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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).
Next: Hand Types
Up: A Bayesian Network for
Previous: A Bayesian Network for
Jason R Carlton
20001113