  Poker is a challenging problem for artificial intelligence, with
non-deterministic dynamics, partial observability, and the added difficulty of
unknown adversaries. Modelling all of the uncertainties in this domain is not
an easy task. In this paper we present a Bayesian probabilistic model for a
broad class of poker games, separating the uncertainty in the game dynamics
from the uncertainty of the opponent's strategy. We then describe approaches to
two key subproblems: (i) inferring a posterior over opponent strategies given a
prior distribution and observations of their play, and (ii) playing an
appropriate response to that distribution. We demonstrate the overall approach
on a reduced version of poker using Dirichlet priors and then on the full game
of Texas hold'em using a more informed prior. We demonstrate methods for
playing effective responses to the opponent, based on the posterior.
