Kuhn Poker

Kuhn poker is a simplified form of poker developed by Dr. Harold W. Kuhn. It is a zero sum two player game. The deck includes only three playing cards, for example a King, Queen, and Jack. One card is dealt to each player, then the first player must bet or pass, then the second player may bet or pass. If any player chooses to bet the opposing player must bet as well ("call") in order to stay in the round. After both players pass or bet the player with the highest card wins the pot. Kuhn demonstrated that there are many game theoretic optimal strategies for the first player in this game, but only one for the second player, and that, when played optimally, the first player should expect to lose at a rate of −1/18 per hand.

In more conventional poker terms:

• Each player antes 1
• Each player is dealt one of the three cards, and the third is put aside unseen
• Player One can check or raise 1
  • If Player One checks then Player Two can check or raise 1
    • If Player Two checks there is a showdown for the pot of 2
    • If Player Two raises then Player One can fold or call
      • If Player One folds then Player Two takes the pot of 3
      • If Player One calls there is a showdown for the pot of 4
  • If Player One raises then Player Two can fold or call
    • If Player Two folds then Player One takes the pot of 3
    • If Player Two calls there is a showdown for the pot of 4