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Kuhn poker is a simplified form of poker developed by Harold W. Kuhn as a simple model zero sum two player imperfect information game, amenable to a complete game theoretic analysis. In Kuhn poker, the deck includes only three playing cards, for example, a King, Queen, and Jack. One card is dealt to each player, which may place bets similarly to a standard poker. If both players bet or both players pass, the player with the higher card wins, otherwise, the betting player wins. It was recently solved using Perfect Bayesian Equilibrium notions by Loriente and Diez (2023).

The game has a mixed strategy Nash equilibrium; when both players play equilibrium strategies, the first player should expect to lose at a rate of −1/18 per hand (as the game is zero sum, the second player should expect to win at a rate of +1/18). There is no pure strategy equilibrium. Kuhn demonstrated there are infinitely many equilibrium strategies for the first player, forming a continuum governed by a single parameter. In one possible formulation, player one freely chooses the probability with which he will bet when having a Jack (otherwise he checks; if the other player bets, he should always fold). When having a King, he should bet with the probability of (otherwise he checks; if the other player bets, he should always call). He should always check when having a Queen, and if the other player bets after this check, he should call with the probability of
The second player has a single equilibrium strategy: Always betting or calling when having a King; when having a Queen, checking if possible, otherwise calling with the probability of 1/3; when having a Jack, never calling and betting with the probability of 1/3.

In addition to the basic version invented by Kuhn, other versions appeared adding bigger deck, more players, betting rounds, etc., increasing the complexity of the game.