pair of Queens beats his Jack. So, the winning rate for this plan is 100%.\n- If GoodGuy holds a King (20% probability), he will likely raise (60%) or call (40%). If he raises, I will call and lose because his pair of Kings beats my pair of Queens. If he calls, I still lose. So, the losing rate for this plan is 100%.\n\nWinning/Lose Payoffs:\n- Plan 1: If I win, the pot will be 12 chips (8 from me, 4 from GoodGuy), so the winning payoff would be 6 chips. If I lose, the pot will be 12 chips, so the losing payoff would be 6 chips.\n- Plan 2: If I fold, I lose the 4 chips I've already put in the pot.\n- Plan 3: If I win, the pot will be 8 chips (4 from me, 4 from GoodGuy), so the winning payoff would be 4 chips. If I lose, the pot will be 8 chips, so the losing payoff would be 4 chips.\n\nExpected Chips Gain:\n- Plan 1: (1.0 * 6) - (0.0 * 6) = 6 chips\n- Plan 2: 0 - 4 = -4 chips\n- Plan 3: (1.0 * 4) - (0.0 * 4) = 4 chips\n\nPlan Selection:\n- Plan 1: Raise (6 chips expected gain)\n- Plan 3: Check (4 chips expected gain)\n- Plan 2: Fold (-4 chips expected loss)\n\nBased on the expected chips gain, I should choose Plan 1: Raise."}}
{"message": "", "16_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (probability 33.3%), he will raise (probability 70%) or call (probability 30%). If he raises, I will lose (probability 100%). If he calls, I will draw (probability 100%).\n- If GoodGuy holds a Queen (probability 33.3%), he will raise (probability 60%) or call (probability 40%). If he raises, I will lose (probability 100%). If he calls, I will draw (probability 100%).\n- If GoodGuy holds a Jack (probability 33.3%), he will raise (probability 40%) or call (probability 60%). If he raises, I will draw (probability 100%). If he calls, I will draw (probability 100%).\n\nPlan 1 overall GoodGuy's Winning/Lose/Draw rates: \n- Winning rate for plan 1: 0%\n- Lose rate for plan 1: 33.3% (King) * 70% (raise) + 33.3% (Queen) * 60% (raise) = 22.2%\n- Draw Rate for plan 1: 33.3% (King) * 30% (call) + 33.3% (Queen) * 40% (call) + 33.3% (Jack) * 100% (raise or call) = 77.8%\n\nPlan 2: Raise\n- If GoodGuy holds a King (probability 33.3%), he will raise (probability 70%) or call (probability 30%). If he raises, I will lose (probability 100%). If he calls, I will draw (probability 100%).\n- If GoodGuy holds a Queen (probability 33.3%), he will raise (probability 60%) or call (probability 40%). If he raises, I will lose (probability 100%). If he calls, I will draw (probability 100%).\n- If GoodGuy holds a Jack (probability 33.3%), he will raise (probability 40%) or call (probability 60%). If he raises, I will draw (probability 100%). If he calls, I will draw (probability 100%).\n\nPlan 2 overall GoodGuy's Winning/Lose/Draw rates: \n- Winning rate for plan 2: 0%\n- Lose rate for plan 2: 33.3% (King) * 70% (raise) + 33.3% (Queen) * 60% (raise) = 22.2%\n- Draw Rate for plan 2: 33.3% (King) * 30% (call) + 33.3% (Queen) * 40% (call) + 33.3% (Jack) * 100% (raise or call) = 77.8%\n\nPlan 3: Fold\n- If GoodGuy holds a King, Queen, or Jack, I will lose (probability 100%).\n\nPlan 3 overall GoodGuy's Winning/Lose/Draw rates: \n- Winning rate for plan 3: 0%\n- Lose rate for plan 3: 100%\n- Draw Rate for plan 3: 0%\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 0. If lose, the lose payoff would be 4.\n- Plan 2: If win, the winning payoff would be 0. If lose, the lose payoff would be 8.\n- Plan 3: If win, the winning payoff would be 0. If lose, the lose payoff would be 2.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0 * 0% - 4 * 22.2% = -0.888 chips\n- Plan 2: 0 * 0% - 8 * 22.2% = -1.776 chips\n- Plan 3: 0 * 0% - 2 * 100% = -2 chips\n\nPlan Selection:\n- Plan 1: -0.888 chips\n- Plan 2: -1.776 chips\n- Plan 3: -2 chips\n\nThe plan with the highest estimated expected chips gain is Plan 1: Call."}}
{"message": "", "16_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (probability 1/3), he will raise (60%) or call (40%). If he raises, I will lose (probability 1). If he calls, I will lose (probability 1). Overall, the winning rate is 0, the losing rate is 1, and the drawing rate is 0.\n- If GoodGuy holds a Queen (probability 1/3), he will raise (80%) or call (20%). If he raises, I will lose (probability 1). If he calls, I will lose (probability 1). Overall, the winning rate is 0, the losing rate is 1, and the drawing rate is 0.\n- If GoodGuy holds a Jack (probability 1/3), he will fold (60%) or call (40%). If he folds, I will win (probability 1). If he calls, we will draw (probability 1). Overall, the winning rate is 0.6, the losing rate is 0, and the drawing rate is 0.4.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of GoodGuy's card. The winning rate is 0, the losing rate is 1, and the drawing rate is 0.\n\nPlan 3: Check\n- If GoodGuy holds a King (probability 1/3), he will raise (60%) or call (40%). If he raises, I will lose (probability 1). If he calls, I will lose (probability 1). Overall, the winning rate is 0, the losing rate is 1, and the drawing rate is 0.\n- If GoodGuy holds a Queen (probability 1/3), he will raise (80%) or call (20%). If he raises, I will lose (probability 1). If he calls, I will lose (probability 1). Overall, the winning rate is 0, the losing rate is 1, and the drawing rate is 0.\n- If GoodGuy holds a Jack (probability 1/3), he will fold (60%) or call (40%). If he folds, I will win (probability 1). If he calls, we will draw (probability 1). Overall, the winning rate is 0.6, the losing rate is 0, and the drawing rate is 0.4.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips. If I lose, the losing payoff would be 4 chips.\n- Plan 2: If I lose, the losing payoff would be 4 chips.\n- Plan 3: If I win, the winning payoff would be 4 chips. If I lose, the losing payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.6 * 4 - 1 * 4 = -1.6 chips\n- Plan 2: Expected Chips Gain = 0 - 1 * 4 = -4 chips\n- Plan 3: Expected Chips Gain = 0.6 * 4 - 1 * 4 = -1.6 chips\n\nPlan Selection:\n- Plan 1: Rank 1\n- Plan 2: Rank 3\n- Plan 3: Rank 1\n\nConsidering both the strategy improvement and the estimated expected chips gain, I should choose Plan 1 or Plan 3. However, since Plan 1 (raise) is more aggressive and may potentially confuse GoodGuy, I will choose Plan 1."}}
{"message": "", "17_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (33.33% chance), he is likely to 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. The estimated winning rate is 33.33% * (70% * 33.33% + 30% * 66.67%) = 22.22%. The estimated losing rate is 33.33% * (70% * 66.67% + 30% * 33.33%) = 44.44%. The estimated draw rate is 33.33% * 0% = 0%.\n- If GoodGuy holds a Queen (33.33% chance), it will be a draw regardless of his action. The estimated winning rate is 0%, the estimated losing rate is 0%, and the estimated draw rate is 33.33%.\n- If GoodGuy holds a Jack (33.33% chance), I will win unless the public card is a King. The estimated winning rate is 33.33% * 66.67% = 22.22%. The estimated losing rate is 33.33% * 33.33% = 11.11%. The estimated draw rate is 0%.\n- The overall winning rate for Plan 1 is 22.22% + 0% + 22.22% = 44.44%. The overall losing rate is 44.44% + 0% + 11.11% = 55.56%. The overall draw rate is 0% + 33.33% + 0% = 33.33%.\n- The expected chips gain for Plan 1 is 44.44% * 3 - 55.56% * 2 = -0.56 chips.\n\nPlan 2: Raise\n- If GoodGuy holds a King (33.33% chance), he is likely to 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. The estimated winning rate is 33.33% * (70% * 33.33% + 30% * 66.67%) = 22.22%. The estimated losing rate is 33.33% * (70% * 66.67% + 30% * 33.33%) = 44.44%. The estimated draw rate is 33.33% * 0% = 0%.\n- If GoodGuy holds a Queen (33.33% chance), it will be a draw regardless of his action. The estimated winning rate is 0%, the estimated losing rate is 0%, and the estimated draw rate is 33.33%.\n- If GoodGuy holds a Jack (33.33% chance), I will win unless the public card is a King. The estimated winning rate is 33.33% * 66.67% = 22.22%. The estimated losing rate is 33.33% * 33.33% = 11.11%. The estimated draw rate is 0%.\n- The overall winning rate for Plan 2 is 22.22% + 0% + 22.22% = 44.44%. The overall losing rate is 44.44% + 0% + 11.11% = 55.56%. The overall draw rate is 0% + 33.33% + 0% = 33.33%.\n- The expected chips gain for Plan 2 is 44.44% * 5 - 55.56% * 4 = -0.56 chips.\n\nPlan 3: Fold\n- If I fold, I will lose 1 chip regardless of GoodGuy's card. The estimated winning rate is 0%, the estimated losing rate is 100%, and the estimated draw rate is 0%.\n- The expected chips loss for Plan 3 is -1 chip.\n\nPlan Selection:\n- Plan 1: -0.56 chips\n- Plan 2: -0.56 chips\n- Plan 3: -1 chip\n\nBased on the estimated expected chips gains, Plan 1 and Plan 2 are equally the best strategies to follow. However, considering the strategy improvement, I should consider calling more often when I have a Queen or Jack, as GoodGuy often raises in these situations. Therefore, I will choose Plan 1: Call."}}
{"message": "", "17_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (0% probability), he will likely fold (100% probability). I will win the pot, which is currently 4 chips. The winning rate for this plan is 0%.\n- If GoodGuy holds a Queen (60% probability), he will likely call (50% probability) or raise (50% probability). If he calls, I will win the pot, which will be 6 chips. If he raises, I will lose the pot, which will be 10 chips. The winning rate for this plan is 30%, and the losing rate is 30%.\n- If GoodGuy holds a Jack (40% probability), he will likely fold (100% probability). I will win the pot, which is currently 4 chips. The winning rate for this plan is 40%.\n\nPlan 2: Fold\n- If I fold, I will lose the pot, which is currently 4 chips. The losing rate for this plan is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (0% probability), he will likely check (100% probability). I will win the pot, which is currently 4 chips. The winning rate for this plan is 0%.\n- If GoodGuy holds a Queen (60% probability), he will likely check (70% probability) or raise (30% probability). If he checks, I will win the pot, which will be 4 chips. If he raises, I will lose the pot, which will be 8 chips. The winning rate for this plan is 42%, and the losing rate is 18%.\n- If GoodGuy holds a Jack (40% probability), he will likely check (100% probability). I will win the pot, which is currently 4 chips. The winning rate for this plan is 40%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 2 chips. If lose, the lose payoff would be 5 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 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.7 * 2 - 0.3 * 5 = 0.4 chips\n- Plan 2: Expected Chips Gain = -2 chips\n- Plan 3: Expected Chips Gain = 0.82 * 2 - 0.18 * 4 = 1.24 chips\n\nPlan Selection:\n- Plan 3 (Check) has the highest expected chips gain, so I will choose this plan."}}
{"message": "", "17_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (50% probability), he is likely to raise (30%) or check (70%). If he raises, I will lose as his card is higher than mine. If he checks, the game will be a draw as neither of us has a matching card with the public card. \n- If GoodGuy holds a Queen (50% probability), he is likely to raise (30%) or check (70%). If he raises, the game will be a draw as we both hold the same card. If he checks, the game will be a draw as neither of us has a matching card with the public card. \n\nPlan 2: Raise\n- If GoodGuy holds a King (50% probability), he is likely to fold (40%) or call (60%). If he folds, I will win. If he calls, I will lose as his card is higher than mine. \n- If GoodGuy holds a Queen (50% probability), he is likely to fold (40%) or call (60%). If he folds, I will win. If he calls, the game will be a draw as we both hold the same card. \n\nPlan 3: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, Chips in the pot: 8. If win, the winning payoff would be 4. If lose, the lose payoff would be 4.\n- Plan 2: After the action, Chips in the pot: 12. If win, the winning payoff would be 6. If lose, the lose payoff would be 6.\n- Plan 3: After the action, Chips in the pot: 6. If lose, the lose payoff would be 3.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0 * Winning Rate - 4 * Lose Rate = -2 chips\n- Plan 2: Expected Chips Gain = 6 * Winning Rate - 6 * Lose Rate = 0 chips\n- Plan 3: Expected Chips Gain = 0 * Winning Rate - 3 * Lose Rate = -1.5 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I will choose this plan."}}
{"message": "", "18_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a Jack (100% probability), and the public card is a King or Queen, GoodGuy will lose. If the public card is a Jack, GoodGuy will win. The overall winning rate is 33.33%, the losing rate is 66.67%, and the draw rate is 0%.\n- After the action, chips in the pot: 8. If win, the winning payoff would be 4. If lose, the lose payoff would be 4.\n\nPlan 2: Raise\n- If GoodGuy holds a Jack (100% probability), and the public card is a King or Queen, GoodGuy will lose. If the public card is a Jack, GoodGuy will win. The overall winning rate is 33.33%, the losing rate is 66.67%, and the draw rate is 0%.\n- After the action, chips in the pot: 12. If win, the winning payoff would be 6. If lose, the lose payoff would be 6.\n\nPlan 3: Fold\n- If GoodGuy folds, he will lose the chips he has already put in the pot. The overall winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n- After the action, chips in the pot: 6. If lose, the lose payoff would be 3.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 33.33% * 4 - 66.67% * 4 = -1.33 chips\n- Plan 2: 33.33% * 6 - 66.67% * 6 = -2 chips\n- Plan 3: 0% * 0 - 100% * 3 = -3 chips\n\nPlan Selection:\n- Plan 1 has the highest estimated expected chips gain of -1.33 chips, followed by Plan 2 with -2 chips, and Plan 3 with -3 chips. Therefore, the best strategy for GoodGuy in this situation is to call."}}
{"message": "", "18_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (40% chance), he will likely raise (60% chance). If he raises, I will lose as his King beats my Jack. Therefore, the lose rate for this plan is 0.4 * 0.6 = 0.24.\n- If GoodGuy holds a Queen (40% chance), he will likely raise (60% chance). If he raises, I will lose as his Queen beats my Jack. Therefore, the lose rate for this plan is 0.4 * 0.6 = 0.24.\n- If GoodGuy holds a Jack (20% chance), he will likely fold (60% chance). If he folds, I will win. Therefore, the win rate for this plan is 0.2 * 0.6 = 0.12.\n- The overall win rate for this plan is 0.12, the overall lose rate is 0.48, and the draw rate is 0.4.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. Therefore, the lose rate for this plan is 1.\n\nPlan 3: Check\n- If GoodGuy holds a King (40% chance), he will likely raise (60% chance). If he raises, I will lose as his King beats my Jack. Therefore, the lose rate for this plan is 0.4 * 0.6 = 0.24.\n- If GoodGuy holds a Queen (40% chance), he will likely raise (60% chance). If he raises, I will lose as his Queen beats my Jack. Therefore, the lose rate for this plan is 0.4 * 0.6 = 0.24.\n- If GoodGuy holds a Jack (20% chance), he will likely check (40% chance). If he checks, it will be a draw. Therefore, the draw rate for this plan is 0.2 * 0.4 = 0.08.\n- The overall win rate for this plan is 0, the overall lose rate is 0.48, and the draw rate is 0.52.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the pot, which is 4 chips. If I lose, the lose payoff would be half of the pot, which is 4 chips.\n- Plan 2: If I lose, the lose payoff would be half of the pot, which is 4 chips.\n- Plan 3: If I win, the winning payoff would be half of the pot, which is 4 chips. If I lose, the lose payoff would be half of the pot, which is 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is 0.12 * 4 - 0.48 * 4 = -1.44 chips.\n- Plan 2: The expected chips gain is -1 * 4 = -4 chips.\n- Plan 3: The expected chips gain is 0 * 4 - 0.48 * 4 = -1.92 chips.\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I will choose Plan 1: Raise."}}
{"message": "", "19_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King, he might raise (70%) or call (30%). If he raises, I will lose unless the public card is a Jack. If he calls, it's a draw unless the public card is a King or Queen. The overall winning rate is 30% (if the public card is a Jack), the losing rate is 70% (if the public card is a King or Queen), and the draw rate is 0%.\n- If GoodGuy holds a Queen, he might raise (60%) or call (40%). If he raises, I will lose unless the public card is a Jack. If he calls, it's a draw unless the public card is a King or Jack. The overall winning rate is 40% (if the public card is a Jack), the losing rate is 60% (if the public card is a King or Queen), and the draw rate is 0%.\n- If GoodGuy holds a Jack, he might call (70%) or raise (30%). If he calls, it's a draw unless the public card is a King or Queen. If he raises, I will lose unless the public card is a Jack. The overall winning rate is 30% (if the public card is a Jack), the losing rate is 70% (if the public card is a King or Queen), and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King, he might raise (70%) or call (30%). If he raises, I will lose unless the public card is a Jack. If he calls, it's a draw unless the public card is a King or Queen. The overall winning rate is 30% (if the public card is a Jack), the losing rate is 70% (if the public card is a King or Queen), and the draw rate is 0%.\n- If GoodGuy holds a Queen, he might raise (60%) or call (40%). If he raises, I will lose unless the public card is a Jack. If he calls, it's a draw unless the public card is a King or Jack. The overall winning rate is 40% (if the public card is a Jack), the losing rate is 60% (if the public card is a King or Queen), and the draw rate is 0%.\n- If GoodGuy holds a Jack, he might call (70%) or raise (30%). If he calls, it's a draw unless the public card is a King or Queen. If he raises, I will lose unless the public card is a Jack. The overall winning rate is 30% (if the public card is a Jack), the losing rate is 70% (if the public card is a King or Queen), and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card. The overall winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips (half of the pot). If I lose, the losing payoff would be 2 chips (half of the pot).\n- Plan 2: If I win, the winning payoff would be 5 chips (half of the pot). If I lose, the losing payoff would be 4 chips (half of the pot).\n- Plan 3: If I lose, the losing payoff would be 2 chips (half of the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 30% * 3 - 70% * 2 = -0.9 chips\n- Plan 2: Expected Chips Gain = 30% * 5 - 70% * 4 = -1.5 chips\n- Plan 3: Expected Chips Gain = -100% * 2 = -2 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain (-0.9 chips), followed by Plan 2 (-1.5 chips) and Plan 3 (-2 chips). Therefore, I should choose Plan 1: Call."}}
{"message": "", "19_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King, he will likely call (60%) or fold (40%). If he calls, I will lose as a King is higher than my Jack. If he folds, I will win. The winning rate is 40%, the losing rate is 60%, and the draw rate is 0%.\n- If GoodGuy holds a Queen, he will likely call (50%) or fold (50%). If he calls, I will lose as a Queen is higher than my Jack. If he folds, I will win. The winning rate is 50%, the losing rate is 50%, and the draw rate is 0%.\n- If GoodGuy holds a Jack, he will likely call (40%) or fold (60%). If he calls, it will be a draw as we both have a Jack. If he folds, I will win. The winning rate is 60%, the losing rate is 0%, and the draw rate is 40%.\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 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King, he will likely raise (40%) or check (60%). If he raises, I will lose as a King is higher than my Jack. If he checks, it will be a draw as we both have a Jack. The winning rate is 0%, the losing rate is 40%, and the draw rate is 60%.\n- If GoodGuy holds a Queen, he will likely raise (50%) or check (50%). If he raises, I will lose as a Queen is higher than my Jack. If he checks, it will be a draw as we both have a Jack. The winning rate is 0%, the losing rate is 50%, and the draw rate is 50%.\n- If GoodGuy holds a Jack, he will likely raise (40%) or check (60%). If he raises, it will be a draw as we both have a Jack. If he checks, it will be a draw as we both have a Jack. The winning rate is 0%, the losing rate is 0%, and the draw rate is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips (half of the pot). If I lose, the losing payoff would be 2 chips (half of the pot).\n- Plan 2: If I lose, the losing payoff would be 2 chips (half of the pot).\n- Plan 3: If I win, the winning payoff would be 2 chips (half of the pot). If I lose, the losing payoff would be 2 chips (half of the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: (0.4 * 4) - (0.6 * 2) = 0.8 chips\n- Plan 2: 0 - (1 * 2) = -2 chips\n- Plan 3: 0 - (0.45 * 2) = -0.9 chips\n\nPlan Selection:\n- Plan 1: 0.8 chips\n- Plan 2: -2 chips\n- Plan 3: -0.9 chips\n\nBased on the estimated expected chips gain, Plan 1 (Raise) is the best strategy to use in this situation."}}
{"message": "", "20_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (90% probability), he is likely to raise (60%) or call (30%) in the second round. If he raises, I will lose unless the public card is a Queen. If he calls, I will win if the public card is a Queen, and lose if it is a King or Jack. The overall winning rate for this plan is 27% (90% * 30%), the losing rate is 63% (90% * 70%), and the draw rate is 10% (90% * 0%).\n- If GoodGuy holds a Jack (10% probability), he is likely to raise (40%) or call (40%) in the second round. If he raises, I will lose unless the public card is a Queen. If he calls, I will win if the public card is a Queen, and lose if it is a King or Jack. The overall winning rate for this plan is 4% (10% * 40%), the losing rate is 6% (10% * 60%), and the draw rate is 0% (10% * 0%).\n\nPlan 2: Raise\n- If GoodGuy holds a King (90% probability), he is likely to call (30%) or fold (10%) in the second round. If he calls, I will lose unless the public card is a Queen. If he folds, I will win. The overall winning rate for this plan is 36% (90% * 40%), the losing rate is 54% (90% * 60%), and the draw rate is 0% (90% * 0%).\n- If GoodGuy holds a Jack (10% probability), he is likely to call (40%) or fold (20%) in the second round. If he calls, I will lose unless the public card is a Queen. If he folds, I will win. The overall winning rate for this plan is 6% (10% * 60%), the losing rate is 4% (10% * 40%), and the draw rate is 0% (10% * 0%).\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot. The overall winning rate for this plan is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 6 chips (half of the pot). If I lose, the lose payoff would be 4 chips (half of the pot).\n- Plan 2: If I win, the winning payoff would be 8 chips (half of the pot). If I lose, the lose payoff would be 6 chips (half of the pot).\n- Plan 3: If I fold, I will lose the 2 chips I have already put in the pot.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is 27% * 6 - 63% * 4 = -0.42 chips.\n- Plan 2: The expected chips gain is 36% * 8 - 54% * 6 = -0.72 chips.\n- Plan 3: The expected chips gain is -2 chips.\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I will choose to call."}}
