Capturing The Information Conveyed By Opponents´ Betting Behavior in Poker

This paper develops an approach to the capture and measurement of the information contained in opponents\´ bet actions in seven card stud poker. We develop a causal model linking downcards with hand strength, thence to bet actions. The model can be inverted to infer probability distributions over possible downcards from bet actions, given knowledge of opponents\´ bet policies. For experimental purposes, we propose a simple yet plausible "default" bet policy including deceptive plays. In simulated games, this apparatus is used to compare the Kullback-Leibler information measure between inference of players\´ hand strength based on dealt cards and players\´ bet actions, versus inference of hand strength based on dealt cards only. We experimentally associate the K-L divergences with the win-lose rates for simulated players who either do or do not exploit knowledge of opponents\´ bet actions. Opponent inference carries up to a 36% information advantage over a cards-only player playing the same betting policy, and is worth on the order of .15 bets/hand