Bayesian reasoning
From PokerAI
Bayesian reasoning is a form of statistical inference based on Bayes' Theorem. In poker this refers primarily to a method for inferring information about an opponent's holding.
The likelihood that a player has a particular holding is:
((The chance that the player has that holding)*(The chance that the player took his past actions with that holding))
divided by the sum, over all holdings of:
((The chance that the player has the other holding)*(The chance that the player took his past actions with this other holding))
A simple example is that if a player always raises preflop with a particular holding (like AA), then if that player limps in, the player is clearly not holding AA, since the numerator in the fraction becomes zero.
Similarly, if villain always raises preflop with AA, KK, QQ, AKs, AKo, and never with anything else and hero is holding QJ, then, we have
- 6/31 chance of AA
- 6/31 chance of KK
- 4/31 chance of AKs
- 12/31 chance of AKo
- 3/31 chance of QQ
since those are the relative probabilities of those holdings.
A primary application of Bayesian reasoning in poker is that it can be applied to generate exploiters. In this application, Bayesian analysis is limited by the accuracy of the opponent model.
Bayesian reasoning can also be combined with Monte Carlo simulation, which has seen great success in computer bridge play.