{"message": "", "20_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (30% probability), he will likely raise (60%) or call (40%). If he raises, I will lose as King is higher than Queen. If he calls, I will win as Queen is higher than Jack. Therefore, the winning rate is 40%, losing rate is 60%, and draw rate is 0%.\n- If GoodGuy holds a Queen (70% probability), he will likely call (40%) or fold (10%). If he calls, it will be a draw as we both have Queens. If he folds, I will win. Therefore, the winning rate is 10%, losing rate is 0%, and draw rate is 40%.\n\nPlan 2: Fold\n- If I fold, I will lose the chips in the pot regardless of GoodGuy's cards. Therefore, the winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King (30% probability), he will likely raise (60%) or check (40%). If he raises, I will lose as King is higher than Queen. If he checks, I will win as Queen is higher than Jack. Therefore, the winning rate is 40%, losing rate is 60%, and draw rate is 0%.\n- If GoodGuy holds a Queen (70% probability), he will likely check (40%) or fold (10%). If he checks, it will be a draw as we both have Queens. If he folds, I will win. Therefore, the winning rate is 10%, losing rate is 0%, and draw rate is 40%.\n\nWinning/Lose Payoffs:\n- Plan 1: If I win, the pot will be 8 chips and I will gain 4 chips. If I lose, I will lose 4 chips.\n- Plan 2: If I fold, I will lose the 4 chips in the pot.\n- Plan 3: If I win, the pot will be 8 chips and I will gain 4 chips. If I lose, I will lose 4 chips.\n\nExpected Chips Gain:\n- Plan 1: (0.4 * 4) - (0.6 * 4) = -0.8 chips\n- Plan 2: -4 chips\n- Plan 3: (0.4 * 4) - (0.6 * 4) = -0.8 chips\n\nPlan Selection:\nBased on the expected chips gain, Plan 1 and Plan 3 are the best strategies as they have the highest expected chips gain (-0.8 chips). However, considering the strategy improvement, Plan 1 (Raise) is more aggressive and could potentially lead to higher gains in the future games. Therefore, I will choose Plan 1: Raise."}}
{"message": "", "21_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King, based on his behavior pattern, he will likely raise (70%) or call (30%). If he raises, I will likely lose as the King is higher than my Queen. If he calls, the outcome will depend on the public card. The overall winning rate for this scenario is 30% (probability of him holding a King * probability of him calling * probability of public card being a Queen or Jack), the losing rate is 70% (probability of him holding a King * probability of him raising), and the draw rate is 0%.\n- If GoodGuy holds a Queen, he will likely call (60%) or raise (40%). In this case, the outcome will depend on the public card. The overall winning rate for this scenario is 60% (probability of him holding a Queen * probability of public card being a Queen), the losing rate is 0%, and the draw rate is 40% (probability of him holding a Queen * probability of public card not being a Queen).\n- If GoodGuy holds a Jack, he will likely call (70%) or raise (30%). If he calls, I will likely win as my Queen is higher than his Jack. If he raises, the outcome will depend on the public card. The overall winning rate for this scenario is 70% (probability of him holding a Jack * probability of him calling), the losing rate is 30% (probability of him holding a Jack * probability of him raising), and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose the chips I have already put in the pot. The overall winning rate for this scenario is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King, he will likely raise (70%) or call (30%). If he raises, I will likely lose as the King is higher than my Queen. If he calls, the outcome will depend on the public card. The overall winning rate for this scenario is 30% (probability of him holding a King * probability of him calling * probability of public card being a Queen or Jack), the losing rate is 70% (probability of him holding a King * probability of him raising), and the draw rate is 0%.\n- If GoodGuy holds a Queen, he will likely call (60%) or raise (40%). In this case, the outcome will depend on the public card. The overall winning rate for this scenario is 60% (probability of him holding a Queen * probability of public card being a Queen), the losing rate is 0%, and the draw rate is 40% (probability of him holding a Queen * probability of public card not being a Queen).\n- If GoodGuy holds a Jack, he will likely call (70%) or raise (30%). If he calls, I will likely win as my Queen is higher than his Jack. If he raises, the outcome will depend on the public card. The overall winning rate for this scenario is 70% (probability of him holding a Jack * probability of him calling), the losing rate is 30% (probability of him holding a Jack * probability of him raising), and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the pot (currently 4 chips, so 2 chips). If I lose, the losing payoff would be the chips I put in the pot (2 chips).\n- Plan 2: If I fold, I will lose the chips I have already put in the pot (2 chips).\n- Plan 3: If I win, the winning payoff would be half of the pot (currently 4 chips, so 2 chips). If I lose, the losing payoff would be the chips I put in the pot (2 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning Rate * Winning Payoff - Losing Rate * Losing Payoff = 0.53 * 2 - 0.47 * 2 = 0.12 chips\n- Plan 2: Expected Chips Gain = Winning Rate * Winning Payoff - Losing Rate * Losing Payoff = 0 * 0 - 1 * 2 = -2 chips\n- Plan 3: Expected Chips Gain = Winning Rate * Winning Payoff - Losing Rate * Losing Payoff = 0.53 * 2 - 0.47 * 2 = 0.12 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 have the highest expected chips gain (0.12 chips), followed by Plan 2 (-2 chips). Therefore, I should either raise (Plan 1) or check (Plan 3). Considering my strategy improvement, I should choose to raise (Plan 1) as it aligns with my aggressive play style."}}
{"message": "", "21_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King, he will likely raise (40%) or check (60%). If he raises, I will likely lose this round as his King matches the public card. If he checks, I have a chance to win if he is bluffing and actually holds a Jack. \n- If GoodGuy holds a Queen, he will likely raise (30%) or check (70%). In both cases, it will be a draw as we both hold Queens. \n- If GoodGuy holds a Jack, he will likely raise (20%) or check (80%). In both cases, I will win as my Queen is higher than his Jack. \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, he will likely raise (40%) or check (60%). If he raises, I will likely lose this round as his King matches the public card. If he checks, I have a chance to win if he is bluffing and actually holds a Jack. \n- If GoodGuy holds a Queen, he will likely raise (30%) or check (70%). In both cases, it will be a draw as we both hold Queens. \n- If GoodGuy holds a Jack, he will likely raise (20%) or check (80%). In both cases, I will win as my Queen is higher than his Jack. \n\nWinning/Lose Payoffs for Each Plan:\n- Plan 1: If I win, the winning payoff would be 4 chips (half of the pot). If I lose, the losing payoff would be 4 chips. \n- Plan 2: If I fold, I will lose 4 chips. \n- Plan 3: If I win, the winning payoff would be 4 chips. If I lose, the losing payoff would be 4 chips. \n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected gain = (0.2 * 4) - (0.4 * 4) = -0.8 chips\n- Plan 2: Expected gain = -4 chips\n- Plan 3: Expected gain = (0.2 * 4) - (0.4 * 4) = -0.8 chips\n\nPlan Selection:\nBased on the expected chips gain, Plan 1 and Plan 3 are the best strategies as they have the highest expected gain. However, considering the strategy improvement, I should choose Plan 1 (Raise) as it aligns with my aggressive play style and can potentially intimidate GoodGuy into folding."}}
{"message": "", "22_0": {"plan": "Plan 1: Call\nIf I call, I will match the number of chips my opponent has put in the pot. This is a safe move that does not reveal much about my hand. \n\n- If GoodGuy holds a King, based on his behavior pattern, he will likely raise (70% probability) or call (30% probability). If he raises, I have a 50% chance of losing (if the public card is a King or Queen) and a 50% chance of winning (if the public card is a Jack). If he calls, I have a 50% chance of winning (if the public card is a Jack) and a 50% chance of losing (if the public card is a King or Queen). \n\n- If GoodGuy holds a Queen, he will likely raise (60% probability) or call (40% probability). If he raises, I have a 50% chance of losing (if the public card is a King or Queen) and a 50% chance of winning (if the public card is a Jack). If he calls, I have a 50% chance of winning (if the public card is a Jack) and a 50% chance of losing (if the public card is a King or Queen). \n\n- If GoodGuy holds a Jack, he will likely call (50% probability) or fold (50% probability). If he calls, I have a 100% chance of winning (as I also hold a Jack). If he folds, I win by default. \n\nPlan 2: Raise\nIf I raise, I will increase the bet by putting more chips into the pot. This is a risky move that could potentially scare off my opponent, but it could also backfire if my opponent has a higher-ranking card. \n\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 losing (if the public card is a King or Queen) and a 50% chance of winning (if the public card is a Jack). If he calls, I have a 50% chance of winning (if the public card is a Jack) and a 50% chance of losing (if the public card is a King or Queen). \n\n- If GoodGuy holds a Queen, he will likely raise (60% probability) or call (40% probability). If he raises, I have a 50% chance of losing (if the public card is a King or Queen) and a 50% chance of winning (if the public card is a Jack). If he calls, I have a 50% chance of winning (if the public card is a Jack) and a 50% chance of losing (if the public card is a King or Queen). \n\n- If GoodGuy holds a Jack, he will likely call (50% probability) or fold (50% probability). If he calls, I have a 100% chance of winning (as I also hold a Jack). If he folds, I win by default. \n\nPlan 3: Fold\nIf I fold, I will forfeit the game. This is the safest move, but it also guarantees that I will not win any chips in this round. \n\n- If GoodGuy holds a King, Queen, or Jack, I lose by default. \n\nBased on the above analysis, the expected chips gain for each plan is as follows: \n\n- Plan 1: Call - (0.5 * Winning Payoff) - (0.5 * Lose Payoff)\n- Plan 2: Raise - (0.5 * Winning Payoff) - (0.5 * Lose Payoff)\n- Plan 3: Fold - 0\n\nGiven that the expected chips gain for Plan 1 and Plan 2 are the same, and both are higher than the expected chips gain for Plan 3, I should either call or raise. However, calling is the safer option as it does not risk as many chips. Therefore, I choose Plan 1: Call."}}
{"message": "", "22_2": {"plan": "Plan 1: Raise\nIf I raise, GoodGuy might think I have a King or Queen. Based on his behavior pattern, if he has a Queen (30% probability), he might check (30% probability) or fold (40% probability). If he has a Jack (70% probability), he might check (70% probability) or fold (30% probability). \n- Winning rate for his Queen: 0.3*0.3 = 0.09\n- Losing rate for his Queen: 0.3*0.4 = 0.12\n- Draw rate for his Queen: 0.3*0.3 = 0.09\n- Winning rate for his Jack: 0.7*0.7 = 0.49\n- Losing rate for his Jack: 0.7*0.3 = 0.21\n- Draw rate for his Jack: 0.7*0.7 = 0.49\nOverall winning rate for Plan 1: 0.09 + 0.49 = 0.58\nOverall losing rate for Plan 1: 0.12 + 0.21 = 0.33\nOverall draw rate for Plan 1: 0.09 + 0.49 = 0.58\n\nPlan 2: Fold\nIf I fold, I will lose the game for sure. So the overall winning rate, losing rate, and draw rate for Plan 2 are 0, 1, and 0 respectively.\n\nPlan 3: Check\nIf I check, GoodGuy might think I have a Jack or Queen. Based on his behavior pattern, if he has a Queen (30% probability), he might check (30% probability) or fold (40% probability). If he has a Jack (70% probability), he might check (70% probability) or fold (30% probability). \n- Winning rate for his Queen: 0.3*0.3 = 0.09\n- Losing rate for his Queen: 0.3*0.4 = 0.12\n- Draw rate for his Queen: 0.3*0.3 = 0.09\n- Winning rate for his Jack: 0.7*0.7 = 0.49\n- Losing rate for his Jack: 0.7*0.3 = 0.21\n- Draw rate for his Jack: 0.7*0.7 = 0.49\nOverall winning rate for Plan 3: 0.09 + 0.49 = 0.58\nOverall losing rate for Plan 3: 0.12 + 0.21 = 0.33\nOverall draw rate for Plan 3: 0.09 + 0.49 = 0.58\n\nWinning Payoff for Each Plan:\nPlan 1: If win, the winning payoff would be half of the pot, which is (2+4)/2 = 3 chips. If lose, the losing payoff would be -4 chips.\nPlan 2: If fold, there is no winning payoff and the losing payoff would be -2 chips.\nPlan 3: If win, the winning payoff would be half of the pot, which is (2+2)/2 = 2 chips. If lose, the losing payoff would be -2 chips.\n\nExpected Chips Gain for Each Plan:\nPlan 1: 0.58*3 - 0.33*4 = 0.74 chips\nPlan 2: 0 - 1*2 = -2 chips\nPlan 3: 0.58*2 - 0.33*2 = 0.5 chips\n\nPlan Selection:\nBased on the expected chips gain, the rank of the plans is Plan 1 > Plan 3 > Plan 2. Therefore, I should choose Plan 1, which is to raise."}}
{"message": "", "23_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King, he will likely raise (70% probability) or call (30% probability). If I win, the winning rate is 0% (since my Queen cannot beat his King), the losing rate is 100%, and the draw rate is 0%. The overall winning rate is 0%, the losing rate is 33.33% (probability of him holding a King * losing rate), and the draw rate is 0%.\n- If GoodGuy holds a Queen, he will likely raise (60% probability) or call (40% probability). If I win, the winning rate is 0% (since it would be a draw), the losing rate is 0%, and the draw rate is 100%. The overall winning rate is 0%, the losing rate is 0%, and the draw rate is 33.33% (probability of him holding a Queen * draw rate).\n- If GoodGuy holds a Jack, he will likely call (60% probability) or raise (40% probability). If I win, the winning rate is 100% (since my Queen can beat his Jack), the losing rate is 0%, and the draw rate is 0%. The overall winning rate is 33.33% (probability of him holding a Jack * winning rate), the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I automatically lose the game. The overall winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- This plan is similar to Plan 1, but with a lower risk since I am not raising the bet. The overall winning, losing, and draw rates are the same as in Plan 1.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips (half of the pot). If I lose, the losing payoff would be 2 chips (half of the pot).\n- Plan 2: If I fold, I lose 2 chips (my initial bet).\n- Plan 3: If I win, the winning payoff would be 2 chips (half of the pot). If I lose, the losing payoff would be 2 chips (my initial bet).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected gain = winning rate * winning payoff - losing rate * losing payoff = 33.33% * 4 - 33.33% * 2 = 0.67 chips\n- Plan 2: Expected gain = 0% * 0 - 100% * 2 = -2 chips\n- Plan 3: Expected gain = 33.33% * 2 - 33.33% * 2 = 0 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I would choose this plan. However, this plan also has the highest risk. If I want to play it safe, I could choose Plan 3, which has a lower expected gain but also a lower risk."}}
{"message": "", "23_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (60% probability), he is likely to call (30% probability) or raise (60% probability). If he calls, I will win with a 0% probability (since his King matches the public card), lose with a 100% probability, and draw with a 0% probability. If he raises, I will win with a 0% probability, lose with a 100% probability, and draw with a 0% probability. Overall, the winning rate for his King is 0%, the losing rate is 100%, and the drawing rate is 0%.\n- If GoodGuy holds a Queen (40% probability), he is likely to call (40% probability) or raise (50% probability). If he calls, I will win with a 50% probability (since we both have Queens), lose with a 0% probability, and draw with a 50% probability. If he raises, I will win with a 50% probability, lose with a 0% probability, and draw with a 50% probability. Overall, the winning rate for his Queen is 50%, the losing rate is 0%, and the drawing rate is 50%.\n\nPlan 2: Fold\n- If I fold, I will lose with a 100% probability, regardless of GoodGuy's card.\n\nPlan 3: Check\n- If GoodGuy holds a King (60% probability), he is likely to call (30% probability) or raise (60% probability). If he calls, I will win with a 0% probability (since his King matches the public card), lose with a 100% probability, and draw with a 0% probability. If he raises, I will win with a 0% probability, lose with a 100% probability, and draw with a 0% probability. Overall, the winning rate for his King is 0%, the losing rate is 100%, and the drawing rate is 0%.\n- If GoodGuy holds a Queen (40% probability), he is likely to call (40% probability) or raise (50% probability). If he calls, I will win with a 50% probability (since we both have Queens), lose with a 0% probability, and draw with a 50% probability. If he raises, I will win with a 50% probability, lose with a 0% probability, and draw with a 50% probability. Overall, the winning rate for his Queen is 50%, the losing rate is 0%, and the drawing rate is 50%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 8 chips (half of the 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 pot). If I lose, the losing payoff would be 8 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is 0% * 8 chips - 100% * 8 chips = -8 chips.\n- Plan 2: The expected chips loss is 4 chips.\n- Plan 3: The expected chips gain is 0% * 8 chips - 100% * 8 chips = -8 chips.\n\nPlan Selection:\n- Plan 1: -8 chips\n- Plan 2: -4 chips\n- Plan 3: -8 chips\n\nBased on the expected chips gain, Plan 2 (Fold) is the best strategy."}}
{"message": "", "24_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (40% probability), he will likely raise (80% probability). If the public card is a Queen or Jack, I will win (probability = 0.4*0.8 = 0.32). If he checks (20% probability), I will also win (probability = 0.4*0.2 = 0.08). \n- If GoodGuy holds a Queen (35% probability), he will likely raise (70% probability). If the public card is a King or Jack, I will win (probability = 0.35*0.7 = 0.245). If he checks (30% probability), I will also win (probability = 0.35*0.3 = 0.105). \n- If GoodGuy holds a Jack (25% probability), he will likely raise (60% probability). If the public card is a King or Queen, I will win (probability = 0.25*0.6 = 0.15). If he checks (40% probability), I will also win (probability = 0.25*0.4 = 0.1). \n\nPlan 1 overall Winning/Lose/Draw rates: \n- Winning rate for plan 1: 0.32 + 0.08 + 0.245 + 0.105 + 0.15 + 0.1 = 1.0\n- Lose rate for plan 1: 0\n- Draw rate for plan 1: 0\n\nPlan 2: Raise\n- If GoodGuy holds a King (40% probability), he will likely raise (80% probability). If the public card is a Queen or Jack, I will win (probability = 0.4*0.8 = 0.32). If he checks (20% probability), I will also win (probability = 0.4*0.2 = 0.08). \n- If GoodGuy holds a Queen (35% probability), he will likely raise (70% probability). If the public card is a King or Jack, I will win (probability = 0.35*0.7 = 0.245). If he checks (30% probability), I will also win (probability = 0.35*0.3 = 0.105). \n- If GoodGuy holds a Jack (25% probability), he will likely raise (60% probability). If the public card is a King or Queen, I will win (probability = 0.25*0.6 = 0.15). If he checks (40% probability), I will also win (probability = 0.25*0.4 = 0.1). \n\nPlan 2 overall Winning/Lose/Draw rates: \n- Winning rate for plan 2: 0.32 + 0.08 + 0.245 + 0.105 + 0.15 + 0.1 = 1.0\n- Lose rate for plan 2: 0\n- Draw rate for plan 2: 0\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card or action. \n\nPlan 3 overall Winning/Lose/Draw rates: \n- Winning rate for plan 3: 0\n- Lose rate for plan 3: 1\n- Draw rate for plan 3: 0\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 2 chips. If lose, the lose payoff would be 2 chips. \n- Plan 2: If win, the winning payoff would be 4 chips. If lose, the lose payoff would be 4 chips. \n- Plan 3: If I fold, I will lose 2 chips. \n\nEstimated Expected Chips Gain for Each Plan:\n- Plan 1: 1.0 * 2 - 0 * 2 = 2 chips\n- Plan 2: 1.0 * 4 - 0 * 4 = 4 chips\n- Plan 3: 0 * 2 - 1 * 2 = -2 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest estimated expected chips gain, so I will choose this plan."}}
{"message": "", "24_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (probability 1/3), he will likely raise (60% probability) or check (40% probability). If he raises, I will win (as my King is higher than his Queen). If he checks, I will also win (as my King is higher than his Queen). So, the winning rate for his Queen is 100%.\n- If GoodGuy holds a King (probability 1/3), he will likely raise (70% probability) or check (30% probability). If he raises, it will be a draw (as we both have Kings). If he checks, it will also be a draw (as we both have Kings). So, the draw rate for his King is 100%.\n- If GoodGuy holds a Jack (probability 1/3), he will likely raise (50% probability) or check (50% probability). If he raises, I will win (as my King is higher than his Jack). If he checks, I will also win (as my King is higher than his Jack). So, the winning rate for his Jack is 100%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. So, the losing rate is 100%.\n\nPlan 3: Check\n- This plan will have the same outcomes as Plan 1, as GoodGuy's actions will not be influenced by my check.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the pot (8 chips). If I lose, the losing payoff would be half of the pot (8 chips).\n- Plan 2: If I lose, the losing payoff would be half of the pot (8 chips).\n- Plan 3: If I win, the winning payoff would be half of the pot (8 chips). If I lose, the losing payoff would be half of the pot (8 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning Rate * Winning Payoff - Losing Rate * Losing Payoff = (2/3 * 8) - (0 * 8) = 5.33 chips\n- Plan 2: Expected Chips Gain = Winning Rate * Winning Payoff - Losing Rate * Losing Payoff = (0 * 8) - (1 * 8) = -8 chips\n- Plan 3: Expected Chips Gain = Winning Rate * Winning Payoff - Losing Rate * Losing Payoff = (2/3 * 8) - (0 * 8) = 5.33 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 have the highest expected chips gain (5.33 chips), while Plan 2 has the lowest expected chips gain (-8 chips). Therefore, I should choose either Plan 1 (Raise) or Plan 3 (Check). Considering my strategy improvement to be more aggressive, I will choose Plan 1 (Raise)."}}
