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