Measuring the Size of Large No-Limit Poker Games

In the field of computational game theory, games are often compared in terms of their size. This can be measured in several ways, including the number of unique game states, the number of decision points, and the total number of legal actions over all decision points. These numbers are either known or estimated for a wide range of classic games such as chess and checkers. In the stochastic and imperfect information game of poker, these sizes are easily computed in "limit" games which restrict the players' available actions, but until now had only been estimated for the more complicated "no-limit" variants. In this paper, we describe a simple algorithm for quickly computing the size of two-player no-limit poker games, provide an implementation of this algorithm, and present for the first time precise counts of the number of game states, information sets, actions and terminal nodes in the no-limit poker games played in the Annual Computer Poker Competition.