Game Theoretic Models of Poker

Abstract

This thesis examines the card game poker from the perspective of game theory. After an initial look into the basic terminology and concepts of game theory, four different models of poker are presented from literature. The models are then solved to find pairs of optimal strategies known as Nash equilibria, which are examined both generally with arbitrarily sized bets as well as in the common special case of so-called ”pot limit” betting.

The thesis then introduces several concepts and principles that are considered fundamentals of good poker play in practice. These principles are then shown to apply even in the heavily simplified models considered in the thesis. This finding is used to lend credence to the correctness of these principles and to provide insight into the underlying mathematical reasons that cause them to emerge.