Analysis of continuous poker models

Janez Starc (2010) Analysis of continuous poker models. EngD thesis.

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Abstract

Poker with continuous values is a variant of poker where cards are replaced by values from some interval. In our work, we describe several such models for two players. In the beginning both players are dealt independent random values according to a uniform distribution on unit interval. This is followed by a round of betting. If one player folds, his opponent wins. On the other hand, if the game comes to the showdown, the player with the higher value wins. The described models are two-player zero-sum Bayesian games with infinite type sets. For each model we find at least one Bayes-Nash equilibrium and the value of the game. Bayes-Nash equilibrium consists of both players’ optimal strategies. Optimal strategy guarantees a player certain expected payoff no matter which strategy his opponent plays. This expected payoff of the player who acts first is also called the value of the game. This value tells us which player has the edge and how big it is. All possible outcomes of the game can be represented by a game tree. Described models have small game trees. Searching for optimal strategies in large game tree models can become unfeasible. In conclusion, possible procedures for searching for optimal strategies are considered. Furthermore, we compare all models and extract some strategic characteristics which can be also found in real poker.

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