{"message": "", "24_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a Queen (probability 35%): GoodGuy has a pair of Queens and will likely raise (probability 60%). If he raises, I will lose (probability 100%). If he checks (probability 40%), I will win (probability 100%). Overall, the winning rate is 14%, the losing rate is 21%, and the draw rate is 0%.\n- If GoodGuy holds a King (probability 40%): GoodGuy has a single King and will likely raise (probability 70%). If he raises, it will be a draw (probability 100%). If he checks (probability 30%), it will be a draw (probability 100%). Overall, the winning rate is 0%, the losing rate is 0%, and the draw rate is 40%.\n- If GoodGuy holds a Jack (probability 25%): GoodGuy has a single Jack and will likely raise (probability 50%). If he raises, I will win (probability 100%). If he checks (probability 50%), I will win (probability 100%). Overall, the winning rate is 25%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 1 overall GoodGuy's Winning/Lose/Draw rates: The Winning rate for plan 1 is 39%, the Lose rate for plan 1 is 21%, and the Draw Rate for plan 1 is 40%.\n\nPlan 2: Fold\n- If GoodGuy holds a Queen (probability 35%): I will lose (probability 100%). Overall, the winning rate is 0%, the losing rate is 35%, and the draw rate is 0%.\n- If GoodGuy holds a King (probability 40%): It will be a draw (probability 100%). Overall, the winning rate is 0%, the losing rate is 0%, and the draw rate is 40%.\n- If GoodGuy holds a Jack (probability 25%): I will win (probability 100%). Overall, the winning rate is 25%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2 overall GoodGuy's Winning/Lose/Draw rates: The Winning rate for plan 2 is 25%, the Lose rate for plan 2 is 35%, and the Draw Rate for plan 2 is 40%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the call, Chips in the pot: 24. If win, the winning payoff would be 12. After the call, Chips in the pot: 24. If lose, the lose payoff would be 12.\n- Plan 2: After the fold, Chips in the pot: 20. If win, the winning payoff would be 10. After the fold, Chips in the pot: 20. If lose, the lose payoff would be 10.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Lose rate * Lose Payoff = 39% * 12 - 21% * 12 = 2.16\n- Plan 2: Expected Chips Gain = Winning rate * Winning Payoff - Lose rate * Lose Payoff = 25% * 10 - 35% * 10 = -1\n\nPlan Selection: Plan 1 has a higher expected chips gain than Plan 2. Therefore, I should choose to call."}}
{"message": "", "25_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (50% probability), he is likely to raise (60%) or call (40%). If he raises, I will win as I hold a King. If he calls, the outcome will depend on the public card in the second round. Overall, the winning rate for this plan is 70% (50% * 60% + 50% * 40% * 50%), the losing rate is 20% (50% * 40% * 50%), and the draw rate is 10% (50% * 40% * 50%).\n- If GoodGuy holds a Jack (50% probability), he is likely to raise (50%) or call (50%). If he raises or calls, I will win as I hold a King. Overall, the winning rate for this plan is 100% (50% * 50% + 50% * 50%).\nPlan 1 overall GoodGuy's Winning/Lose/Draw rates: The Winning rate for plan 1 is 85% (70% + 100%), Lose rate for plan 1 is 10% (20% + 0%), Draw Rate for plan 1 is 5% (10% + 0%).\n\nPlan 2: Fold\n- If I fold, I will lose regardless of GoodGuy's card. The losing rate for this plan is 100%, and the winning and draw rates are both 0%.\n\nPlan 3: Check\n- If GoodGuy holds a Queen (50% probability), he is likely to raise (60%) or check (40%). If he raises, I will win as I hold a King. If he checks, the outcome will depend on the public card in the second round. Overall, the winning rate for this plan is 70% (50% * 60% + 50% * 40% * 50%), the losing rate is 20% (50% * 40% * 50%), and the draw rate is 10% (50% * 40% * 50%).\n- If GoodGuy holds a Jack (50% probability), he is likely to raise (50%) or check (50%). If he raises or checks, I will win as I hold a King. Overall, the winning rate for this plan is 100% (50% * 50% + 50% * 50%).\nPlan 3 overall GoodGuy's Winning/Lose/Draw rates: The Winning rate for plan 3 is 85% (70% + 100%), Lose rate for plan 3 is 10% (20% + 0%), Draw Rate for plan 3 is 5% (10% + 0%).\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, Chips in the pot: 8. If win, the winning payoff would be 4. If lose, the lose payoff would be 4.\n- Plan 2: After the action, Chips in the pot: 2. If lose, the lose payoff would be 1.\n- Plan 3: After the action, Chips in the pot: 2. If win, the winning payoff would be 1. If lose, the lose payoff would be 1.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 85% * 4 - 10% * 4 = 3\n- Plan 2: Expected Chips Gain = 0% * 0 - 100% * 1 = -1\n- Plan 3: Expected Chips Gain = 85% * 1 - 10% * 1 = 0.75\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": "", "25_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (35% chance), he is likely to raise (80%) or check (20%). If he raises, I will win (0% chance), draw (0% chance), or lose (100% chance). If he checks, I will win (100% chance), draw (0% chance), or lose (0% chance). Overall, my winning rate is 7%, losing rate is 28%, and drawing rate is 0%.\n- If GoodGuy holds a Queen (30% chance), he is likely to raise (60%) or fold (40%). If he raises, I will win (100% chance), draw (0% chance), or lose (0% chance). If he folds, I will win (100% chance), draw (0% chance), or lose (0% chance). Overall, my winning rate is 30%, losing rate is 0%, and drawing rate is 0%.\n- If GoodGuy holds a Jack (25% chance), he is likely to raise (50%) or fold (50%). If he raises, I will win (100% chance), draw (0% chance), or lose (0% chance). If he folds, I will win (100% chance), draw (0% chance), or lose (0% chance). Overall, my winning rate is 25%, losing rate is 0%, and drawing rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose 100% of the time, regardless of what card GoodGuy holds. My winning rate is 0%, losing rate is 100%, and drawing rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King (35% chance), he is likely to raise (80%) or check (20%). If he raises, I will win (0% chance), draw (0% chance), or lose (100% chance). If he checks, I will win (100% chance), draw (0% chance), or lose (0% chance). Overall, my winning rate is 7%, losing rate is 28%, and drawing rate is 0%.\n- If GoodGuy holds a Queen (30% chance), he is likely to raise (60%) or fold (40%). If he raises, I will win (100% chance), draw (0% chance), or lose (0% chance). If he folds, I will win (100% chance), draw (0% chance), or lose (0% chance). Overall, my winning rate is 30%, losing rate is 0%, and drawing rate is 0%.\n- If GoodGuy holds a Jack (25% chance), he is likely to raise (50%) or fold (50%). If he raises, I will win (100% chance), draw (0% chance), or lose (0% chance). If he folds, I will win (100% chance), draw (0% chance), or lose (0% chance). Overall, my winning rate is 25%, losing rate is 0%, 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 8 chips. If I lose, the losing payoff would be 4 chips.\n- Plan 2: If I fold, I will lose 4 chips.\n- Plan 3: If I win, the winning payoff would be 4 chips. If I lose, the losing payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: (62% * 8) - (28% * 4) = 3.76 chips\n- Plan 2: -4 chips\n- Plan 3: (62% * 4) - (28% * 4) = 1.36 chips\n\nPlan Selection:\n- Plan 1: 3.76 chips\n- Plan 2: -4 chips\n- Plan 3: 1.36 chips\n\nBased on the estimated expected chips gains, I should choose Plan 1 (Raise)."}}
{"message": "", "26_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a Jack (30% probability), he is likely to raise (70%) or call (30%). If he raises, I will win as I hold a King. If he calls, the outcome will depend on the public card. The overall winning rate for this plan is 70% * 30% = 21%.\n- If GoodGuy holds a Queen (20% probability), he is likely to raise (80%) or call (20%). If he raises, I will win as I hold a King. If he calls, the outcome will depend on the public card. The overall winning rate for this plan is 80% * 20% = 16%.\n- If GoodGuy holds a King (50% probability), he is likely to raise (90%) or call (10%). If he raises or calls, it will be a draw as we both hold a King. The overall draw rate for this plan is 100% * 50% = 50%.\n\nPlan 2: Raise\n- If GoodGuy holds a Jack (30% probability), he is likely to call (30%) or fold (70%). If he calls, I will win as I hold a King. If he folds, I will also win. The overall winning rate for this plan is 100% * 30% = 30%.\n- If GoodGuy holds a Queen (20% probability), he is likely to call (20%) or fold (80%). If he calls, I will win as I hold a King. If he folds, I will also win. The overall winning rate for this plan is 100% * 20% = 20%.\n- If GoodGuy holds a King (50% probability), he is likely to call (10%) or fold (90%). If he calls, it will be a draw as we both hold a King. If he folds, I will win. The overall winning rate for this plan is 90% * 50% = 45%.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of GoodGuy's card. The overall losing rate for this plan is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, Chips in the pot: 3. If win, the winning payoff would be 1.5. If lose, the lose payoff would be 1.5.\n- Plan 2: After the action, Chips in the pot: 5. If win, the winning payoff would be 2.5. If lose, the lose payoff would be 2.5.\n- Plan 3: After the action, Chips in the pot: 3. If lose, the lose payoff would be 1.5.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 21% * 1.5 - 79% * 1.5 = -0.87\n- Plan 2: 75% * 2.5 - 25% * 2.5 = 1.25\n- Plan 3: 0 * 1.5 - 100% * 1.5 = -1.5\n\nPlan Selection:\n- Plan 2: Raise\n- Plan 1: Call\n- Plan 3: Fold\n\nBased on the estimated expected chips gains, the best plan would be to raise."}}
{"message": "", "26_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (45% chance), he is likely to raise (80% chance) or call (15% chance). If he raises, I will win (since I also have a King). If he calls, I will also win. Therefore, the winning rate for this plan is 45% * (80% + 15%) = 42.75%.\n- If GoodGuy holds a Queen (35% chance), he is likely to raise (70% chance) or call (20% chance). If he raises, it will be a draw (since the public card is a Queen). If he calls, I will win. Therefore, the draw rate for this plan is 35% * 70% = 24.5%, and the winning rate is 35% * 20% = 7%.\n- If GoodGuy holds a Jack (20% chance), he is likely to raise (60% chance), call (20% chance), or fold (20% chance). If he raises or calls, I will win. If he folds, there will be no change in chips. Therefore, the winning rate for this plan is 20% * (60% + 20%) = 16%.\n\nPlan 2: Fold\n- If I fold, I will lose the chips in the pot. Therefore, the losing rate for this plan is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (45% chance), he is likely to raise (80% chance) or call (15% chance). If he raises, I will win (since I also have a King). If he calls, I will also win. Therefore, the winning rate for this plan is 45% * (80% + 15%) = 42.75%.\n- If GoodGuy holds a Queen (35% chance), he is likely to raise (70% chance) or call (20% chance). If he raises, it will be a draw (since the public card is a Queen). If he calls, I will win. Therefore, the draw rate for this plan is 35% * 70% = 24.5%, and the winning rate is 35% * 20% = 7%.\n- If GoodGuy holds a Jack (20% chance), he is likely to raise (60% chance), call (20% chance), or fold (20% chance). If he raises or calls, I will win. If he folds, there will be no change in chips. Therefore, the winning rate for this plan is 20% * (60% + 20%) = 16%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the pot (8 chips). If I lose, the lose payoff would be half of the pot (8 chips).\n- Plan 2: If I lose, the lose payoff would be half of the pot (8 chips).\n- Plan 3: If I win, the winning payoff would be half of the pot (8 chips). If I lose, the lose payoff would be half of the pot (8 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning Rate * Winning Payoff - Losing Rate * Losing Payoff = 42.75% * 8 - 0% * 8 = 3.42 chips\n- Plan 2: Expected Chips Gain = 0% * 8 - 100% * 8 = -8 chips\n- Plan 3: Expected Chips Gain = 42.75% * 8 - 0% * 8 = 3.42 chips\n\nPlan Selection:\n- Plan 1: 3.42 chips\n- Plan 2: -8 chips\n- Plan 3: 3.42 chips\n\nTherefore, I should choose either Plan 1 or Plan 3, as they both have the highest expected chips gain. However, considering my strategy improvement, I should choose Plan 1 (Raise) to be more aggressive when I have a strong hand."}}
{"message": "", "27_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% chance), he will likely raise (70% chance). If the public card is a King, I will lose. If the public card is a Queen or Jack, I have a chance to win. \n- If GoodGuy holds a Queen (60% chance), he will likely raise (60% chance). If the public card is a Queen, I will lose. If the public card is a King or Jack, I have a chance to win. \n- If GoodGuy holds a Jack (40% chance), he will likely call (60% chance). If the public card is a Jack, it will be a draw. If the public card is a King or Queen, I will lose. \n\nPlan 2: Raise\n- If GoodGuy holds a King (70% chance), he will likely raise (70% chance). If the public card is a King, I will lose. If the public card is a Queen or Jack, I have a chance to win. \n- If GoodGuy holds a Queen (60% chance), he will likely raise (60% chance). If the public card is a Queen, I will lose. If the public card is a King or Jack, I have a chance to win. \n- If GoodGuy holds a Jack (40% chance), he will likely call (60% chance). If the public card is a Jack, it will be a draw. If the public card is a King or Queen, I will lose. \n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 2 chips. If I lose, the lose payoff would be 2 chips. \n- Plan 2: If I win, the winning payoff would be 6 chips. If I lose, the lose payoff would be 6 chips. \n- Plan 3: If I fold, the lose payoff would be 2 chips. \n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.7 * 2 - 0.3 * 2 = 0.8 chips\n- Plan 2: Expected Chips Gain = 0.7 * 6 - 0.3 * 6 = 2.4 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": "", "27_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King, he will likely raise (70%) or call (30%). If he raises, I will lose as my Jack is lower than his King. If he calls, I will also lose as my Jack is lower than the public Queen. Therefore, the winning rate for this plan is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a Queen, he will likely raise (80%) or check (20%). If he raises or checks, I will lose as my Jack is lower than his Queen and the public Queen. Therefore, the winning rate for this plan is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a Jack, he will likely raise (40%) or call (60%). If he raises or calls, it will be a draw as my Jack is equal to his Jack and lower than the public Queen. Therefore, the winning rate for this plan is 0%, the losing rate is 0%, and the draw rate is 100%.\n\nPlan 2: Fold\n- If I fold, I will lose the chips I have already put into the pot, but I will not lose any more chips. Therefore, the winning rate for this plan is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King, he will likely raise (50%) or check (30%) or fold (20%). If he raises, I will lose as my Jack is lower than his King. If he checks or folds, it will be a draw as my Jack is lower than the public Queen. Therefore, the winning rate for this plan is 0%, the losing rate is 50%, and the draw rate is 50%.\n- If GoodGuy holds a Queen, he will likely raise (80%) or check (20%). If he raises or checks, I will lose as my Jack is lower than his Queen and the public Queen. Therefore, the winning rate for this plan is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a Jack, he will likely raise (40%) or check (30%) or fold (30%). If he raises or checks or folds, it will be a draw as my Jack is equal to his Jack and lower than the public Queen. Therefore, the winning rate for this plan is 0%, the losing rate is 0%, and the draw rate is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 8 chips (half of the pot). If I lose, the lose payoff would be 4 chips (half of the pot).\n- Plan 2: If I win, the winning payoff would be 0 chips (as I have folded). If I lose, the lose payoff would be 4 chips (half of the pot).\n- Plan 3: If I win, the winning payoff would be 8 chips (half of the pot). If I lose, the lose payoff would be 4 chips (half of the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0% * 8 chips - 100% * 4 chips = -4 chips\n- Plan 2: Expected Chips Gain = 0% * 0 chips - 100% * 4 chips = -4 chips\n- Plan 3: Expected Chips Gain = 0% * 8 chips - 50% * 4 chips = -2 chips\n\nPlan Selection:\n- Plan 1: -4 chips\n- Plan 2: -4 chips\n- Plan 3: -2 chips\n\nTherefore, I should select Plan 3 (Check) as it has the highest estimated expected chips gain."}}
{"message": "", "27_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (40% chance), he will likely raise (50% chance). If he raises, I will lose as King is higher than my Jack. The overall losing rate for this plan is 0.4*0.5=0.2.\n- If GoodGuy holds a Queen (40% chance), he will likely raise (80% chance). If he raises, I will lose as Queen matches the public card. The overall losing rate for this plan is 0.4*0.8=0.32.\n- If GoodGuy holds a Jack (20% chance), he will likely check (30% chance) or fold (20% chance). If he checks or folds, I will win as my Jack matches his Jack. The overall winning rate for this plan is 0.2*0.5=0.1.\n\nPlan 2: Raise\n- If GoodGuy holds a King (40% chance), he will likely raise (50% chance). If he raises, I will lose as King is higher than my Jack. The overall losing rate for this plan is 0.4*0.5=0.2.\n- If GoodGuy holds a Queen (40% chance), he will likely raise (80% chance). If he raises, I will lose as Queen matches the public card. The overall losing rate for this plan is 0.4*0.8=0.32.\n- If GoodGuy holds a Jack (20% chance), he will likely check (30% chance) or fold (20% chance). If he checks or folds, I will win as my Jack matches his Jack. The overall winning rate for this plan is 0.2*0.5=0.1.\n\nPlan 3: Fold\n- If I fold, I will lose the game and the chips I have already put in the pot. The overall losing rate for this plan is 1.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the pot (8 chips). If I lose, the lose payoff would be half of the pot (8 chips).\n- Plan 2: If I win, the winning payoff would be half of the pot (12 chips). If I lose, the lose payoff would be half of the pot (12 chips).\n- Plan 3: If I lose, 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 = 0.1*8 - 0.52*8 = -3.36 chips\n- Plan 2: Expected Chips Gain = 0.1*12 - 0.52*12 = -5.04 chips\n- Plan 3: Expected Chips Gain = -8 chips\n\nPlan Selection:\n- Plan 1: -3.36 chips\n- Plan 2: -5.04 chips\n- Plan 3: -8 chips\n\nBased on the estimated expected chips gains, Plan 1 (Call) is the best strategy to follow in this situation."}}
{"message": "", "28_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (20% chance), he might raise (70% chance) or call (30% chance). If he raises, I would lose unless the public card is a Jack. If he calls, the outcome would depend on the public card. The overall winning rate is 6%, losing rate is 14%, and drawing rate is 0%.\n- If GoodGuy holds a Queen (20% chance), he might raise (60% chance) or call (40% chance). If he raises, I would lose unless the public card is a Jack. If he calls, the outcome would depend on the public card. The overall winning rate is 8%, losing rate is 12%, and drawing rate is 0%.\n- If GoodGuy holds a Jack (60% chance), he might call (60% chance) or raise (40% chance). If he raises, I would draw unless the public card is a Jack. If he calls, the outcome would depend on the public card. The overall winning rate is 24%, losing rate is 0%, and drawing rate is 36%.\n\nPlan 1 overall GoodGuy's Winning/Lose/Draw rates: Winning rate is 38%, losing rate is 26%, and drawing rate is 36%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (20% chance), he might raise (70% chance) or call (30% chance). If he raises, I would lose unless the public card is a Jack. If he calls, the outcome would depend on the public card. The overall winning rate is 6%, losing rate is 14%, and drawing rate is 0%.\n- If GoodGuy holds a Queen (20% chance), he might raise (60% chance) or call (40% chance). If he raises, I would lose unless the public card is a Jack. If he calls, the outcome would depend on the public card. The overall winning rate is 8%, losing rate is 12%, and drawing rate is 0%.\n- If GoodGuy holds a Jack (60% chance), he might call (60% chance) or raise (40% chance). If he raises, I would draw unless the public card is a Jack. If he calls, the outcome would depend on the public card. The overall winning rate is 24%, losing rate is 0%, and drawing rate is 36%.\n\nPlan 2 overall GoodGuy's Winning/Lose/Draw rates: Winning rate is 38%, losing rate is 26%, and drawing rate is 36%.\n\nPlan 3: Fold\n- If I fold, I would lose the game immediately. The overall winning rate is 0%, losing rate is 100%, and drawing rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, chips in the pot would be 4. If win, the winning payoff would be 2 chips. If lose, the lose payoff would be 2 chips.\n- Plan 2: After the action, chips in the pot would be 6. If win, the winning payoff would be 3 chips. If lose, the lose payoff would be 3 chips.\n- Plan 3: After the action, chips in the pot would be 3. If lose, the lose payoff would be 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected chips gain is 38% * 2 - 26% * 2 = 0.24 chips.\n- Plan 2: Expected chips gain is 38% * 3 - 26% * 3 = 0.36 chips.\n- Plan 3: Expected chips gain is -1 chip.\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I would choose this plan."}}
{"message": "", "28_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (50% probability), he will likely raise (70% probability). If he raises, I will lose (as King is higher than Jack). So, the losing rate for this scenario is 50% * 70% = 35%.\n- If GoodGuy holds a Queen (30% probability), he will likely check (30% probability). If he checks, I will win (as Queen matches the public card). So, the winning rate for this scenario is 30% * 30% = 9%.\n- If GoodGuy holds a Jack (20% probability), he will likely check (40% probability). If he checks, it will be a draw (as both of us hold Jack). So, the draw rate for this scenario is 20% * 40% = 8%.\n\nPlan 2: Fold\n- If I fold, I will lose the chips in the pot. The losing rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (50% probability), he will likely raise (70% probability). If he raises, I will lose (as King is higher than Jack). So, the losing rate for this scenario is 50% * 70% = 35%.\n- If GoodGuy holds a Queen (30% probability), he will likely check (30% probability). If he checks, I will win (as Queen matches the public card). So, the winning rate for this scenario is 30% * 30% = 9%.\n- If GoodGuy holds a Jack (20% probability), he will likely check (40% probability). If he checks, it will be a draw (as both of us hold Jack). So, the draw rate for this scenario is 20% * 40% = 8%.\n\nWinning/Lose Payoffs for Each Plan:\n- Plan 1: If I win, the winning payoff would be half of the pot (4 chips). If I lose, the losing payoff would be half of the pot (4 chips).\n- Plan 2: If I fold, I will lose the chips in the pot (4 chips).\n- Plan 3: If I win, the winning payoff would be half of the pot (4 chips). If I lose, the losing payoff would be half of the pot (4 chips).\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 9% * 4 - 35% * 4 = -1.04 chips\n- Plan 2: Expected Chips Gain = -100% * 4 = -4 chips\n- Plan 3: Expected Chips Gain = 9% * 4 - 35% * 4 = -1.04 chips\n\nPlan Selection:\n- Plan 1: -1.04 chips\n- Plan 2: -4 chips\n- Plan 3: -1.04 chips\n\nBased on the expected chips gain, Plan 1 and Plan 3 are the best strategies to follow as they have the highest expected chips gain (-1.04 chips). However, considering the strategy improvement, I should choose Plan 3 (Check) as it is less risky and more cautious when GoodGuy raises, especially in the second round."}}
