Optimal Poker Strategies Under Collusion Simulating Fictitious Play in Simplified Poker Variants

Abstract

We create modular software to construct and solve general hold’em poker games. Because most poker variants, like Texas Hold’em, are prohibitively complicated to analyze directly, we instead use the flexibility of our software to look at a variety of stripped-down hold’em-like games. In these simplified games, we answer questions about how game rules, player position, and betting history affect a player’s strategy to give insight into optimal strategies for more complicated poker variants. We simulate these variants with collusion and find that collusion leads to an overall increase in aggression by colluding players. We find that although strong collusion leads to a significant advantage for colluding players, weak collusion does not.