# Consider the simplified poker game we demonstrated in class. We foun.pdf

27 de Mar de 2023
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### Consider the simplified poker game we demonstrated in class. We foun.pdf

• 1. Consider the simplified poker game we demonstrated in class. We found out that this was not a fair game, because the person who received the card on average won 1/3 each hand. In order to try to make it fair, the payoffs to all of the bets involving a King are cut in half. So the payoffs are as follows: If Player 1 gets a King and Folds, Player 1 loses \$.50 and player 2 wins \$.50. If Player 1 gets a King and Bets, then if Player 2 folds, Player 1 wins \$.50 and player 2 loses \$.50. If Player 1 gets a King and Bets, then if Player 2 calls, Player 1 wins \$1.00 and Player 2 loses \$1.00. The payoffs involving a Queen are the same as in class: If Player 1 gets a Queen and Folds, Player 1 loses \$1.00 and player 2 wins \$1.00. If Player 1 gets a Queen and Bets, then if Player 2 folds, Player 1 wins \$1.00 and player 2 loses \$1.00. If Player 1 gets a Queen and Bets, then if Player 2 calls, Player 1 loses \$2.00 and Player 2 wins \$2.00. a) (16 points) In the following table, Player 1 Solution a. In this case we can compute the expected payoffs by considering all the possible strategies that the players can play. Here, Player 1 has the lead, and so after he made his move, player 2 gets the chance of playing his move which he thinks will be best for him. The probability that player 1 gets a King is