{"message": "", "29_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% chance), he will likely raise (70% chance). If the public card is a King or a Queen, I will lose. If the public card is a Jack, it's a draw. \n- If GoodGuy holds a Queen (50% chance), he will likely raise (50% chance) or call (50% chance). If the public card is a King, I will lose. If the public card is a Queen or a Jack, I will win.\n- If GoodGuy holds a Jack (40% chance), he will likely call (60% chance). If the public card is a King or a Queen, I will win. If the public card is a Jack, it's a draw.\n\nPlan 2: Raise\n- If GoodGuy holds a King (70% chance), he will likely raise (70% chance). If the public card is a King or a Queen, I will lose. If the public card is a Jack, it's a draw. \n- If GoodGuy holds a Queen (50% chance), he will likely raise (50% chance) or call (50% chance). If the public card is a King, I will lose. If the public card is a Queen or a Jack, I will win.\n- If GoodGuy holds a Jack (40% chance), he will likely fold (40% chance). If the public card is a King or a Queen, I will win. If the public card is a Jack, it's a draw.\n\nPlan 3: Fold\n- If I fold, I will lose the chips in the pot regardless of GoodGuy's card or the public card.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 6 chips. If I lose, the lose payoff would be 2 chips.\n- Plan 2: If I win, the winning payoff would be 10 chips. If I lose, the lose payoff would be 4 chips.\n- Plan 3: If I fold, the lose payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: (0.5 * 6) - (0.5 * 2) = 2 chips\n- Plan 2: (0.5 * 10) - (0.5 * 4) = 3 chips\n- Plan 3: -2 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest estimated expected chips gain, so I will choose this plan."}}
{"message": "", "29_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen, he will likely raise (80% probability). If he raises, I will win because my card matches the public card. The winning rate for his Queen is 0.8 (probability of him holding a Queen) * 0.8 (probability of him raising) = 0.64.\n- If GoodGuy holds a King or Jack, he will likely check (60% probability) or fold (40% probability). If he checks or folds, I will win because my card matches the public card. The winning rate for his King or Jack is 0.2 (probability of him holding a King or Jack) * 1 (probability of him checking or folding) = 0.2.\n- The overall winning rate for Plan 1 is 0.64 + 0.2 = 0.84.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. The overall losing rate for Plan 2 is 1.\n\nPlan 3: Check\n- If GoodGuy holds a Queen, he will likely raise (80% probability). If he raises, I will win because my card matches the public card. The winning rate for his Queen is 0.8 (probability of him holding a Queen) * 0.8 (probability of him raising) = 0.64.\n- If GoodGuy holds a King or Jack, he will likely check (60% probability) or fold (40% probability). If he checks or folds, I will win because my card matches the public card. The winning rate for his King or Jack is 0.2 (probability of him holding a King or Jack) * 1 (probability of him checking or folding) = 0.2.\n- The overall winning rate for Plan 3 is 0.64 + 0.2 = 0.84.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the pot, which is 6 chips. If I lose, the lose payoff would be half of the pot, which is 6 chips.\n- Plan 2: If I fold, I will lose half of the pot, which is 6 chips.\n- Plan 3: If I win, the winning payoff would be half of the pot, which is 6 chips. If I lose, the lose payoff would be half of the pot, which is 6 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is 0.84 * 6 - 0.16 * 6 = 4.08 chips.\n- Plan 2: The expected chips gain is -6 chips.\n- Plan 3: The expected chips gain is 0.84 * 6 - 0.16 * 6 = 4.08 chips.\n\nPlan Selection:\n- Plan 1 and Plan 3 have the highest expected chips gain, so I should choose either Plan 1 or Plan 3. Since Plan 1 is more aggressive and can potentially confuse GoodGuy, I will choose Plan 1."}}
{"message": "", "30_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (50% probability), he is likely to raise (70%) or call (30%) in the next round. If he raises, I will win (70%) or lose (30%) based on the public card. If he calls, I will win (70%) or lose (30%) based on the public card. Overall, the winning rate is 0.5*(0.7*0.7+0.3*0.7)=0.35, the losing rate is 0.5*(0.7*0.3+0.3*0.3)=0.15.\n- If GoodGuy holds a Queen (50% probability), he is likely to raise (40%) or call (60%) in the next round. If he raises, I will win (60%) or lose (40%) based on the public card. If he calls, I will win (60%) or lose (40%) based on the public card. Overall, the winning rate is 0.5*(0.4*0.6+0.6*0.6)=0.3, the losing rate is 0.5*(0.4*0.4+0.6*0.4)=0.2.\n- The chips in the pot would be 8 if I win, and the winning payoff would be 4. If I lose, the chips in the pot would be 8, and the losing payoff would be 4.\n- The expected chips gain for Plan 1 is 0.35*4-0.15*4=0.8.\n\nPlan 2: Raise\n- If GoodGuy holds a King (50% probability), he is likely to raise (70%) or call (30%) in the next round. If he raises, I will win (70%) or lose (30%) based on the public card. If he calls, I will win (70%) or lose (30%) based on the public card. Overall, the winning rate is 0.5*(0.7*0.7+0.3*0.7)=0.35, the losing rate is 0.5*(0.7*0.3+0.3*0.3)=0.15.\n- If GoodGuy holds a Queen (50% probability), he is likely to raise (40%) or call (60%) in the next round. If he raises, I will win (60%) or lose (40%) based on the public card. If he calls, I will win (60%) or lose (40%) based on the public card. Overall, the winning rate is 0.5*(0.4*0.6+0.6*0.6)=0.3, the losing rate is 0.5*(0.4*0.4+0.6*0.4)=0.2.\n- The chips in the pot would be 12 if I win, and the winning payoff would be 6. If I lose, the chips in the pot would be 12, and the losing payoff would be 6.\n- The expected chips gain for Plan 2 is 0.35*6-0.15*6=1.2.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put into the pot, which is 2. The expected chips loss for Plan 3 is -2.\n\nPlan Selection:\n- The estimated expected chips gains for Plan 1, Plan 2, and Plan 3 are 0.8, 1.2, and -2, respectively. Therefore, the rank of the plans based on the estimated expected chips gains is Plan 2 > Plan 1 > Plan 3.\n- Considering the strategy improvement, I should select Plan 2, which is to raise. This plan is more aggressive and has the highest estimated expected chips gain."}}
{"message": "", "30_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (70% chance), he is likely to raise (80%) or check (20%). If he raises, I will win (50%) or lose (50%) as we both have Kings. If he checks, I will win (100%). Overall, the winning rate is 70% * (80% * 50% + 20% * 100%) = 42%.\n- If GoodGuy holds a Queen (20% chance), he is likely to raise (60%) or check (40%). If he raises, I will win (100%). If he checks, I will win (100%). Overall, the winning rate is 20% * (60% * 100% + 40% * 100%) = 20%.\n- If GoodGuy holds a Jack (10% chance), he is likely to check (60%) or fold (40%). If he checks, I will win (100%). If he folds, I will win (100%). Overall, the winning rate is 10% * (60% * 100% + 40% * 100%) = 10%.\n\nPlan 2: Fold\n- If I fold, I will lose (100%). The losing rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (70% chance), he is likely to raise (80%) or check (20%). If he raises, I will win (50%) or lose (50%) as we both have Kings. If he checks, I will win (100%). Overall, the winning rate is 70% * (80% * 50% + 20% * 100%) = 42%.\n- If GoodGuy holds a Queen (20% chance), he is likely to raise (60%) or check (40%). If he raises, I will win (100%). If he checks, I will win (100%). Overall, the winning rate is 20% * (60% * 100% + 40% * 100%) = 20%.\n- If GoodGuy holds a Jack (10% chance), he is likely to check (60%) or fold (40%). If he checks, I will win (100%). If he folds, I will win (100%). Overall, the winning rate is 10% * (60% * 100% + 40% * 100%) = 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 pot (6 chips + 4 chips I raise) = 5 chips. If I lose, the losing payoff would be half of the pot (6 chips + 4 chips I raise) = 5 chips.\n- Plan 2: If I fold, I will lose the 6 chips I have already put in the pot.\n- Plan 3: If I win, the winning payoff would be half of the pot (6 chips) = 3 chips. If I lose, the losing payoff would be half of the pot (6 chips) = 3 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning Rate * Winning Payoff - Losing Rate * Losing Payoff = 72% * 5 chips - 28% * 5 chips = 2.2 chips\n- Plan 2: Expected Chips Gain = -6 chips\n- Plan 3: Expected Chips Gain = 72% * 3 chips - 28% * 3 chips = 1.32 chips\n\nPlan Selection:\n- Plan 1: Raise (Expected Chips Gain = 2.2 chips)\n- Plan 3: Check (Expected Chips Gain = 1.32 chips)\n- Plan 2: Fold (Expected Chips Gain = -6 chips)\n\nBased on the expected chips gain, I should choose Plan 1: Raise."}}
{"message": "", "30_5": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he will likely raise (80% probability). If he raises, I will win (as we both have Kings, but I called first). The winning rate for his King is 0.7 * 0.8 = 0.56.\n- If GoodGuy holds a Queen (30% probability), he will likely raise (60% probability). If he raises, I will win (as my King is higher than his Queen). The winning rate for his Queen is 0.3 * 0.6 = 0.18.\n- Overall, the winning rate for Plan 1 is 0.56 + 0.18 = 0.74. The lose rate is 0 (as I will not lose in this scenario), and the draw rate is 0.26 (as we both have Kings, but I called first).\n\nPlan 2: Fold\n- If I fold, I will lose regardless of GoodGuy's cards. The lose rate for Plan 2 is 1, and the winning and draw rates are both 0.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the call, the chips in the pot will be 28. If I win, the winning payoff would be 14. If I lose, the lose payoff would be 14.\n- Plan 2: If I fold, I will lose the 14 chips I have already put into the pot.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is the winning rate * winning payoff - lose rate * lose payoff = 0.74 * 14 - 0 * 14 = 10.36 chips.\n- Plan 2: The expected chips gain is the winning rate * winning payoff - lose rate * lose payoff = 0 * 14 - 1 * 14 = -14 chips.\n\nPlan Selection:\n- The rank of estimated expected chips gains for every plan is: Plan 1 > Plan 2.\n- Therefore, I should select Plan 1 (Call) as it has the highest estimated expected chips gain."}}
{"message": "", "31_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a Jack, he tends to call (60%) or raise (40%). If he calls, the pot will be 4 chips. If he raises, the pot will be 8 chips. \n- If GoodGuy holds a Queen, he tends to raise (70%) or call (30%). If he calls, the pot will be 4 chips. If he raises, the pot will be 8 chips. \n- If GoodGuy holds a King, he tends to raise (80%) or call (20%). If he calls, the pot will be 4 chips. If he raises, the pot will be 8 chips. \n\nPlan 2: Raise\n- If GoodGuy holds a Jack, he tends to call (60%) or raise (40%). If he calls, the pot will be 6 chips. If he raises, the pot will be 10 chips. \n- If GoodGuy holds a Queen, he tends to raise (70%) or call (30%). If he calls, the pot will be 6 chips. If he raises, the pot will be 10 chips. \n- If GoodGuy holds a King, he tends to raise (80%) or call (20%). If he calls, the pot will be 6 chips. If he raises, the pot will be 10 chips. \n\nPlan 3: Fold\n- If GoodGuy holds a Jack, Queen, or King, the pot will remain at 3 chips and I will lose 1 chip. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be 2 chips. If lose, the lose payoff would be 2 chips. \n- Plan 2: If win, the winning payoff would be 3 chips. If lose, the lose payoff would be 3 chips. \n- Plan 3: If win, the winning payoff would be 0 chips. If lose, the lose payoff would be 1 chip. \n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: (0.6 * 2) - (0.4 * 2) = 0.4 chips\n- Plan 2: (0.6 * 3) - (0.4 * 3) = 0.6 chips\n- Plan 3: (0 * 0) - (1 * 1) = -1 chip\n\nPlan Selection:\n- Plan 2 (Raise) has the highest estimated expected chips gain, so I will choose this plan."}}
{"message": "", "31_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Jack (60% probability), he might check (50%), raise (30%), or fold (20%). If he checks or folds, I would win as my card is higher. If he raises, it would be a draw. So, the winning rate is 70%, the losing rate is 0%, and the draw rate is 30%.\n- If GoodGuy holds a Queen (30% probability), he would raise (90%) or check (10%). If he raises, I would lose as his card matches the public card. If he checks, I would win as my card is higher. So, the winning rate is 10%, the losing rate is 90%, and the draw rate is 0%.\n- If GoodGuy holds a King (10% probability), he might check (50%), raise (30%), or fold (20%). If he checks or folds, I would lose as his card is higher. If he raises, I would also lose. So, 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 would lose the chips in the pot regardless of GoodGuy's card. So, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a Jack (60% probability), he might check (50%), raise (30%), or fold (20%). If he checks or folds, I would win as my card is higher. If he raises, it would be a draw. So, the winning rate is 70%, the losing rate is 0%, and the draw rate is 30%.\n- If GoodGuy holds a Queen (30% probability), he would raise (90%) or check (10%). If he raises, I would lose as his card matches the public card. If he checks, I would win as my card is higher. So, the winning rate is 10%, the losing rate is 90%, and the draw rate is 0%.\n- If GoodGuy holds a King (10% probability), he might check (50%), raise (30%), or fold (20%). If he checks or folds, I would lose as his card is higher. If he raises, I would also lose. So, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips (half of the pot). If I lose, the losing payoff would be 4 chips.\n- Plan 2: If I fold, I would lose the 4 chips in the pot.\n- Plan 3: If I win, the winning payoff would be 4 chips (half of the pot). If I lose, the losing payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.7 * 4 - 0.3 * 4 = 1.6 chips\n- Plan 2: Expected Chips Gain = 0 - 1 * 4 = -4 chips\n- Plan 3: Expected Chips Gain = 0.7 * 4 - 0.3 * 4 = 1.6 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 have the highest expected chips gain (1.6 chips), so I would choose either of these plans. However, considering the strategy improvement, I should consider bluffing occasionally to keep GoodGuy guessing about my strategy. Therefore, I would choose Plan 1: Raise."}}
{"message": "", "32_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King, he is likely to raise (70%) or call (30%). If he raises, I will lose (probability = 70%). If he calls, it will be a draw (probability = 30%).\n- If GoodGuy holds a Queen, it will be a draw (probability = 100%).\n- If GoodGuy holds a Jack, he is likely to call (60%) or raise (40%). If he calls, I will win (probability = 60%). If he raises, I will lose (probability = 40%).\n\nPlan 2: Raise\n- If GoodGuy holds a King, he is likely to call (30%) or fold (70%). If he calls, I will lose (probability = 30%). If he folds, I will win (probability = 70%).\n- If GoodGuy holds a Queen, he is likely to call (40%) or fold (60%). If he calls, it will be a draw (probability = 40%). If he folds, I will win (probability = 60%).\n- If GoodGuy holds a Jack, he is likely to call (40%) or fold (60%). If he calls, I will win (probability = 40%). If he folds, I will win (probability = 60%).\n\nPlan 3: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips. If I lose, the lose payoff would be 2 chips.\n- Plan 2: If I win, the winning payoff would be 5 chips. If I lose, the lose payoff would be 4 chips.\n- Plan 3: If I fold, the lose payoff would be 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 60% * 3 - 70% * 2 = 0.8 chips\n- Plan 2: Expected Chips Gain = 70% * 5 - 30% * 4 = 2.5 chips\n- Plan 3: Expected Chips Gain = -1 chip\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain, so I should choose to raise."}}
{"message": "", "32_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (100% probability), he will raise (80% probability). If he raises, considering the game rules, I will win (80% probability), draw (20% probability), and lose (0% probability). The overall winning rate for his Queen is 80%, the losing rate is 0%, and the draw rate is 20%.\n- After the action, chips in the pot would be 16. If win, the winning payoff would be 8. If lose, the lose payoff would be 8.\n\nPlan 2: Fold\n- If GoodGuy holds a Queen (100% probability), he will check (20% probability). If he checks, considering the game rules, I will win (0% probability), draw (0% probability), and lose (100% probability). The overall winning rate for his Queen is 0%, the losing rate is 100%, and the draw rate is 0%.\n- After the action, chips in the pot would be 8. If win, the winning payoff would be 4. If lose, the lose payoff would be 4.\n\nPlan 3: Check\n- If GoodGuy holds a Queen (100% probability), he will raise (80% probability). If he raises, considering the game rules, I will win (80% probability), draw (20% probability), and lose (0% probability). The overall winning rate for his Queen is 80%, the losing rate is 0%, and the draw rate is 20%.\n- After the action, chips in the pot would be 12. If win, the winning payoff would be 6. If lose, the lose payoff would be 6.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 80% * 8 - 0% * 8 = 6.4 chips\n- Plan 2: 0% * 4 - 100% * 4 = -4 chips\n- Plan 3: 80% * 6 - 0% * 6 = 4.8 chips\n\nPlan Selection:\n- Plan 1: 6.4 chips\n- Plan 2: -4 chips\n- Plan 3: 4.8 chips\n\nThe rank of estimated expected chips gains for every plan is Plan 1 > Plan 3 > Plan 2. Therefore, the plan with the highest estimated expected chips gain is Plan 1: Raise."}}
{"message": "", "33_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a Jack (33.3% chance), he might raise (60%) or call (40%). If he raises, I will win as my King is higher than his Jack. If he calls, it will be a draw. So, the winning rate is 33.3%*60% = 20%, the draw rate is 33.3%*40% = 13.3%, and the lose rate is 0%.\n- If GoodGuy holds a Queen (33.3% chance), he might raise (70%) or call (30%). If he raises, I will win as my King is higher than his Queen. If he calls, it will be a draw. So, the winning rate is 33.3%*70% = 23.3%, the draw rate is 33.3%*30% = 10%, and the lose rate is 0%.\n- If GoodGuy holds a King (33.3% chance), he might raise (80%) or call (20%). If he raises or calls, it will be a draw as we both hold Kings. So, the draw rate is 33.3%, and the winning and lose rates are both 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a Jack (33.3% chance), he might raise (60%) or call (40%). If he raises, I will win as my King is higher than his Jack. If he calls, it will be a draw. So, the winning rate is 33.3%*60% = 20%, the draw rate is 33.3%*40% = 13.3%, and the lose rate is 0%.\n- If GoodGuy holds a Queen (33.3% chance), he might raise (70%) or call (30%). If he raises, I will win as my King is higher than his Queen. If he calls, it will be a draw. So, the winning rate is 33.3%*70% = 23.3%, the draw rate is 33.3%*30% = 10%, and the lose rate is 0%.\n- If GoodGuy holds a King (33.3% chance), he might raise (80%) or call (20%). If he raises or calls, it will be a draw as we both hold Kings. So, the draw rate is 33.3%, and the winning and lose rates are both 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card. So, the lose rate is 100%, and the winning and draw rates are both 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the pot (6 chips). If I lose, the lose payoff would be half of the pot (6 chips).\n- Plan 2: If I win, the winning payoff would be half of the pot (8 chips). If I lose, the lose payoff would be half of the pot (8 chips).\n- Plan 3: If I lose, the lose payoff would be half of the pot (4 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 20%*6 - 0%*6 = 1.2 chips\n- Plan 2: Expected Chips Gain = 23.3%*8 - 0%*8 = 1.864 chips\n- Plan 3: Expected Chips Gain = 0%*0 - 100%*4 = -4 chips\n\nPlan Selection:\n- Plan 1: 1.2 chips\n- Plan 2: 1.864 chips\n- Plan 3: -4 chips\n\nBased on the estimated expected chips gain, Plan 2 (Raise) is the best strategy to use in the current game."}}
{"message": "", "33_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (70% probability), he will likely raise (70% probability). If he raises, I will win (0% probability), lose (100% probability), or draw (0% probability). The overall winning rate is 0%, the losing rate is 49% (70% * 70%), and the drawing rate is 0%.\n- If GoodGuy holds a Queen (30% probability), he will likely raise (60% probability) or fold (40% probability). If he raises, I will win (100% probability), lose (0% probability), or draw (0% probability). The overall winning rate is 18% (30% * 60%), the losing rate is 0%, and the drawing rate is 0%.\n\nPlan 2: Fold\n- If GoodGuy holds a King (70% probability), he will likely raise (70% probability). If I fold, I will lose (100% probability). The overall losing rate is 49% (70% * 70%).\n- If GoodGuy holds a Queen (30% probability), he will likely raise (60% probability) or fold (40% probability). If I fold, I will lose (100% probability). The overall losing rate is 18% (30% * 60%).\n\nPlan 3: Check\n- If GoodGuy holds a King (70% probability), he will likely raise (70% probability). If he raises, I will win (0% probability), lose (100% probability), or draw (0% probability). The overall winning rate is 0%, the losing rate is 49% (70% * 70%), and the drawing rate is 0%.\n- If GoodGuy holds a Queen (30% probability), he will likely raise (60% probability) or fold (40% probability). If he raises, I will win (100% probability), lose (0% probability), or draw (0% probability). The overall winning rate is 18% (30% * 60%), the losing rate is 0%, and the drawing rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 6 chips (half of the pot). If I lose, the losing payoff would be 6 chips.\n- Plan 2: If I lose, the losing payoff would be 6 chips.\n- Plan 3: If I win, the winning payoff would be 6 chips. If I lose, the losing payoff would be 6 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 18% * 6 - 49% * 6 = -1.86 chips\n- Plan 2: Expected Chips Gain = -100% * 6 = -6 chips\n- Plan 3: Expected Chips Gain = 18% * 6 - 49% * 6 = -1.86 chips\n\nPlan Selection:\n- Plan 1: -1.86 chips\n- Plan 2: -6 chips\n- Plan 3: -1.86 chips\n\nThe plan with the highest estimated expected chips gain is Plan 1 and Plan 3. However, considering the strategy improvement, I should choose Plan 1 (Raise) as it aligns with my strategy to raise more often when I have a high-ranking card."}}
{"message": "", "33_5": {"plan": "Plan 1: Call\n- If GoodGuy holds a Jack, he has a pair with the public card. He will likely call (50% probability) or fold (50% probability). If he calls, I will lose (as a pair beats a single King). If he folds, I will win. Overall, the winning rate for this plan is 50% (probability = 1/3 * 50%), the losing rate is 50% (probability = 1/3 * 50%), and the draw rate is 0%.\n- If GoodGuy holds a Queen, he has a single Queen. He will likely call (60% probability) or fold (40% probability). If he calls, I will win (as a King beats a Queen). If he folds, I will also win. Overall, the winning rate for this plan is 100% (probability = 1/3 * 100%), the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a King, he has a single King like me. He will likely call (70% probability) or fold (30% probability). If he calls, it will be a draw (as we both have a King). If he folds, I will win. Overall, the winning rate for this plan is 30% (probability = 1/3 * 30%), the losing rate is 0%, and the draw rate is 70% (probability = 1/3 * 70%).\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. The winning rate for this plan is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, chips in the pot: 24. If win, the winning payoff would be 12. If lose, the lose payoff would be 12.\n- Plan 2: After the action, chips in the pot: 14. If lose, the lose payoff would be 7.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = winning rate * Winning Payoff - lose rate * Lose Payoff = (50% + 100% + 30%) * 12 - (50% + 0% + 0%) * 12 = 9 chips\n- Plan 2: Expected Chips Gain = winning rate * Winning Payoff - lose rate * Lose Payoff = 0% * 12 - 100% * 7 = -7 chips\n\nPlan Selection:\n- Plan 1 has an expected chips gain of 9, while Plan 2 has an expected chips gain of -7. Therefore, Plan 1 (Call) is the better strategy."}}
