Capturing The Information Conveyed By Opponents' Betting Behavior in Poker

摘要

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.