Quantifying the Benefit of Card Sharing in Poker

Abstract

Collusion refers to secret, illegal cooperation among competitors to gain an un fair advantage, often at the expense of others. This type of behavior is strongly condemned and sanctioned, but remains difficult to detect, resulting in too many players being insufficiently deterred from unfair play. In online poker, this is an ongoing issue, because real money is at stake and the strategic deviations stemming from collusion are often subtle and hard to recognize. This thesis addresses this issue by introducing a formal model of collusion in Pot Limit Omaha poker, where players can collude by secretly revealing their cards to one another. This thesis uses Counterfactual Regret Minimization to approximate the strategies of colluding and non-colluding players in this model, showing how the model can be used to identify or approximate behavior associated with collusion. The strategies that were identified revealed significant advantages for colluding players, highlighting the severity of the issue and the need for further research into collusion detection, which may utilize the model developed in this research as the foundation