{"message": "", "34_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (30% chance), he will likely raise (70% chance). If the public card is a King, I will win (100% chance). If the public card is a Queen or Jack, I will lose (50% chance). Overall, the winning rate is 21%, the losing rate is 15%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (60% chance), he will likely call (60% chance). If the public card is a King or Queen, I will win (66.67% chance). If the public card is a Jack, I will lose (33.33% chance). Overall, the winning rate is 24%, the losing rate is 12%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (10% chance), he will likely call (50% chance). If the public card is a King or Queen, I will win (66.67% chance). If the public card is a Jack, I will lose (33.33% chance). Overall, the winning rate is 3.33%, the losing rate is 1.67%, 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 is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King (30% chance), he will likely raise (70% chance). If the public card is a King, I will win (100% chance). If the public card is a Queen or Jack, I will lose (50% chance). Overall, the winning rate is 21%, the losing rate is 15%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (60% chance), he will likely call (60% chance). If the public card is a King or Queen, I will win (66.67% chance). If the public card is a Jack, I will lose (33.33% chance). Overall, the winning rate is 24%, the losing rate is 12%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (10% chance), he will likely call (50% chance). If the public card is a King or Queen, I will win (66.67% chance). If the public card is a Jack, I will lose (33.33% chance). Overall, the winning rate is 3.33%, the losing rate is 1.67%, 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 6 chips. If I lose, the losing payoff would be 6 chips.\n- Plan 2: If I fold, I will lose 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: (0.48 * 6) - (0.29 * 6) = 1.14 chips\n- Plan 2: -2 chips\n- Plan 3: (0.48 * 4) - (0.29 * 4) = 0.76 chips\n\nPlan Selection:\n- Plan 1: 1.14 chips\n- Plan 2: -2 chips\n- Plan 3: 0.76 chips\n\nBased on the estimated expected chips gains, I should choose Plan 1 (Raise) as it has the highest expected chips gain."}}
{"message": "", "34_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (70% probability), he will likely raise (30% probability). If he raises, it will be a draw. If he checks (50% probability) or folds (20% probability), I will win. \n- If GoodGuy holds a Queen (20% probability), he will likely check (50% probability) or raise (30% probability). If he raises, I will win. If he checks or folds, I will also win. \n- If GoodGuy holds a Jack (10% probability), he will likely check (50% probability), raise (30% probability), or fold (20% probability). If he raises or checks, I will lose. If he folds, I will win. \n\nPlan 2: Fold\n- If GoodGuy holds a King (70% probability), he will likely raise (30% probability). If he raises, it will be a draw. If he checks (50% probability) or folds (20% probability), I will lose. \n- If GoodGuy holds a Queen (20% probability), he will likely check (50% probability) or raise (30% probability). If he raises, I will lose. If he checks or folds, I will also lose. \n- If GoodGuy holds a Jack (10% probability), he will likely check (50% probability), raise (30% probability), or fold (20% probability). If he raises or checks, I will lose. If he folds, it will be a draw. \n\nPlan 3: Check\n- If GoodGuy holds a King (70% probability), he will likely raise (30% probability). If he raises, it will be a draw. If he checks (50% probability) or folds (20% probability), I will win. \n- If GoodGuy holds a Queen (20% probability), he will likely check (50% probability) or raise (30% probability). If he raises, I will win. If he checks or folds, I will also win. \n- If GoodGuy holds a Jack (10% probability), he will likely check (50% probability), raise (30% probability), or fold (20% probability). If he raises or checks, I will lose. If he folds, I will win. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips. If I lose, the lose payoff would be 4 chips.\n- Plan 2: If I win, the winning payoff would be 0 chips. If I lose, the lose payoff would be 0 chips.\n- Plan 3: If I win, the winning payoff would be 4 chips. If I lose, the lose payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.7 * 4 - 0.3 * 4 = 1.6 chips\n- Plan 2: Expected Chips Gain = 0 * 0 - 1 * 0 = 0 chips\n- Plan 3: Expected Chips Gain = 0.7 * 4 - 0.3 * 4 = 1.6 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 have the highest expected chips gain, so I should choose either of these plans. Considering the strategy improvement, I should choose Plan 1 (Raise) as it aligns with my strategy to raise when holding a King or Queen."}}
{"message": "", "35_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a Jack (20% probability), he might raise (40%) or call (60%). If he raises and the public card is a Jack, I will lose. If he calls and the public card is a Jack, I will win. If the public card is a Queen or King, I will win regardless of his action. Overall, the winning rate is 60%, the losing rate is 20%, and the draw rate is 20%.\n- If GoodGuy holds a Queen (35% probability), he might raise (70%) or call (30%). If he raises and the public card is a Queen, I will lose. If he calls and the public card is a Queen, I will lose. If the public card is a Jack or King, I will win regardless of his action. Overall, the winning rate is 30%, the losing rate is 70%, and the draw rate is 0%.\n- If GoodGuy holds a King (45% probability), he might raise (80%) or call (20%). If he raises and the public card is a King, I will lose. If he calls and the public card is a King, I will lose. If the public card is a Jack or Queen, I will win regardless of his action. Overall, the winning rate is 20%, the losing rate is 80%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a Jack (20% probability), he might raise (40%) or call (60%). If he raises and the public card is a Jack, I will lose. If he calls and the public card is a Jack, I will win. If the public card is a Queen or King, I will win regardless of his action. Overall, the winning rate is 60%, the losing rate is 20%, and the draw rate is 20%.\n- If GoodGuy holds a Queen (35% probability), he might raise (70%) or call (30%). If he raises and the public card is a Queen, I will lose. If he calls and the public card is a Queen, I will lose. If the public card is a Jack or King, I will win regardless of his action. Overall, the winning rate is 30%, the losing rate is 70%, and the draw rate is 0%.\n- If GoodGuy holds a King (45% probability), he might raise (80%) or call (20%). If he raises and the public card is a King, I will lose. If he calls and the public card is a King, I will lose. If the public card is a Jack or Queen, I will win regardless of his action. Overall, the winning rate is 20%, the losing rate is 80%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose the round regardless of GoodGuy's card 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 4 chips. If I lose, the losing payoff would be 2 chips.\n- Plan 2: If I win, the winning payoff would be 8 chips. If I lose, the losing payoff would be 4 chips.\n- Plan 3: If I lose, the losing payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 60% * 4 - 20% * 2 = 2.0 chips\n- Plan 2: Expected Chips Gain = 60% * 8 - 20% * 4 = 4.0 chips\n- Plan 3: Expected Chips Gain = -100% * 2 = -2.0 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I should choose this plan."}}
{"message": "", "35_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (probability 33.33%), he will likely raise (90%). If he raises, considering the Single Game Win/Draw/Lose Rule, I will lose (probability 100%). The overall lose rate for his King is 33.33% * 90% = 30%.\n- If GoodGuy holds a Queen (probability 33.33%), he will likely check (50%), raise (30%), or fold (20%). If he checks or raises, considering the Single Game Win/Draw/Lose Rule, I will lose (probability 100%). If he folds, I will win (probability 100%). The overall lose rate for his Queen is 33.33% * 80% = 26.67%. The overall win rate for his Queen is 33.33% * 20% = 6.67%.\n- If GoodGuy holds a Jack (probability 33.33%), he will likely check (50%), raise (30%), or fold (20%). If he checks or raises, considering the Single Game Win/Draw/Lose Rule, I will draw (probability 100%). If he folds, I will win (probability 100%). The overall draw rate for his Jack is 33.33% * 80% = 26.67%. The overall win rate for his Jack is 33.33% * 20% = 6.67%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of GoodGuy's card. The overall lose rate is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (probability 33.33%), he will likely raise (90%). If he raises, considering the Single Game Win/Draw/Lose Rule, I will lose (probability 100%). The overall lose rate for his King is 33.33% * 90% = 30%.\n- If GoodGuy holds a Queen (probability 33.33%), he will likely check (50%), raise (30%), or fold (20%). If he checks or raises, considering the Single Game Win/Draw/Lose Rule, I will lose (probability 100%). If he folds, I will win (probability 100%). The overall lose rate for his Queen is 33.33% * 80% = 26.67%. The overall win rate for his Queen is 33.33% * 20% = 6.67%.\n- If GoodGuy holds a Jack (probability 33.33%), he will likely check (50%), raise (30%), or fold (20%). If he checks or raises, considering the Single Game Win/Draw/Lose Rule, I will draw (probability 100%). If he folds, I will win (probability 100%). The overall draw rate for his Jack is 33.33% * 80% = 26.67%. The overall win rate for his Jack is 33.33% * 20% = 6.67%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, chips in the pot: 14. If win, the winning payoff would be 7. If lose, the lose payoff would be 7.\n- Plan 2: After the action, chips in the pot: 6. If lose, the lose payoff would be 3.\n- Plan 3: After the action, chips in the pot: 6. If win, the winning payoff would be 3. If lose, the lose payoff would be 3.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 13.33% * 7 - 56.67% * 7 = -3.03\n- Plan 2: Expected Chips Gain = 0 * 0 - 100% * 3 = -3\n- Plan 3: Expected Chips Gain = 13.33% * 3 - 56.67% * 3 = -1.3\n\nPlan Selection:\n- Plan 1: 3rd\n- Plan 2: 2nd\n- Plan 3: 1st\n\nTherefore, I should choose Plan 3 (Check) as it has the highest estimated expected chips gain."}}
{"message": "", "35_5": {"plan": "Plan 1: Call\n- If GoodGuy holds a Jack (60% probability), he will likely check (50% probability). If he checks, I will win as Jack is higher than Queen. Therefore, the winning rate for this plan is 60% * 50% = 30%.\n- If GoodGuy holds a Queen (30% probability), he will likely fold (20% probability). If he folds, I will win. Therefore, the winning rate for this plan is 30% * 20% = 6%.\n- If GoodGuy holds a King (10% probability), he will likely raise (90% probability). If he raises, I will lose as King is higher than Jack. Therefore, the losing rate for this plan is 10% * 90% = 9%.\n\nPlan 2: Raise\n- If GoodGuy holds a Jack (60% probability), he will likely fold (20% probability). If he folds, I will win. Therefore, the winning rate for this plan is 60% * 20% = 12%.\n- If GoodGuy holds a Queen (30% probability), he will likely call (30% probability). If he calls, I will win as Jack is higher than Queen. Therefore, the winning rate for this plan is 30% * 30% = 9%.\n- If GoodGuy holds a King (10% probability), he will likely call (20% probability). If he calls, I will lose as King is higher than Jack. Therefore, the losing rate for this plan is 10% * 20% = 2%.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot. 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 win, the winning payoff would be half of the pot (16 chips). If I lose, the losing payoff would be the chips I have put in the pot (10 chips).\n- Plan 2: If I win, the winning payoff would be half of the pot (18 chips). If I lose, the losing payoff would be the chips I have put in the pot (14 chips).\n- Plan 3: If I lose, the losing payoff would be the chips I have put in the pot (10 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 30% * 16 - 9% * 10 = 4.8 - 0.9 = 3.9 chips\n- Plan 2: Expected Chips Gain = 21% * 18 - 2% * 14 = 3.78 - 0.28 = 3.5 chips\n- Plan 3: Expected Chips Gain = -100% * 10 = -10 chips\n\nPlan Selection:\n- Plan 1: 3.9 chips\n- Plan 2: 3.5 chips\n- Plan 3: -10 chips\n\nTherefore, I should select Plan 1 (Call) as it has the highest estimated expected chips gain."}}
{"message": "", "36_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (50% chance), he is likely to raise (70%) or call (30%). If he raises, I will win (70%) or draw (30%). If he calls, I will win (100%). The overall winning rate for this plan is 0.5*(0.7*0.7 + 0.3*1) = 0.35 + 0.15 = 0.5 (50%).\n- If GoodGuy holds a Queen (50% chance), he is likely to raise (40%) or call (60%). If he raises, I will win (100%). If he calls, I will win (100%). The overall winning rate for this plan is 0.5*(0.4*1 + 0.6*1) = 0.2 + 0.3 = 0.5 (50%).\n- The overall winning rate for Plan 1 is 0.5 + 0.5 = 1 (100%). The overall losing rate is 0 (0%). The overall drawing rate is 0 (0%).\n\nPlan 2: Raise\n- If GoodGuy holds a King (50% chance), he is likely to raise (70%) or call (30%). If he raises, I will win (70%) or draw (30%). If he calls, I will win (100%). The overall winning rate for this plan is 0.5*(0.7*0.7 + 0.3*1) = 0.35 + 0.15 = 0.5 (50%).\n- If GoodGuy holds a Queen (50% chance), he is likely to fold (60%) or call (40%). If he folds, I will win (100%). If he calls, I will win (100%). The overall winning rate for this plan is 0.5*(0.6*1 + 0.4*1) = 0.3 + 0.2 = 0.5 (50%).\n- The overall winning rate for Plan 2 is 0.5 + 0.5 = 1 (100%). The overall losing rate is 0 (0%). The overall drawing rate is 0 (0%).\n\nPlan 3: Fold\n- If I fold, I will lose the round and the chips I have already put into the pot. The overall winning rate for this plan is 0 (0%). The overall losing rate is 1 (100%). The overall drawing rate is 0 (0%).\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the pot (currently 6 chips), so 3 chips. If I lose, the losing payoff would be half of the pot, so 3 chips.\n- Plan 2: If I win, the winning payoff would be half of the pot (currently 6 chips plus my raise of 4 chips), so 5 chips. If I lose, the losing payoff would be half of the pot, so 5 chips.\n- Plan 3: If I fold, I will lose the chips I have already put into the pot, so the losing payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: The expected chips gain is winning rate * winning payoff - losing rate * losing payoff = 1 * 3 - 0 * 3 = 3 chips.\n- Plan 2: The expected chips gain is winning rate * winning payoff - losing rate * losing payoff = 1 * 5 - 0 * 5 = 5 chips.\n- Plan 3: The expected chips gain is winning rate * winning payoff - losing rate * losing payoff = 0 * 0 - 1 * 4 = -4 chips.\n\nPlan Selection:\n- Plan 1: Expected chips gain = 3 chips\n- Plan 2: Expected chips gain = 5 chips\n- Plan 3: Expected chips gain = -4 chips\n\nThe rank of estimated expected chips gains for every plan is: Plan 2 > Plan 1 > Plan 3. Therefore, I should choose Plan 2 (Raise) as it has the highest estimated expected chips gain."}}
{"message": "", "36_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (50% probability), he is likely to raise (70%) or call (30%). If he raises, we will have a draw (50%). If he calls, I will win (50%). Overall, the winning rate is 15%, the losing rate is 0%, and the draw rate is 35%.\n- If GoodGuy holds a Queen (50% probability), he is likely to check (60%) or fold (40%). If he checks, I will win (60%). If he folds, I will also win (40%). Overall, 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 King (50% probability), he is likely to raise (70%) or call (30%). If I fold, I will lose regardless of his action. Overall, the winning rate is 0%, the losing rate is 50%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (50% probability), he is likely to check (60%) or fold (40%). If I fold, I will lose regardless of his action. Overall, 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 King (50% probability), he is likely to raise (70%) or call (30%). If he raises, I will lose (70%). If he calls, I will win (30%). Overall, the winning rate is 15%, the losing rate is 35%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (50% probability), he is likely to check (60%) or fold (40%). If he checks, I will win (60%). If he folds, I will also win (40%). Overall, the winning rate is 50%, the losing rate is 0%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If 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 (since I fold). If lose, the lose payoff would be 6 chips.\n- Plan 3: If win, the winning payoff would be 6 chips. If lose, the lose payoff would be 6 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.65 * 6 - 0 * 6 = 3.9 chips\n- Plan 2: Expected Chips Gain = 0 * 0 - 1 * 6 = -6 chips\n- Plan 3: Expected Chips Gain = 0.65 * 6 - 0.35 * 6 = 1.8 chips\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is as follows:\n1. Plan 1: Raise (3.9 chips)\n2. Plan 3: Check (1.8 chips)\n3. Plan 2: Fold (-6 chips)\n\nTherefore, the best plan to select is Plan 1: Raise."}}
{"message": "", "36_5": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he will likely check (60%) or raise (40%). If he checks, I will win as my King is higher than his Jack. If he raises, I will lose as he has a pair of Kings. Therefore, the winning rate is 70%*60% = 42%, and the losing rate is 70%*40% = 28%.\n- If GoodGuy holds a Jack (30% probability), he will likely raise (70%) or call (30%). If he raises, I will lose as he has a pair of Jacks. If he calls, I will win as my King is higher than his Jack. Therefore, the winning rate is 30%*30% = 9%, and the losing rate is 30%*70% = 21%.\n\nPlan 2: Fold\n- If GoodGuy holds a King (70% probability), I will lose as I have folded. Therefore, the losing rate is 70%.\n- If GoodGuy holds a Jack (30% probability), I will lose as I have folded. Therefore, the losing rate is 30%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the call action, chips in the pot: 28. If win, the winning payoff would be 14. If lose, the lose payoff would be 14.\n- Plan 2: After the fold action, chips in the pot: 24. If lose, the lose payoff would be 12.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected chips gain = winning rate * winning payoff - losing rate * losing payoff = 42%*14 - 28%*14 = 1.96 chips\n- Plan 2: Expected chips gain = - losing rate * losing payoff = -100%*12 = -12 chips\n\nPlan Selection:\n- Plan 1 has a higher expected chips gain than Plan 2. Therefore, I should choose to call."}}
{"message": "", "37_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (30% probability), he might raise (70%) or call (30%). If he raises, I will lose (70% * 30% = 21%). If he calls, I have a 50% chance of winning if the public card is a Queen (15% * 30% = 4.5%) and a 50% chance of losing if the public card is a King or Jack (15% * 30% = 4.5%).\n- If GoodGuy holds a Queen (35% probability), he might raise (50%) or call (50%). If he raises, I will lose (50% * 35% = 17.5%). If he calls, I have a 33% chance of winning if the public card is a Queen (11.55% * 35% = 4.04%) and a 67% chance of losing if the public card is a King or Jack (23.45% * 35% = 8.21%).\n- If GoodGuy holds a Jack (35% probability), he might raise (40%) or call (60%). If he raises, I will lose (40% * 35% = 14%). If he calls, I have a 67% chance of winning if the public card is a Queen or King (22.45% * 35% = 7.86%) and a 33% chance of losing if the public card is a Jack (11.55% * 35% = 4.04%).\n\nPlan 2: Raise\n- If GoodGuy holds a King (30% probability), he might raise (70%) or call (30%). If he raises, I will lose (70% * 30% = 21%). If he calls, I have a 50% chance of winning if the public card is a Queen (15% * 30% = 4.5%) and a 50% chance of losing if the public card is a King or Jack (15% * 30% = 4.5%).\n- If GoodGuy holds a Queen (35% probability), he might raise (50%) or call (50%). If he raises, I will lose (50% * 35% = 17.5%). If he calls, I have a 33% chance of winning if the public card is a Queen (11.55% * 35% = 4.04%) and a 67% chance of losing if the public card is a King or Jack (23.45% * 35% = 8.21%).\n- If GoodGuy holds a Jack (35% probability), he might raise (40%) or call (60%). If he raises, I will lose (40% * 35% = 14%). If he calls, I have a 67% chance of winning if the public card is a Queen or King (22.45% * 35% = 7.86%) and a 33% chance of losing if the public card is a Jack (11.55% * 35% = 4.04%).\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 3 chips. If I lose, the losing payoff would be 2 chips.\n- Plan 2: If I win, the winning payoff would be 6 chips. If I lose, the losing payoff would be 4 chips.\n- Plan 3: If I fold, the losing payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: (4.5% + 4.04% + 7.86%) * 3 - (21% + 17.5% + 14%) * 2 = -0.18 chips\n- Plan 2: (4.5% + 4.04% + 7.86%) * 6 - (21% + 17.5% + 14%) * 4 = -0.36 chips\n- Plan 3: 0 * 0 - 100% * 2 = -2 chips\n\nPlan Selection:\n- Plan 1: -0.18 chips\n- Plan 2: -0.36 chips\n- Plan 3: -2 chips\n\nBased on the estimated expected chips gain, Plan 1 (Call) is the best strategy."}}
{"message": "", "37_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King, he will likely raise (30%) or check (70%). If he raises, I will win (0%) or lose (100%). If he checks, I will win (100%) or lose (0%). Overall, the winning rate is 70%, the losing rate is 30%, and the draw rate is 0%.\n- If GoodGuy holds a Queen, he will likely raise (80%) or check (20%). If he raises, I will win (100%) or lose (0%). If he checks, I will win (100%) or lose (0%). Overall, the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Jack, he will likely check (60%), raise (30%), or fold (10%). If he checks, I will win (100%) or lose (0%). If he raises, I will win (100%) or lose (0%). If he folds, I will win (100%). Overall, the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose 100% of the time regardless of GoodGuy's card.\n\nPlan 3: Check\n- If GoodGuy holds a King, he will likely raise (30%) or check (70%). If he raises, I will win (0%) or lose (100%). If he checks, I will win (100%) or lose (0%). Overall, the winning rate is 70%, the losing rate is 30%, and the draw rate is 0%.\n- If GoodGuy holds a Queen, he will likely raise (80%) or check (20%). If he raises, I will win (100%) or lose (0%). If he checks, I will win (100%) or lose (0%). Overall, the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n- If GoodGuy holds a Jack, he will likely check (60%), raise (30%), or fold (10%). If he checks, I will win (100%) or lose (0%). If he raises, I will win (100%) or lose (0%). If he folds, I will win (100%). Overall, the winning rate is 100%, the losing rate is 0%, and the draw rate is 0%.\n\nWinning/Lose Payoffs for Each Plan:\n- Plan 1: If I win, the winning payoff would be 6 chips (half of the pot). If I lose, the losing payoff would be 2 chips (half of the pot).\n- Plan 2: If I fold, I will lose 2 chips (my initial bet).\n- Plan 3: If I win, the winning payoff would be 4 chips (half of the pot). If I lose, the losing payoff would be 2 chips (half of the pot).\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected gain = 0.7 * 6 - 0.3 * 2 = 3.6 chips\n- Plan 2: Expected gain = -2 chips\n- Plan 3: Expected gain = 0.7 * 4 - 0.3 * 2 = 2.2 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I will choose to raise."}}
