Network Structure

BPP makes use of a simple Bayesian belief network [PearlPearl1988], a data structure which can intuitively represent the conditional dependencies between variables and be used to do probabilistic inference. The network structure used, which can be seen in Figure 1, models the relationships between current hand type, final hand type and the behaviour of the opponent. Such a network structure is maintained for each of the four rounds of play (the betting rounds after two, three, four and five cards have been dealt). The number of cards involved in the current and observed hand types, and the conditional probability matrices for them, vary for each round: in effect, four distinct Bayesian networks are used to govern play.

  

Figure 1: The original Bayesian Poker network for a single round

The node OPP Final represents the opponent's final hand type, while BPP Final represents BPP's final hand type; that is, these represent the hand types they will have after all five cards are dealt. Whether or not BPP will win is the value of the variable BPP Win; this will deterministically depend on the final hand types of both players. At any given stage in the game, BPP's current hand type is represented by the node BPP Current (an observed variable), while OPP Current represents its opponent's current hand type. Since BPP cannot observe its opponent's current hand type, this must be inferred from the information available: the opponent's upcard hand type, represented by node OPP Upcards, and the opponent's actions, represented by node OPP Action. Note that until the final round BPP Current, OPP Current and OPP Upcards represent partial hand types (e.g., three cards to a flush).