5.1 Pre-Flop Evaluation

Hand strength for pre-flop play has been extensively studied in the poker literature. For example, [14] attempts to explain strong play in human understandable terms, by classifying all the initial two-card pre-flop combinations into nine betting categories. For each hand category, a suggested betting strategy is given, based on the strength of the hand, the number of players in the game, the position at the table (relative to the dealer), and the type of opponents. For a poker program, these ideas could be implemented as an expert system, but a more general approach would be preferable.

For the initial two cards, there are ${52\choose2} = 1,326$ possible combinations, but only 169 distinct hand types (13 paired hands, ${13\choose2} = 78$ suited hands and $13*{4\choose2} = 78$ unsuited hands). For each one of the 169 possible hand types, a simulation of 1,000,000 games was done against each of one, three and six random opponents (to cover the 2, 3-4 and 5 or more player scenarios^5.1). Each opponent was simple and always called to the end of the hand. This produced a statistical measure of the approximate income rate (IR) for each starting hand; income rate measures the return on investment.

$$IR \: = \: \frac{net\_bankroll}{hands\_played}$$ (5.1)

The computed values are presented in Appendix A. These numbers must always be viewed in the current context. They were obtained using a simplifying assumption, where the players always call to the end. However, this experiment gives a good first approximation of how strong a hand is. For example, in the 7-player simulation the best hand is a pair of aces and the worst hand is a 2 and 7 of different suits. While the absolute IR value may not be useful, the relative order of the hands is. As we discuss in Appendix A, there is a strong correlation between these simulation results and the pre-flop card ordering given in [14].