{"message": "", "38_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (70% probability), he might raise (80% probability) or check (20% probability). If he raises, I will win (as I also hold a King). If he checks, I will also win (as my card is higher). \n- If GoodGuy holds a Queen (20% probability), he might raise (70% probability) or check (30% probability). If he raises, I will win (as my card is higher). If he checks, I will also win (as my card is higher). \n- If GoodGuy holds a Jack (10% probability), he might raise (40% probability) or check (60% probability). If he raises, I will win (as my card is higher). If he checks, I will also win (as my card is higher). \n\nPlan 2: Raise\n- If GoodGuy holds a King (70% probability), he might call (30% probability) or fold (70% probability). If he calls, I will win (as I also hold a King). If he folds, I will also win (as my card is higher). \n- If GoodGuy holds a Queen (20% probability), he might call (30% probability) or fold (70% probability). If he calls, I will win (as my card is higher). If he folds, I will also win (as my card is higher). \n- If GoodGuy holds a Jack (10% probability), he might call (30% probability) or fold (70% probability). If he calls, I will win (as my card is higher). If he folds, I will also win (as my card is higher). \n\nPlan 3: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 6 chips (half of the pot). If I lose, the lose payoff would be 2 chips (half of the pot). \n- Plan 2: If I win, the winning payoff would be 8 chips (half of the pot). If I lose, the lose payoff would be 4 chips (half of the pot). \n- Plan 3: If I fold, I will lose 2 chips (half of the pot). \n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.7 * 6 - 0.3 * 2 = 3.6 chips\n- Plan 2: Expected Chips Gain = 0.7 * 8 - 0.3 * 4 = 4.8 chips\n- Plan 3: Expected Chips Gain = -2 chips\n\nPlan Selection:\n- Plan 2 (Raise) has the highest expected chips gain, so I will choose this plan."}}
{"message": "", "38_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (80% probability), he is likely to raise (80% probability) or check (20% probability). If he raises, I will lose (probability = 0.8 * 0.8 = 0.64). If he checks, I will win (probability = 0.8 * 0.2 = 0.16).\n- If GoodGuy holds a King (60% probability), he is likely to fold (60% probability) or check (40% probability). If he folds, I will win (probability = 0.6 * 0.6 = 0.36). If he checks, I will draw (probability = 0.6 * 0.4 = 0.24).\n- If GoodGuy holds a Jack (80% probability), he is likely to fold (80% probability) or check (20% probability). If he folds, I will win (probability = 0.8 * 0.8 = 0.64). If he checks, I will win (probability = 0.8 * 0.2 = 0.16).\nPlan 1 overall Winning/Lose/Draw rates: Winning rate = 0.16 + 0.36 + 0.64 = 1.16; Lose rate = 0.64; Draw rate = 0.24.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of GoodGuy's cards. Therefore, the lose rate is 1.\nPlan 2 overall Winning/Lose/Draw rates: Winning rate = 0; Lose rate = 1; Draw rate = 0.\n\nPlan 3: Check\n- If GoodGuy holds a Queen (80% probability), he is likely to raise (80% probability) or check (20% probability). If he raises, I will lose (probability = 0.8 * 0.8 = 0.64). If he checks, I will win (probability = 0.8 * 0.2 = 0.16).\n- If GoodGuy holds a King (60% probability), he is likely to fold (60% probability) or check (40% probability). If he folds, I will win (probability = 0.6 * 0.6 = 0.36). If he checks, I will draw (probability = 0.6 * 0.4 = 0.24).\n- If GoodGuy holds a Jack (80% probability), he is likely to fold (80% probability) or check (20% probability). If he folds, I will win (probability = 0.8 * 0.8 = 0.64). If he checks, I will win (probability = 0.8 * 0.2 = 0.16).\nPlan 3 overall Winning/Lose/Draw rates: Winning rate = 0.16 + 0.36 + 0.64 = 1.16; Lose rate = 0.64; Draw rate = 0.24.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If win, the winning payoff would be half of the pot (6 chips) = 3 chips. If lose, the lose payoff would be half of the pot (6 chips) = 3 chips.\n- Plan 2: If lose, the lose payoff would be half of the pot (6 chips) = 3 chips.\n- Plan 3: If win, the winning payoff would be half of the pot (6 chips) = 3 chips. If lose, the lose payoff would be half of the pot (6 chips) = 3 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Lose rate * Lose Payoff = 1.16 * 3 - 0.64 * 3 = 1.56 chips\n- Plan 2: Expected Chips Gain = - Lose rate * Lose Payoff = -1 * 3 = -3 chips\n- Plan 3: Expected Chips Gain = Winning rate * Winning Payoff - Lose rate * Lose Payoff = 1.16 * 3 - 0.64 * 3 = 1.56 chips\n\nPlan Selection:\n- Plan 1: 1.56 chips\n- Plan 2: -3 chips\n- Plan 3: 1.56 chips\n\nTherefore, I should choose either Plan 1 or Plan 3 as they both have the highest estimated expected chips gain."}}
{"message": "", "39_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (0% probability), he will likely raise (70%) or call (30%). The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (0% probability), he will likely call (60%) or raise (40%). The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (100% probability), he will likely call (70%) or fold (30%). The winning rate is 0%, the losing rate is 0%, and the draw rate is 100%.\n\nPlan 1 overall GoodGuy's Winning/Lose/Draw rates: The Winning rate for plan 1 is 0%, Lose rate for plan 1 is 66.67%, Draw Rate for plan 1 is 33.33%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (0% probability), he will likely raise (70%) or call (30%). The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (0% probability), he will likely call (60%) or raise (40%). The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (100% probability), he will likely call (70%) or fold (30%). The winning rate is 0%, the losing rate is 0%, and the draw rate is 100%.\n\nPlan 2 overall GoodGuy's Winning/Lose/Draw rates: The Winning rate for plan 2 is 0%, Lose rate for plan 2 is 66.67%, Draw Rate for plan 2 is 33.33%.\n\nPlan 3: Fold\n- If GoodGuy holds a King (0% probability), he will likely raise (70%) or call (30%). The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (0% probability), he will likely call (60%) or raise (40%). The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (100% probability), he will likely call (70%) or fold (30%). The winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3 overall GoodGuy's Winning/Lose/Draw rates: The Winning rate for plan 3 is 0%, Lose rate for plan 3 is 100%, Draw Rate for plan 3 is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, Chips in the pot: 4. If win, the winning payoff would be 2. If lose, the lose payoff would be 2.\n- Plan 2: After the action, Chips in the pot: 6. If win, the winning payoff would be 3. If lose, the lose payoff would be 3.\n- Plan 3: After the action, Chips in the pot: 3. If win, the winning payoff would be 1.5. If lose, the lose payoff would be 1.5.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0% * 2 - 66.67% * 2 = -1.33 chips\n- Plan 2: 0% * 3 - 66.67% * 3 = -2 chips\n- Plan 3: 0% * 1.5 - 100% * 1.5 = -1.5 chips\n\nPlan Selection: \nThe rank of estimated expected chips gains for every plan is: Plan 1 > Plan 3 > Plan 2. Therefore, the best plan to execute is Plan 1: Call."}}
{"message": "", "39_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (20% chance), he will likely call (20% chance). I will lose as his King pairs with the public card. \n- If GoodGuy holds a Queen (50% chance), he will likely call (50% chance), raise (30% chance), or fold (20% chance). I will win if he folds, lose if he raises, and draw if he calls.\n- If GoodGuy holds a Jack (60% chance), he will likely fold (60% chance) or call (40% chance). I will win if he folds, and draw if he calls.\n\nPlan 1 overall Winning/Lose/Draw rates: \n- Winning rate: 0.2 (probability of GoodGuy holding a Queen) * 0.2 (probability of him folding) + 0.6 (probability of GoodGuy holding a Jack) * 0.6 (probability of him folding) = 0.4\n- Lose rate: 0.2 (probability of GoodGuy holding a King) * 0.2 (probability of him calling) + 0.5 (probability of GoodGuy holding a Queen) * 0.3 (probability of him raising) = 0.17\n- Draw rate: 0.5 (probability of GoodGuy holding a Queen) * 0.5 (probability of him calling) + 0.6 (probability of GoodGuy holding a Jack) * 0.4 (probability of him calling) = 0.43\n\nPlan 2: Fold\n- If I fold, I will lose the game regardless of GoodGuy's cards.\n\nPlan 2 overall Winning/Lose/Draw rates: \n- Winning rate: 0\n- Lose rate: 1\n- Draw rate: 0\n\nPlan 3: Check\n- If GoodGuy holds a King (20% chance), he will likely raise (80% chance) or call (20% chance). I will lose as his King pairs with the public card. \n- If GoodGuy holds a Queen (50% chance), he will likely call (50% chance), raise (30% chance), or fold (20% chance). I will win if he folds, lose if he raises, and draw if he calls.\n- If GoodGuy holds a Jack (60% chance), he will likely fold (60% chance) or call (40% chance). I will win if he folds, and draw if he calls.\n\nPlan 3 overall Winning/Lose/Draw rates: \n- Winning rate: 0.2 (probability of GoodGuy holding a Queen) * 0.2 (probability of him folding) + 0.6 (probability of GoodGuy holding a Jack) * 0.6 (probability of him folding) = 0.4\n- Lose rate: 0.2 (probability of GoodGuy holding a King) * 0.8 (probability of him raising) + 0.5 (probability of GoodGuy holding a Queen) * 0.3 (probability of him raising) = 0.31\n- Draw rate: 0.5 (probability of GoodGuy holding a Queen) * 0.5 (probability of him calling) + 0.6 (probability of GoodGuy holding a Jack) * 0.4 (probability of him calling) = 0.43\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: 0.4 * 4 - 0.17 * 4 = 0.92 chips\n- Plan 2: 0 - 1 * 2 = -2 chips\n- Plan 3: 0.4 * 2 - 0.31 * 2 = 0.18 chips\n\nPlan Selection:\n- Plan 1: 0.92 chips\n- Plan 2: -2 chips\n- Plan 3: 0.18 chips\n\nBased on the estimated expected chips gains, I should select Plan 1 (Raise) as it has the highest expected chips gain."}}
{"message": "", "40_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (20% chance), he will likely raise (80% chance). If he raises, I will win (as we both have Kings and it's a draw). The overall winning rate for this scenario is 0.2*0.8 = 0.16 (16%).\n- If GoodGuy holds a Queen (40% chance), he will likely raise (60% chance). If he raises, I will win (as my King is higher than his Queen). The overall winning rate for this scenario is 0.4*0.6 = 0.24 (24%).\n- If GoodGuy holds a Jack (40% chance), he will likely call (70% chance). If he calls, I will win (as my King is higher than his Jack). The overall winning rate for this scenario is 0.4*0.7 = 0.28 (28%).\n\nPlan 2: Raise\n- If GoodGuy holds a King (20% chance), he will likely raise (80% chance). If he raises, I will win (as we both have Kings and it's a draw). The overall winning rate for this scenario is 0.2*0.8 = 0.16 (16%).\n- If GoodGuy holds a Queen (40% chance), he will likely raise (60% chance). If he raises, I will win (as my King is higher than his Queen). The overall winning rate for this scenario is 0.4*0.6 = 0.24 (24%).\n- If GoodGuy holds a Jack (40% chance), he will likely call (70% chance). If he calls, I will win (as my King is higher than his Jack). The overall winning rate for this scenario is 0.4*0.7 = 0.28 (28%).\n\nPlan 3: Fold\n- If I fold, I will 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 half of the pot (3 chips). If I lose, the losing payoff would be half of the pot (3 chips).\n- Plan 2: If I win, the winning payoff would be half of the pot (6 chips). If I lose, the losing payoff would be half of the pot (6 chips).\n- Plan 3: If I fold, I will lose 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected gain = winning rate * winning payoff - losing rate * losing payoff = (0.16+0.24+0.28)*3 - (1-(0.16+0.24+0.28))*3 = 0.68*3 - 0.32*3 = 1.08 chips.\n- Plan 2: Expected gain = (0.16+0.24+0.28)*6 - (1-(0.16+0.24+0.28))*6 = 0.68*6 - 0.32*6 = 2.16 chips.\n- Plan 3: Expected gain = -2 chips (as I will lose 2 chips if I fold).\n\nPlan Selection:\n- Plan 1: Expected gain = 1.08 chips.\n- Plan 2: Expected gain = 2.16 chips.\n- Plan 3: Expected gain = -2 chips.\n\nTherefore, the best plan is Plan 2 (Raise), followed by Plan 1 (Call), and the worst plan is Plan 3 (Fold)."}}
{"message": "", "40_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (30% chance), he will likely raise (80% chance). If he raises, I will lose as my King does not match the public card (Queen). So, the losing rate for this plan is 0.3*0.8=0.24.\n- If GoodGuy holds a Queen (40% chance), he will likely raise (90% chance). If he raises, I will lose as his Queen matches the public card. So, the losing rate for this plan is 0.4*0.9=0.36.\n- If GoodGuy holds a Jack (30% chance), he will likely check (60% chance). If he checks, I will win as my King is higher than his Jack. So, the winning rate for this plan is 0.3*0.6=0.18.\n\nPlan 2: Fold\n- If I fold, I will lose the chips I have already put in the pot. So, the losing rate for this plan is 1.\n\nPlan 3: Check\n- If GoodGuy holds a King (30% chance), he will likely raise (80% chance). If he raises, I will lose as my King does not match the public card (Queen). So, the losing rate for this plan is 0.3*0.8=0.24.\n- If GoodGuy holds a Queen (40% chance), he will likely raise (90% chance). If he raises, I will lose as his Queen matches the public card. So, the losing rate for this plan is 0.4*0.9=0.36.\n- If GoodGuy holds a Jack (30% chance), he will likely check (60% chance). If he checks, I will win as my King is higher than his Jack. So, the winning rate for this plan is 0.3*0.6=0.18.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the pot (4 chips). If I lose, the lose payoff would be the chips I have put in the pot (4 chips).\n- Plan 2: If I fold, I will lose 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 pot (4 chips). If I lose, the lose payoff would be the chips I have put in the pot (4 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = winning rate * Winning Payoff - losing rate * Lose Payoff = 0.18*4 - 0.6*4 = -1.68 chips\n- Plan 2: Expected Chips Gain = -4 chips\n- Plan 3: Expected Chips Gain = 0.18*4 - 0.6*4 = -1.68 chips\n\nPlan Selection:\n- Plan 1: -1.68 chips\n- Plan 2: -4 chips\n- Plan 3: -1.68 chips\n\nBased on the estimated expected chips gains, Plan 1 and Plan 3 are the best strategies to follow as they have the highest expected chips gain (-1.68 chips). However, considering the strategy improvement, I should consider folding if GoodGuy raises and the public card is a higher rank. Therefore, I will choose Plan 2: Fold."}}
{"message": "", "41_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (80% probability), he will likely raise (80% probability). If the public card is a King, I will win (probability = 0.8*0.8 = 0.64). If the public card is not a King, I will lose (probability = 0.8*0.2 = 0.16).\n- If GoodGuy holds a Queen (10% probability), he will likely call (70% probability). If the public card is a Queen, I will lose (probability = 0.1*0.7 = 0.07). If the public card is not a Queen, I will win (probability = 0.1*0.3 = 0.03).\n- If GoodGuy holds a Jack (10% probability), he will likely call (80% probability). If the public card is a Jack, I will lose (probability = 0.1*0.8 = 0.08). If the public card is not a Jack, I will win (probability = 0.1*0.2 = 0.02).\n- Overall, the winning rate for plan 1 is 0.64 + 0.03 + 0.02 = 0.69. The losing rate for plan 1 is 0.16 + 0.07 + 0.08 = 0.31. The draw rate for plan 1 is 0.\n\nPlan 2: Raise\n- If GoodGuy holds a King (80% probability), he will likely raise (80% probability). If the public card is a King, I will win (probability = 0.8*0.8 = 0.64). If the public card is not a King, I will lose (probability = 0.8*0.2 = 0.16).\n- If GoodGuy holds a Queen (10% probability), he will likely call (70% probability). If the public card is a Queen, I will lose (probability = 0.1*0.7 = 0.07). If the public card is not a Queen, I will win (probability = 0.1*0.3 = 0.03).\n- If GoodGuy holds a Jack (10% probability), he will likely call (80% probability). If the public card is a Jack, I will lose (probability = 0.1*0.8 = 0.08). If the public card is not a Jack, I will win (probability = 0.1*0.2 = 0.02).\n- Overall, the winning rate for plan 2 is 0.64 + 0.03 + 0.02 = 0.69. The losing rate for plan 2 is 0.16 + 0.07 + 0.08 = 0.31. The draw rate for plan 2 is 0.\n\nPlan 3: Fold\n- If I fold, I will lose all the chips I have put into the pot. The winning rate for plan 3 is 0. The losing rate for plan 3 is 1. The draw rate for plan 3 is 0.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the pot (3 chips). If I lose, the lose payoff would be half of the pot (3 chips).\n- Plan 2: If I win, the winning payoff would be half of the pot (6 chips). If I lose, the lose payoff would be half of the pot (6 chips).\n- Plan 3: If I fold, I will lose all the chips I have put into the pot (1 chip).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.69 * 3 - 0.31 * 3 = 1.14 chips\n- Plan 2: Expected Chips Gain = 0.69 * 6 - 0.31 * 6 = 2.28 chips\n- Plan 3: Expected Chips Gain = 0 - 1 = -1 chip\n\nPlan Selection:\n- Plan 2 has the highest expected chips gain (2.28 chips), followed by Plan 1 (1.14 chips), and Plan 3 (-1 chip). Therefore, I should choose Plan 2: Raise."}}
{"message": "", "41_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (70% probability), he will likely raise (90% probability). If he raises, I will lose as his Queen matches the public card. If he calls (10% probability), I will still lose. So, the overall losing rate for this plan if GoodGuy holds a Queen is 70%.\n- If GoodGuy holds a Jack (30% probability), he will likely call (80% probability). If he calls, I will win as my King is higher than his Jack. If he raises (20% probability), I will still win. So, the overall winning rate for this plan if GoodGuy holds a Jack is 30%.\n\nPlan 2: Fold\n- If I fold, I will lose the chips I have already put in the pot. The losing rate for this plan is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a Queen (70% probability), he will likely raise (90% probability). If he raises, I will lose as his Queen matches the public card. If he calls (10% probability), I will still lose. So, the overall losing rate for this plan if GoodGuy holds a Queen is 70%.\n- If GoodGuy holds a Jack (30% probability), he will likely call (80% probability). If he calls, I will win as my King is higher than his Jack. If he raises (20% probability), I will still win. So, the overall winning rate for this plan if GoodGuy holds a Jack is 30%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the pot (8 chips). If I lose, the losing payoff would be the chips I have put in the pot (4 chips).\n- Plan 2: If I fold, I will lose 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 pot (8 chips). If I lose, the losing payoff would be the chips I have put in the pot (4 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 30% * 8 chips - 70% * 4 chips = -0.8 chips\n- Plan 2: Expected Chips Gain = -4 chips\n- Plan 3: Expected Chips Gain = 30% * 8 chips - 70% * 4 chips = -0.8 chips\n\nPlan Selection:\n- Plan 1: -0.8 chips\n- Plan 2: -4 chips\n- Plan 3: -0.8 chips\n\nBased on the expected chips gain, Plan 1 and Plan 3 are the best strategies to follow as they have the highest expected chips gain (-0.8 chips). However, considering the strategy improvement, I should choose Plan 1 (Raise) as it is more aggressive and may confuse GoodGuy."}}
{"message": "", "42_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (40% probability), he will likely raise (80% probability). If the public card is a Queen or Jack, I will lose. If the public card is a King, it's a draw. The overall winning rate is 0%, losing rate is 80%, and drawing rate is 20%.\n- If GoodGuy holds a Queen (35% probability), he will likely raise (70% probability). If the public card is a King or Jack, I will win. If the public card is a Queen, it's a draw. The overall winning rate is 70%, losing rate is 0%, and drawing rate is 30%.\n- If GoodGuy holds a Jack (25% probability), he will likely call (60% probability). If the public card is a King or Queen, I will win. If the public card is a Jack, it's a draw. The overall winning rate is 60%, losing rate is 0%, and drawing rate is 40%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (40% probability), he will likely call (15% probability). If the public card is a Queen or Jack, I will lose. If the public card is a King, it's a draw. The overall winning rate is 0%, losing rate is 85%, and drawing rate is 15%.\n- If GoodGuy holds a Queen (35% probability), he will likely call (20% probability). If the public card is a King or Jack, I will win. If the public card is a Queen, it's a draw. The overall winning rate is 80%, losing rate is 0%, and drawing rate is 20%.\n- If GoodGuy holds a Jack (25% probability), he will likely fold (10% probability). If the public card is a King or Queen, I will win. If the public card is a Jack, it's a draw. The overall winning rate is 90%, losing rate is 0%, and drawing rate is 10%.\n\nPlan 3: Fold\n- If I fold, I will lose the chips I have already put in the pot. The overall winning rate is 0%, losing rate is 100%, and drawing rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, Chips in the pot: 6. If win, the winning payoff would be 3. If lose, the lose payoff would be 3.\n- Plan 2: After the action, Chips in the pot: 10. If win, the winning payoff would be 5. If lose, the lose payoff would be 5.\n- Plan 3: After the action, Chips in the pot: 4. If lose, the lose payoff would be 2.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0.7 * 3 - 0.8 * 3 = -0.3\n- Plan 2: 0.8 * 5 - 0.85 * 5 = -0.25\n- Plan 3: 0 - 1 * 2 = -2\n\nPlan Selection:\n- Plan 1: -0.3\n- Plan 2: -0.25\n- Plan 3: -2\n\nBased on the estimated expected chips gains, Plan 2 (Raise) is the best strategy to follow."}}
{"message": "", "42_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King, he will likely raise (70%). If he raises, I will lose as his King beats my Queen. The losing rate for this scenario is 0.7 (probability of him having a King) * 0.7 (probability of him raising) = 0.49. \n- If GoodGuy holds a Queen, he will likely raise (60%) or call (30%). If he raises or calls, it will be a draw as we both have Queens. The drawing rate for this scenario is 0.5 (probability of him having a Queen) * (0.6 + 0.3) = 0.45. \n- If GoodGuy holds a Jack, he will likely call (50%) or fold (20%). If he calls, I will win as my Queen beats his Jack. If he folds, I will also win. The winning rate for this scenario is 0.5 (probability of him having a Jack) * (0.5 + 0.2) = 0.35. \n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. The losing rate for this scenario is 1. \n\nPlan 3: Check\n- If GoodGuy holds a King, he will likely raise (70%). If he raises, I will lose as his King beats my Queen. The losing rate for this scenario is 0.7 (probability of him having a King) * 0.7 (probability of him raising) = 0.49. \n- If GoodGuy holds a Queen, he will likely raise (60%) or call (30%). If he raises or calls, it will be a draw as we both have Queens. The drawing rate for this scenario is 0.5 (probability of him having a Queen) * (0.6 + 0.3) = 0.45. \n- If GoodGuy holds a Jack, he will likely call (50%) or fold (20%). If he calls, I will win as my Queen beats his Jack. If he folds, I will also win. The winning rate for this scenario is 0.5 (probability of him having a Jack) * (0.5 + 0.2) = 0.35. \n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 6 chips (half of the pot). If I lose, the losing payoff would be 6 chips. \n- Plan 2: If I fold, I will lose 6 chips. \n- Plan 3: If I win, the winning payoff would be 6 chips. If I lose, the losing payoff would be 6 chips. \n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.35 * 6 - 0.49 * 6 = -0.84 chips\n- Plan 2: Expected Chips Gain = -6 chips\n- Plan 3: Expected Chips Gain = 0.35 * 6 - 0.49 * 6 = -0.84 chips\n\nPlan Selection:\n- Plan 1: Rank 2\n- Plan 2: Rank 3\n- Plan 3: Rank 2\n\nBased on the estimated expected chips gain, Plan 1 and Plan 3 are the best strategies to follow. However, considering the strategy improvement, I should choose Plan 1 (Raise) as it is more aggressive and can potentially throw GoodGuy off."}}
{"message": "", "43_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (25% probability), he might raise (70% probability) or call (30% probability). If he raises, I will lose (70% probability). If he calls, I will win (30% probability). Overall, the winning rate for his King is 7.5%, the losing rate is 17.5%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (25% probability), he might raise (60% probability) or call (40% probability). If he raises, I will lose (60% probability). If he calls, I will win (40% probability). Overall, the winning rate for his Queen is 10%, the losing rate is 15%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (50% probability), he might raise (50% probability) or call (50% probability). If he raises, it will be a draw (50% probability). If he calls, I will win (50% probability). Overall, the winning rate for his Jack is 25%, the losing rate is 0%, and the draw rate is 25%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. The losing rate is 100%, and the winning and draw rates are both 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King (25% probability), he might raise (70% probability) or check (30% probability). If he raises, I will lose (70% probability). If he checks, it will be a draw (30% probability). Overall, the winning rate for his King is 0%, the losing rate is 17.5%, and the draw rate is 7.5%.\n- If GoodGuy holds a Queen (25% probability), he might raise (60% probability) or check (40% probability). If he raises, I will lose (60% probability). If he checks, it will be a draw (40% probability). Overall, the winning rate for his Queen is 0%, the losing rate is 15%, and the draw rate is 10%.\n- If GoodGuy holds a Jack (50% probability), he might raise (50% probability) or check (50% probability). If he raises, it will be a draw (50% probability). If he checks, I will win (50% probability). Overall, the winning rate for his Jack is 25%, the losing rate is 0%, and the draw rate is 25%.\n\nPlan 1 overall GoodGuy's Winning/Lose/Draw rates: Winning rate is 42.5%, Losing rate is 32.5%, Draw rate is 25%.\nPlan 2 overall GoodGuy's Winning/Lose/Draw rates: Winning rate is 0%, Losing rate is 100%, Draw rate is 0%.\nPlan 3 overall GoodGuy's Winning/Lose/Draw rates: Winning rate is 25%, Losing rate is 32.5%, Draw rate is 42.5%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, Chips in the pot: 8. If win, the winning payoff would be 4. If lose, the lose payoff would be 4.\n- Plan 2: After the action, Chips in the pot: 2. If lose, the lose payoff would be 1.\n- Plan 3: After the action, Chips in the pot: 2. If win, the winning payoff would be 1. If lose, the lose payoff would be 1.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 42.5% * 4 - 32.5% * 4 = 0.4 chips\n- Plan 2: 0% * 0 - 100% * 1 = -1 chip\n- Plan 3: 25% * 1 - 32.5% * 1 = -0.075 chips\n\nPlan Selection: \nThe rank of estimated expected chips gains for every plan is: Plan 1 > Plan 3 > Plan 2. Therefore, I should select Plan 1: Raise."}}
{"message": "", "43_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (35% probability), he is likely to raise (60% probability) or check (40% probability). If he raises, I will lose (probability = 35% * 60% = 21%). If he checks, I will win (probability = 35% * 40% = 14%).\n- If GoodGuy holds a Queen (30% probability), he is likely to raise (50% probability) or check (50% probability). If he raises, I will lose (probability = 30% * 50% = 15%). If he checks, I will win (probability = 30% * 50% = 15%).\n- If GoodGuy holds a Jack (25% probability), he is likely to raise (40% probability) or check (60% probability). If he raises, it will be a draw (probability = 25% * 40% = 10%). If he checks, I will win (probability = 25% * 60% = 15%).\n- Overall, the winning rate for plan 1 is 44%, the losing rate is 36%, and the draw rate is 10%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. The losing rate for plan 2 is 100%.\n\nPlan 3: Check\n- If GoodGuy holds a King (35% probability), he is likely to raise (60% probability) or check (40% probability). If he raises, I will lose (probability = 35% * 60% = 21%). If he checks, I will win (probability = 35% * 40% = 14%).\n- If GoodGuy holds a Queen (30% probability), he is likely to raise (50% probability) or check (50% probability). If he raises, I will lose (probability = 30% * 50% = 15%). If he checks, I will win (probability = 30% * 50% = 15%).\n- If GoodGuy holds a Jack (25% probability), he is likely to raise (40% probability) or check (60% probability). If he raises, it will be a draw (probability = 25% * 40% = 10%). If he checks, I will win (probability = 25% * 60% = 15%).\n- Overall, the winning rate for plan 3 is 44%, the losing rate is 36%, and the draw rate is 10%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 8 chips. If I lose, the losing payoff would be 4 chips.\n- Plan 2: If I lose, the losing payoff would be 4 chips.\n- Plan 3: If I win, the winning payoff would be 4 chips. If I lose, the losing payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 44% * 8 - 36% * 4 = 1.6 chips\n- Plan 2: Expected Chips Gain = -100% * 4 = -4 chips\n- Plan 3: Expected Chips Gain = 44% * 4 - 36% * 4 = 0.32 chips\n\nPlan Selection:\n- Plan 1: 1.6 chips\n- Plan 2: -4 chips\n- Plan 3: 0.32 chips\n\nBased on the estimated expected chips gains, the best plan to execute is Plan 1: Raise."}}
{"message": "", "44_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a Jack (20% probability), he will likely raise (80% probability). If the public card is not a Queen, I will win (probability = 20% * 80% = 16%). If the public card is a Queen, it's a draw (probability = 20% * 80% = 16%). \n- If GoodGuy holds a Queen (30% probability), he will likely raise (70% probability). If the public card is a Queen, it's a draw (probability = 30% * 70% = 21%). If the public card is not a Queen, I will lose (probability = 30% * 70% = 21%).\n- If GoodGuy holds a King (50% probability), he will likely raise (90% probability). If the public card is a Queen, I will lose (probability = 50% * 90% = 45%). If the public card is not a Queen, I will win (probability = 50% * 90% = 45%).\n- Winning payoff: 4 chips (half of the pot)\n- Losing payoff: 4 chips (half of the pot)\n- Expected chips gain: 16% * 4 - 21% * 4 - 45% * 4 = -2 chips\n\nPlan 2: Raise\n- If GoodGuy holds a Jack (20% probability), he will likely call (20% probability). If the public card is not a Queen, I will win (probability = 20% * 20% = 4%). If the public card is a Queen, it's a draw (probability = 20% * 20% = 4%).\n- If GoodGuy holds a Queen (30% probability), he will likely call (30% probability). If the public card is a Queen, it's a draw (probability = 30% * 30% = 9%). If the public card is not a Queen, I will lose (probability = 30% * 30% = 9%).\n- If GoodGuy holds a King (50% probability), he will likely call (10% probability). If the public card is a Queen, I will lose (probability = 50% * 10% = 5%). If the public card is not a Queen, I will win (probability = 50% * 10% = 5%).\n- Winning payoff: 6 chips (half of the pot)\n- Losing payoff: 6 chips (half of the pot)\n- Expected chips gain: 4% * 6 - 9% * 6 - 5% * 6 = -0.6 chips\n\nPlan 3: Fold\n- If I fold, I will lose 2 chips (the chips I have already put in the pot), regardless of GoodGuy's card or action.\n\nPlan Selection:\n- Plan 1: -2 chips\n- Plan 2: -0.6 chips\n- Plan 3: -2 chips\n\nBased on the expected chips gain, Plan 2 (Raise) is the best strategy."}}
{"message": "", "44_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (50% probability), he will likely raise (60% probability) or fold (40% probability). If he raises, I will lose as his King is higher than my Queen. If he folds, I will win. Therefore, the winning rate is 20% (50% * 40%), the losing rate is 30% (50% * 60%), and the draw rate is 0%.\n- If GoodGuy holds a Queen (50% probability), he will likely raise (90% probability) or call (10% probability). If he raises or calls, it will be a draw as we both hold a Queen. Therefore, the winning rate is 0%, the losing rate is 0%, and the draw rate is 50% (50% * 100%).\n\nPlan 2: Fold\n- If GoodGuy holds a King (50% probability), I will lose regardless of his action. Therefore, the winning rate is 0%, the losing rate is 50%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (50% probability), I will lose regardless of his action. Therefore, 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 King (50% probability), he will likely raise (60% probability) or fold (40% probability). If he raises, I will lose as his King is higher than my Queen. If he folds, I will win. Therefore, the winning rate is 20% (50% * 40%), the losing rate is 30% (50% * 60%), and the draw rate is 0%.\n- If GoodGuy holds a Queen (50% probability), he will likely raise (90% probability) or call (10% probability). If he raises or calls, it will be a draw as we both hold a Queen. Therefore, the winning rate is 0%, the losing rate is 0%, and the draw rate is 50% (50% * 100%).\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 pot). If lose, the lose payoff would be 4 chips (half of the pot).\n- Plan 2: If win, the winning payoff would be 0 chips (as I fold). If lose, the lose payoff would be 4 chips (half of the pot).\n- Plan 3: If win, the winning payoff would be 8 chips (half of the pot). If lose, the lose payoff would be 4 chips (half of the pot).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 20% * 8 chips - 30% * 4 chips = 0.8 chips\n- Plan 2: Expected Chips Gain = 0% * 0 chips - 50% * 4 chips = -2 chips\n- Plan 3: Expected Chips Gain = 20% * 8 chips - 30% * 4 chips = 0.8 chips\n\nPlan Selection:\n- Plan 1 and Plan 3 have the highest expected chips gain (0.8 chips), while Plan 2 has the lowest expected chips gain (-2 chips). Therefore, I should either raise (Plan 1) or check (Plan 3) to maximize my expected chips gain. Considering my strategy improvement, I should be more aggressive in the first round, especially when I hold a King. Therefore, I will choose Plan 1: Raise."}}
{"message": "", "44_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a Jack (probability 70%): GoodGuy will likely raise (probability 90%). If he raises, I will lose as his Jack matches the public card. The losing rate is 0.7*0.9=0.63.\n- If GoodGuy holds a Queen (probability 30%): GoodGuy will likely check (probability 70%) or raise (probability 30%). If he checks, I will win as my Queen is higher than the public card. The winning rate is 0.3*0.7=0.21. If he raises, it will be a draw as we both hold Queens. The draw rate is 0.3*0.3=0.09.\n\nPlan 2: Fold\n- If GoodGuy holds a Jack (probability 70%): I will lose as I forfeit the game. The losing rate is 0.7.\n- If GoodGuy holds a Queen (probability 30%): I will lose as I forfeit the game. The losing rate is 0.3.\n\nWinning/Lose Payoff for Each Plan:\n- Plan 1: After the call, chips in the pot: 16. If win, the winning payoff would be 8. If lose, the lose payoff would be 8.\n- Plan 2: After the fold, chips in the pot: 12. If lose, the lose payoff would be 6.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = winning rate * Winning Payoff - lose rate * Lose Payoff = 0.21*8 - 0.63*8 = -3.36\n- Plan 2: Expected Chips Gain = - lose rate * Lose Payoff = -1*6 = -6\n\nPlan Selection:\nThe rank of estimated expected chips gains for every plan is: Plan 1 > Plan 2. Therefore, I should choose Plan 1: Call. This plan has the highest estimated expected chips gain and is more aggressive, which aligns with the strategy improvement."}}
{"message": "", "45_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (45% probability), he will likely raise (90% probability). If the public card is a King, I will win (probability = 0.45 * 0.9 = 0.405). If the public card is a Queen or Jack, I will lose (probability = 0.45 * 0.1 = 0.045).\n- If GoodGuy holds a Queen (40% probability), he will likely raise (80% probability). If the public card is a Queen, I will lose (probability = 0.4 * 0.8 = 0.32). If the public card is a King or Jack, I will win (probability = 0.4 * 0.2 = 0.08).\n- If GoodGuy holds a Jack (15% probability), he will likely raise (70% probability). If the public card is a Jack, I will lose (probability = 0.15 * 0.7 = 0.105). If the public card is a King or Queen, I will win (probability = 0.15 * 0.3 = 0.045).\n- Overall, the winning rate for Plan 1 is 0.405 + 0.08 + 0.045 = 0.53, the losing rate is 0.045 + 0.32 + 0.105 = 0.47, and the draw rate is 0.\n\nPlan 2: Raise\n- If GoodGuy holds a King (45% probability), he will likely call (10% probability). If the public card is a King, I will win (probability = 0.45 * 0.1 = 0.045). If the public card is a Queen or Jack, I will lose (probability = 0.45 * 0.9 = 0.405).\n- If GoodGuy holds a Queen (40% probability), he will likely fold (30% probability). If the public card is a Queen, I will lose (probability = 0.4 * 0.7 = 0.28). If the public card is a King or Jack, I will win (probability = 0.4 * 0.3 = 0.12).\n- If GoodGuy holds a Jack (15% probability), he will likely fold (40% probability). If the public card is a Jack, I will lose (probability = 0.15 * 0.6 = 0.09). If the public card is a King or Queen, I will win (probability = 0.15 * 0.4 = 0.06).\n- Overall, the winning rate for Plan 2 is 0.045 + 0.12 + 0.06 = 0.225, the losing rate is 0.405 + 0.28 + 0.09 = 0.775, and the draw rate is 0.\n\nPlan 3: Fold\n- If I fold, I will lose the game regardless of GoodGuy's card or the public card. The losing rate is 1, and the winning and draw rates are 0.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips (half of the pot). If I lose, the losing payoff would be 1 chip (half of the pot).\n- Plan 2: If I win, the winning payoff would be 5 chips (half of the pot). If I lose, the losing payoff would be 2 chips (half of the pot).\n- Plan 3: If I fold, I will lose 1 chip.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.53 * 3 - 0.47 * 1 = 1.12 chips\n- Plan 2: Expected Chips Gain = 0.225 * 5 - 0.775 * 2 = -0.775 chips\n- Plan 3: Expected Chips Gain = -1 chip\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I will choose to call."}}
{"message": "", "45_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (40% probability), he will likely fold if I raise (30% probability). This would result in me winning the pot, which is currently 4 chips. The winning rate for this scenario is 0.4 * 0.3 = 0.12.\n- If GoodGuy holds a Jack (60% probability), he will likely call if I raise (20% probability). This would result in a showdown, and since he has a pair of Jacks, I would lose. The losing rate for this scenario is 0.6 * 0.2 = 0.12.\n\nPlan 2: Fold\n- If I fold, I would lose the pot regardless of what card GoodGuy holds. The losing rate for this scenario is 1.\n\nPlan 3: Check\n- If GoodGuy holds a Queen (40% probability), he will likely check as well (60% probability). This would result in a showdown, and since I have a King, I would win. The winning rate for this scenario is 0.4 * 0.6 = 0.24.\n- If GoodGuy holds a Jack (60% probability), he will likely raise (80% probability). This would force me to either call or fold. If I call, I would lose, and if I fold, I would also lose. The losing rate for this scenario is 0.6 * 0.8 = 0.48.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the pot, which is currently 4 chips, so 2 chips. If I lose, the losing payoff would be half of the pot, so 2 chips.\n- Plan 2: If I fold, I would lose the pot, so the losing payoff would be 2 chips.\n- Plan 3: If I win, the winning payoff would be half of the pot, which is currently 4 chips, so 2 chips. If I lose, the losing payoff would be half of the pot, so 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning Rate * Winning Payoff - Losing Rate * Losing Payoff = 0.12 * 2 - 0.12 * 2 = 0\n- Plan 2: Expected Chips Gain = -1 * 2 = -2\n- Plan 3: Expected Chips Gain = 0.24 * 2 - 0.48 * 2 = -0.48\n\nPlan Selection:\n- Plan 1: 0\n- Plan 2: -2\n- Plan 3: -0.48\n\nBased on the expected chips gain, Plan 1 (Raise) is the best strategy to use in this situation."}}
{"message": "", "45_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a Jack, he will likely raise (40% probability) or check (60% probability). If he raises, I will lose as his Jack pairs with the public card. If he checks, I will win as my King is higher than his Jack. The overall winning rate is 60%, losing rate is 40%, and draw rate is 0%.\n- If GoodGuy holds a Queen, he will likely raise (30% probability) or check (70% probability). If he raises, I will lose as his Queen is higher than my King. If he checks, I will win as my King is higher than his Queen. The overall winning rate is 70%, losing rate is 30%, and draw rate is 0%.\n- If GoodGuy holds a King, he will likely raise (20% probability) or check (80% probability). If he raises or checks, it will be a draw as we both hold Kings. The overall winning rate is 0%, losing rate is 0%, and draw rate is 100%.\n\nPlan 2: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. The overall winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the call action, chips in the pot would be 20. If win, the winning payoff would be 10. If lose, the lose payoff would be 10.\n- Plan 2: After the fold action, chips in the pot would be 16. If lose, the lose payoff would be 8.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = (0.6+0.7+0) * 10 - (0.4+0.3+0) * 10 = 3 chips\n- Plan 2: Expected Chips Gain = Winning rate * Winning Payoff - Losing rate * Losing Payoff = 0 * 10 - 1 * 8 = -8 chips\n\nPlan Selection:\n- Plan 1 has an expected chips gain of 3, while Plan 2 has an expected chips gain of -8. Therefore, Plan 1 (Call) is the better strategy."}}
{"message": "", "46_1": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King (30% probability), he might raise (70% probability) or call (30% probability). If he raises, I would lose (70% probability) or draw (30% probability). If he calls, I would win (70% probability) or draw (30% probability). Overall, the winning rate is 21%, the losing rate is 49%, and the draw rate is 30%.\n- If GoodGuy holds a Queen (40% probability), he might raise (60% probability) or call (40% probability). If he raises, I would draw (100% probability). If he calls, I would win (60% probability) or draw (40% probability). Overall, the winning rate is 24%, the losing rate is 0%, and the draw rate is 76%.\n- If GoodGuy holds a Jack (30% probability), he might call (60% probability) or raise (40% probability). If he calls, I would win (100% probability). If he raises, I would win (60% probability) or draw (40% probability). Overall, the winning rate is 78%, the losing rate is 0%, and the draw rate is 22%.\n\nPlan 1 overall GoodGuy's Winning/Lose/Draw rates: The Winning rate for plan 1 is 123%, Lose rate for plan 1 is 49%, and Draw Rate for plan 1 is 128%.\n\nPlan 2: Check\n- If GoodGuy holds a King (30% probability), he might raise (70% probability) or call (30% probability). If he raises, I would lose (70% probability) or draw (30% probability). If he calls, I would win (70% probability) or draw (30% probability). Overall, the winning rate is 21%, the losing rate is 49%, and the draw rate is 30%.\n- If GoodGuy holds a Queen (40% probability), he might raise (60% probability) or call (40% probability). If he raises, I would draw (100% probability). If he calls, I would win (60% probability) or draw (40% probability). Overall, the winning rate is 24%, the losing rate is 0%, and the draw rate is 76%.\n- If GoodGuy holds a Jack (30% probability), he might call (60% probability) or raise (40% probability). If he calls, I would win (100% probability). If he raises, I would win (60% probability) or draw (40% probability). Overall, the winning rate is 78%, the losing rate is 0%, and the draw rate is 22%.\n\nPlan 2 overall GoodGuy's Winning/Lose/Draw rates: The Winning rate for plan 2 is 123%, Lose rate for plan 2 is 49%, and Draw Rate for plan 2 is 128%.\n\nPlan 3: Fold\n- If GoodGuy holds a King (30% probability), he might raise (70% probability) or call (30% probability). If he raises, I would lose (100% probability). If he calls, I would 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 Queen (40% probability), he might raise (60% probability) or call (40% probability). If he raises, I would lose (100% probability). If he calls, I would 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 Jack (30% probability), he might call (60% probability) or raise (40% probability). If he calls, I would lose (100% probability). If he raises, I would lose (100% probability). Overall, the winning rate is 0%, the losing rate is 100%, and the draw rate is 0%.\n\nPlan 3 overall GoodGuy's Winning/Lose/Draw rates: The Winning rate for plan 3 is 0%, Lose rate for plan 3 is 300%, and Draw Rate for plan 3 is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: After the action, Chips in the pot: 4. If win, the winning payoff would be 2. After the action, Chips in the pot: 4. If lose, the lose payoff would be 2.\n- Plan 2: After the action, Chips in the pot: 2. If win, the winning payoff would be 1. After the action, Chips in the pot: 2. If lose, the lose payoff would be 1.\n- Plan 3: After the action, Chips in the pot: 2. If win, the winning payoff would be 1. After the action, Chips in the pot: 2. If lose, the lose payoff would be 1.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 123% * 2 - 49% * 2 = 148%\n- Plan 2: 123% * 1 - 49% * 1 = 74%\n- Plan 3: 0% * 1 - 300% * 1 = -300%\n\nPlan Selection:\n- Plan 1: 148%\n- Plan 2: 74%\n- Plan 3: -300%\n\nBased on the above analysis, I should choose Plan 1 (Raise) as it has the highest estimated expected chips gain."}}
{"message": "", "46_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King, he is likely to raise (80%) or call (20%). If I win, the winning payoff would be half of the pot, which would be 6 chips. If I lose, the losing payoff would be half of the pot, which would be 6 chips.\n- If GoodGuy holds a Queen, he is likely to raise (70%) or call (30%). If I win, the winning payoff would be half of the pot, which would be 6 chips. If I lose, the losing payoff would be half of the pot, which would be 6 chips.\n- If GoodGuy holds a Jack, he is likely to call (50%) or fold (50%). If I win, the winning payoff would be half of the pot, which would be 6 chips. If I lose, the losing payoff would be half of the pot, which would be 6 chips.\n\nPlan 2: Fold\n- If I fold, I would lose the 4 chips I have already put in the pot.\n\nPlan 3: Check\n- If GoodGuy holds a King, he is likely to raise (80%) or call (20%). If I win, the winning payoff would be half of the pot, which would be 4 chips. If I lose, the losing payoff would be half of the pot, which would be 4 chips.\n- If GoodGuy holds a Queen, he is likely to raise (70%) or call (30%). If I win, the winning payoff would be half of the pot, which would be 4 chips. If I lose, the losing payoff would be half of the pot, which would be 4 chips.\n- If GoodGuy holds a Jack, he is likely to call (50%) or fold (50%). If I win, the winning payoff would be half of the pot, which would be 4 chips. If I lose, the losing payoff would be half of the pot, which would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: (0.8 * 6) - (0.2 * 6) = 4.8 chips\n- Plan 2: -4 chips\n- Plan 3: (0.8 * 4) - (0.2 * 4) = 3.2 chips\n\nPlan Selection:\nBased on the estimated expected chips gains, the ranking of the plans is as follows:\n1. Plan 1: Raise\n2. Plan 3: Check\n3. Plan 2: Fold\n\nTherefore, the plan with the highest estimated expected chips gain is Plan 1: Raise."}}
{"message": "", "47_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (33.33% probability), he will likely raise (70% probability). If the public card is a Queen or Jack, I will lose. If the public card is a King, I will draw. The overall winning rate is 0, the losing rate is 23.33%, and the drawing rate is 10%.\n- If GoodGuy holds a Queen (33.33% probability), he will likely raise (60% probability) or call (40% probability). If the public card is a King or Jack, I will lose. If the public card is a Queen, I will draw. The overall winning rate is 0, the losing rate is 20%, and the drawing rate is 13.33%.\n- If GoodGuy holds a Jack (33.33% probability), he will likely call (50% probability) or raise (50% probability). If the public card is a King, I will lose. If the public card is a Queen or Jack, I will win. The overall winning rate is 16.67%, the losing rate is 16.67%, and the drawing rate is 0.\n- The overall winning rate for Plan 1 is 16.67%, the losing rate is 60%, and the drawing rate is 23.33%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (33.33% probability), he will likely call (30% probability). If the public card is a Queen or Jack, I will lose. If the public card is a King, I will draw. The overall winning rate is 0, the losing rate is 10%, and the drawing rate is 10%.\n- If GoodGuy holds a Queen (33.33% probability), he will likely call (40% probability) or fold (20% probability). If the public card is a King or Jack, I will win. If the public card is a Queen, I will draw. The overall winning rate is 20%, the losing rate is 0, and the drawing rate is 13.33%.\n- If GoodGuy holds a Jack (33.33% probability), he will likely call (40% probability) or fold (20% probability). If the public card is a King, I will win. If the public card is a Queen or Jack, I will draw. The overall winning rate is 13.33%, the losing rate is 0, and the drawing rate is 13.33%.\n- The overall winning rate for Plan 2 is 33.33%, the losing rate is 10%, and the drawing rate is 36.67%.\n\nPlan 3: Fold\n- If I fold, I will lose the 2 chips I have already put in the pot. The overall winning rate is 0, the losing rate is 100%, and the drawing rate is 0.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 3 chips. If I lose, the losing payoff would be 2 chips.\n- Plan 2: If I win, the winning payoff would be 5 chips. If I lose, the losing payoff would be 4 chips.\n- Plan 3: If I fold, the losing payoff would be 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 16.67% * 3 - 60% * 2 = -0.67 chips\n- Plan 2: 33.33% * 5 - 10% * 4 = 1.33 chips\n- Plan 3: 0 * 0 - 100% * 2 = -2 chips\n\nPlan Selection:\n- Plan 2 > Plan 1 > Plan 3\n- I should choose Plan 2: Raise."}}
{"message": "", "47_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King, he will likely raise (60% probability). If he raises, I will lose as his King matches the public card. If he calls (40% probability), I will win if he holds a Queen or Jack. Overall, the winning rate is 40%, losing rate is 60%, and draw rate is 0%.\n- If GoodGuy holds a Queen, he will likely raise (50% probability), call (30% probability), or fold (20% probability). If he raises or calls, it will be a draw as we both hold a Queen. If he folds, I will win. Overall, the winning rate is 20%, losing rate is 0%, and draw rate is 80%.\n- If GoodGuy holds a Jack, he will likely raise (40% probability), call (40% probability), or fold (20% probability). If he raises or calls, I will win as my Queen is higher than his Jack. If he folds, I will also win. Overall, the winning rate is 100%, losing rate is 0%, and draw rate is 0%.\n\nPlan 2: Fold\n- If I fold, I will lose the chips I have already put in the pot. The winning rate is 0%, losing rate is 100%, and draw rate is 0%.\n\nPlan 3: Check\n- If GoodGuy holds a King, he will likely raise (60% probability). If he raises, I will lose as his King matches the public card. If he calls (40% probability), I will win if he holds a Queen or Jack. Overall, the winning rate is 40%, losing rate is 60%, and draw rate is 0%.\n- If GoodGuy holds a Queen, he will likely raise (50% probability), call (30% probability), or fold (20% probability). If he raises or calls, it will be a draw as we both hold a Queen. If he folds, I will win. Overall, the winning rate is 20%, losing rate is 0%, and draw rate is 80%.\n- If GoodGuy holds a Jack, he will likely raise (40% probability), call (40% probability), or fold (20% probability). If he raises or calls, I will win as my Queen is higher than his Jack. If he folds, I will also win. Overall, the winning rate is 100%, losing rate is 0%, and draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 4 chips (half of the pot). If I lose, the lose payoff would be 4 chips.\n- Plan 2: If I fold, I will lose 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 lose payoff would be 4 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.4 * 4 - 0.6 * 4 = -0.8 chips\n- Plan 2: Expected Chips Gain = 0 - 1 * 4 = -4 chips\n- Plan 3: Expected Chips Gain = 0.4 * 4 - 0.6 * 4 = -0.8 chips\n\nPlan Selection:\n- Plan 1: -0.8 chips\n- Plan 2: -4 chips\n- Plan 3: -0.8 chips\n\nBased on the estimated expected chips gains, Plan 1 and Plan 3 are the best strategies as they have the highest expected chips gain. However, considering the strategy improvement, Plan 1 (Raise) might be a better choice as it shows more aggression and could potentially confuse GoodGuy."}}
{"message": "", "48_1": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (33% chance), he will likely raise (80% chance). If the public card is a King, I will win (100% chance). If the public card is not a King, I will draw (50% chance) or lose (50% chance). Overall, the winning rate is 26.4%, the losing rate is 13.2%, and the draw rate is 13.2%.\n- If GoodGuy holds a Queen (50% chance), he will likely raise (60% chance) or call (40% chance). If the public card is a King or Queen, I will win (100% chance). If the public card is a Jack, I will lose (100% chance). Overall, the winning rate is 30%, the losing rate is 20%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (17% chance), he will likely call (70% chance) or raise (30% chance). If the public card is a King, I will win (100% chance). If the public card is a Queen or Jack, I will lose (100% chance). Overall, the winning rate is 11.9%, the losing rate is 5.1%, and the draw rate is 0%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (33% chance), he will likely call (20% chance). If the public card is a King, I will win (100% chance). If the public card is not a King, I will draw (50% chance) or lose (50% chance). Overall, the winning rate is 26.4%, the losing rate is 13.2%, and the draw rate is 13.2%.\n- If GoodGuy holds a Queen (50% chance), he will likely call (40% chance) or fold (60% chance). If the public card is a King or Queen, I will win (100% chance). If the public card is a Jack, I will lose (100% chance). Overall, the winning rate is 20%, the losing rate is 30%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (17% chance), he will likely fold (40% chance) or call (60% chance). If the public card is a King, I will win (100% chance). If the public card is a Queen or Jack, I will lose (100% chance). Overall, the winning rate is 10.2%, the losing rate is 6.8%, and the draw rate is 0%.\n\nPlan 3: Fold\n- If I fold, I will lose 100% of the time, regardless of what card GoodGuy holds.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be 6 chips. If I lose, the losing payoff would be 2 chips.\n- Plan 2: If I win, the winning payoff would be 8 chips. If I lose, the losing payoff would be 4 chips.\n- Plan 3: If I fold, I will lose 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: (26.4% * 6) - (13.2% * 2) = 1.32 chips\n- Plan 2: (20% * 8) - (30% * 4) = 0.4 chips\n- Plan 3: -2 chips\n\nPlan Selection:\n- Plan 1: 1.32 chips\n- Plan 2: 0.4 chips\n- Plan 3: -2 chips\n\nBased on the estimated expected chips gains, I should choose Plan 1 (Call) as it has the highest expected chips gain."}}
{"message": "", "48_3": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (probability 33.3%), he will likely raise (90%). If he raises, I will lose because he has a pair of Queens. So, the losing rate for his Queen is 33.3% * 90% = 30%.\n- If GoodGuy holds a King (probability 33.3%), he will likely call (60%) or fold (40%). If he calls, it will be a draw because we both have a King. If he folds, I will win. So, the winning rate for his King is 33.3% * 40% = 13.3%, and the draw rate is 33.3% * 60% = 20%.\n- If GoodGuy holds a Jack (probability 33.3%), he will likely call (60%) or fold (40%). If he calls or folds, I will win because my King beats his Jack. So, the winning rate for his Jack is 33.3% * 100% = 33.3%.\n\nPlan 2: Check\n- If GoodGuy holds a Queen (probability 33.3%), he will likely raise (50%) or call (50%). If he raises or calls, I will lose because he has a pair of Queens. So, the losing rate for his Queen is 33.3% * 100% = 33.3%.\n- If GoodGuy holds a King (probability 33.3%), he will likely raise (50%) or call (50%). If he raises or calls, it will be a draw because we both have a King. So, the draw rate for his King is 33.3% * 100% = 33.3%.\n- If GoodGuy holds a Jack (probability 33.3%), he will likely raise (50%) or call (50%). If he raises or calls, I will win because my King beats his Jack. So, the winning rate for his Jack is 33.3% * 100% = 33.3%.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. So, the losing rate is 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the pot (8 chips). If I lose, the losing payoff would be half of the pot (8 chips).\n- Plan 2: If I win, the winning payoff would be half of the pot (8 chips). If I lose, the losing payoff would be half of the pot (8 chips).\n- Plan 3: If I lose, the losing payoff would be half of the pot (8 chips).\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = winning rate * Winning Payoff - losing rate * Losing Payoff = (46.6% * 8) - (30% * 8) = 1.32 chips\n- Plan 2: Expected Chips Gain = (33.3% * 8) - (33.3% * 8) = 0 chips\n- Plan 3: Expected Chips Gain = 0% * Winning Payoff - 100% * Losing Payoff = -8 chips\n\nPlan Selection:\n- Plan 1: 1.32 chips\n- Plan 2: 0 chips\n- Plan 3: -8 chips\n\nBased on the estimated expected chips gains, I should select Plan 1 (Raise) as it has the highest expected chips gain."}}
{"message": "", "49_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (33.3% chance), he might raise (70%) or call (30%). If he raises, I will lose unless the public card is a Jack. If he calls, I will win if the public card is a Jack, and lose otherwise. So, the winning rate is 33.3% * 30% * 33.3% = 3.3%, the losing rate is 33.3% * (70% * 66.7% + 30% * 66.7%) = 22%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (33.3% chance), he might raise (60%) or call (40%). If he raises, I will lose unless the public card is a Jack. If he calls, I will win if the public card is a Jack, and lose otherwise. So, the winning rate is 33.3% * 40% * 33.3% = 4.4%, the losing rate is 33.3% * (60% * 66.7% + 40% * 66.7%) = 22%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (33.3% chance), he might call (70%) or raise (30%). If he calls, it will be a draw. If he raises, I will lose unless the public card is a Jack. So, the winning rate is 0%, the losing rate is 33.3% * 30% * 66.7% = 6.7%, and the draw rate is 33.3% * 70% = 23.3%.\n\nPlan 1 overall GoodGuy's Winning/Lose/Draw rates: Winning rate = 3.3% + 4.4% = 7.7%, Lose rate = 22% + 22% + 6.7% = 50.7%, Draw rate = 23.3%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (33.3% chance), he might raise (70%) or call (30%). If he raises, I will lose unless the public card is a Jack. If he calls, I will win if the public card is a Jack, and lose otherwise. So, the winning rate is 33.3% * 30% * 33.3% = 3.3%, the losing rate is 33.3% * (70% * 66.7% + 30% * 66.7%) = 22%, and the draw rate is 0%.\n- If GoodGuy holds a Queen (33.3% chance), he might raise (60%) or call (40%). If he raises, I will lose unless the public card is a Jack. If he calls, I will win if the public card is a Jack, and lose otherwise. So, the winning rate is 33.3% * 40% * 33.3% = 4.4%, the losing rate is 33.3% * (60% * 66.7% + 40% * 66.7%) = 22%, and the draw rate is 0%.\n- If GoodGuy holds a Jack (33.3% chance), he might call (70%) or raise (30%). If he calls, it will be a draw. If he raises, I will lose unless the public card is a Jack. So, the winning rate is 0%, the losing rate is 33.3% * 30% * 66.7% = 6.7%, and the draw rate is 33.3% * 70% = 23.3%.\n\nPlan 2 overall GoodGuy's Winning/Lose/Draw rates: Winning rate = 3.3% + 4.4% = 7.7%, Lose rate = 22% + 22% + 6.7% = 50.7%, Draw rate = 23.3%.\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: After the action, Chips in the pot: 3. If win, the winning payoff would be 1.5. If lose, the lose payoff would be 1.5.\n- Plan 2: After the action, Chips in the pot: 6. If win, the winning payoff would be 3. If lose, the lose payoff would be 3.\n- Plan 3: After the action, Chips in the pot: 2. If lose, the lose payoff would be 1.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 7.7% * 1.5 - 50.7% * 1.5 = -0.6435\n- Plan 2: 7.7% * 3 - 50.7% * 3 = -1.287\n- Plan 3: 0% * 0 - 100% * 1 = -1\n\nPlan Selection: \n- Plan 1: -0.6435\n- Plan 2: -1.287\n- Plan 3: -1\n\nTherefore, Plan 1 (Call) is the best strategy with the highest estimated expected chips gain."}}
{"message": "", "49_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a Queen (60% probability), he will likely call (60% probability). If he calls, I will lose as Queen is higher than Jack. \n- If GoodGuy holds a Jack (40% probability), he will likely call (70% probability). If he calls, it will be a draw as we both hold Jacks. \n\nPlan 2: Fold\n- If I fold, I will lose the chips in the pot regardless of GoodGuy's hand. \n\nPlan 3: Check\n- If GoodGuy holds a Queen (60% probability), he will likely call (60% probability). If he calls, I will lose as Queen is higher than Jack. \n- If GoodGuy holds a Jack (40% probability), he will likely call (70% probability). If he calls, it will be a draw as we both hold Jacks. \n\nWinning/Lose/Draw Rate for Each Plan:\n- Plan 1: Winning rate = 0%, Lose rate = 60%, Draw rate = 40%\n- Plan 2: Winning rate = 0%, Lose rate = 100%, Draw rate = 0%\n- Plan 3: Winning rate = 0%, Lose rate = 60%, Draw rate = 40%\n\nNumber of Winning and Lose Payoffs for Each Plan:\n- Plan 1: If win, the winning payoff would be 0. If lose, the lose payoff would be 4 (half of the pot).\n- Plan 2: If win, the winning payoff would be 0. If lose, the lose payoff would be 2 (half of the pot).\n- Plan 3: If win, the winning payoff would be 0. If lose, the lose payoff would be 2 (half of the pot).\n\nEstimated Expected Chips Gain for Each Plan:\n- Plan 1: Expected chips gain = 0 * 0 - 0.6 * 4 = -2.4\n- Plan 2: Expected chips gain = 0 * 0 - 1 * 2 = -2\n- Plan 3: Expected chips gain = 0 * 0 - 0.6 * 2 = -1.2\n\nPlan Selection:\n- Plan 1: 3rd place\n- Plan 2: 2nd place\n- Plan 3: 1st place\n\nBased on the above analysis, I should choose Plan 3 (Check) as it has the highest estimated expected chips gain. This plan aligns with my strategy improvement of being more conservative when holding a Jack."}}
{"message": "", "49_4": {"plan": "Plan 1: Call\n- If GoodGuy holds a Queen (60% chance), he will likely raise (60% chance). If he raises, I will lose (as Queen > Jack), so the lose rate is 60% * 60% = 36%. If he calls (40% chance), it will be a draw, so the draw rate is 60% * 40% = 24%.\n- If GoodGuy holds a Jack (40% chance), he will likely call (70% chance), leading to a draw, so the draw rate is 40% * 70% = 28%. If he raises (30% chance), it will also be a draw, so the draw rate is 40% * 30% = 12%.\n- Overall, the winning rate for Plan 1 is 0%, the lose rate is 36%, and the draw rate is 64%.\n\nPlan 2: Raise\n- If GoodGuy holds a Queen (60% chance), he will likely raise (60% chance). If he raises, I will lose (as Queen > Jack), so the lose rate is 60% * 60% = 36%. If he calls (40% chance), it will be a draw, so the draw rate is 60% * 40% = 24%.\n- If GoodGuy holds a Jack (40% chance), he will likely call (70% chance), leading to a draw, so the draw rate is 40% * 70% = 28%. If he raises (30% chance), it will also be a draw, so the draw rate is 40% * 30% = 12%.\n- Overall, the winning rate for Plan 2 is 0%, the lose rate is 36%, and the draw rate is 64%.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of GoodGuy's card or action. So, the winning rate for Plan 3 is 0%, the lose rate is 100%, and the draw rate is 0%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan 1: If I win, the winning payoff would be half of the pot (8 chips), so 0 chips. If I lose, the lose payoff would be half of the pot (8 chips), so -4 chips.\n- Plan 2: If I win, the winning payoff would be half of the pot (14 chips), so 0 chips. If I lose, the lose payoff would be half of the pot (14 chips), so -7 chips.\n- Plan 3: If I fold, I will lose 2 chips.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan 1: 0% * 8 chips - 36% * 8 chips = -2.88 chips\n- Plan 2: 0% * 14 chips - 36% * 14 chips = -5.04 chips\n- Plan 3: -2 chips\n\nPlan Selection:\n- Plan 1: -2.88 chips\n- Plan 2: -5.04 chips\n- Plan 3: -2 chips\n\nBased on the estimated expected chips gain, Plan 3 (Fold) is the best strategy. Although it guarantees a loss of 2 chips, it minimizes the potential loss compared to the other plans."}}
{"message": "", "50_0": {"plan": "Plan 1: Call\n- If GoodGuy holds a King (33.33%), he is likely to raise (80%) or call (20%). If he raises, I will lose (probability = 33.33% * 80% = 26.67%). If he calls, it will be a draw (probability = 33.33% * 20% = 6.67%).\n- If GoodGuy holds a Queen (16.67%), he is likely to call (60%) or raise (40%). If he calls, it will be a draw (probability = 16.67% * 60% = 10%). If he raises, I will lose (probability = 16.67% * 40% = 6.67%).\n- If GoodGuy holds a Jack (50%), he is likely to call (70%) or fold (30%). If he calls, I will win (probability = 50% * 70% = 35%). If he folds, I will win (probability = 50% * 30% = 15%).\nPlan1 overall GoodGuy's Winning/Lose/Draw rates: Winning rate = 50%, Lose rate = 33.34%, Draw rate = 16.67%.\n\nPlan 2: Raise\n- If GoodGuy holds a King (33.33%), he is likely to raise (80%) or call (20%). If he raises, I will lose (probability = 33.33% * 80% = 26.67%). If he calls, it will be a draw (probability = 33.33% * 20% = 6.67%).\n- If GoodGuy holds a Queen (16.67%), he is likely to call (60%) or raise (40%). If he calls, it will be a draw (probability = 16.67% * 60% = 10%). If he raises, I will lose (probability = 16.67% * 40% = 6.67%).\n- If GoodGuy holds a Jack (50%), he is likely to call (40%) or fold (30%). If he calls, I will win (probability = 50% * 40% = 20%). If he folds, I will win (probability = 50% * 30% = 15%).\nPlan2 overall GoodGuy's Winning/Lose/Draw rates: Winning rate = 35%, Lose rate = 33.34%, Draw rate = 16.67%.\n\nPlan 3: Fold\n- If I fold, I will lose regardless of what card GoodGuy holds. Lose rate = 100%.\n\nThe number of winning and lose payoffs for each plan:\n- Plan1: After the action, Chips in the pot: 3. If win, the winning payoff would be 1.5. If lose, the lose payoff would be 1.5.\n- Plan2: After the action, Chips in the pot: 5. If win, the winning payoff would be 2.5. If lose, the lose payoff would be 2.5.\n- Plan3: After the action, Chips in the pot: 1. If lose, the lose payoff would be 0.5.\n\nEstimate Expected Chips Gain for Each Plan:\n- Plan1: Expected Chips Gain = 50% * 1.5 - 33.34% * 1.5 = 0.25\n- Plan2: Expected Chips Gain = 35% * 2.5 - 33.34% * 2.5 = 0.042\n- Plan3: Expected Chips Gain = -100% * 0.5 = -0.5\n\nPlan Selection:\n- Plan1: 0.25\n- Plan2: 0.042\n- Plan3: -0.5\n\nBased on the estimated expected chips gains, Plan 1 (Call) is the best strategy to use in this situation."}}
{"message": "", "50_2": {"plan": "Plan 1: Raise\n- If GoodGuy holds a King, he is likely to call (20%) or raise (80%). If he raises, I will lose as King is higher than Queen. If he calls, I will win as Queen is higher than the public card Jack. \n- If GoodGuy holds a Queen, he is likely to call (50%), raise (30%), or fold (20%). If he raises or calls, it will be a draw as we both have Queens. If he folds, I will win. \n- If GoodGuy holds a Jack, he is likely to call (40%), raise (30%), or fold (30%). If he raises or calls, I will win as Queen is higher than Jack. If he folds, I will also win. \n\nPlan 2: Fold\n- If I fold, I will lose the 2 chips in the pot regardless of what card GoodGuy holds.\n\nPlan 3: Check\n- If GoodGuy holds a King, he is likely to raise (80%) or check (20%). If he raises, I will lose as King is higher than Queen. If he checks, I will win as Queen is higher than the public card Jack. \n- If GoodGuy holds a Queen, he is likely to raise (30%), check (50%), or fold (20%). If he raises or checks, it will be a draw as we both have Queens. If he folds, I will win. \n- If GoodGuy holds a Jack, he is likely to raise (30%), check (40%), or fold (30%). If he raises or checks, I will win as Queen is higher than Jack. If he folds, I will also win. \n\nWinning/Lose Payoff for Each Plan:\n- Plan 1: If I win, the pot will be 6 chips (2 chips from me, 2 chips from GoodGuy, and 2 chips from my raise), so my winning payoff would be 3 chips. If I lose, my lose payoff would be 2 chips.\n- Plan 2: If I fold, my lose payoff would be 2 chips.\n- Plan 3: If I win, the pot will be 4 chips (2 chips from me and 2 chips from GoodGuy), so my winning payoff would be 2 chips. If I lose, my lose payoff would be 2 chips.\n\nExpected Chips Gain for Each Plan:\n- Plan 1: Expected Chips Gain = 0.7 * 3 - 0.3 * 2 = 1.1 chips\n- Plan 2: Expected Chips Gain = -2 chips\n- Plan 3: Expected Chips Gain = 0.7 * 2 - 0.3 * 2 = 0.8 chips\n\nPlan Selection:\n- Plan 1 has the highest expected chips gain, so I should choose to raise."}}
