One of the first areas identified as a weakness in BPP was the assumed independence between opposing players' hands. Since both hands are dealt from the same deck, it is known that this is indeed not the case. If one player was known to be holding three aces, that should have an effect on our belief in the number of aces their opposing player is likely to have (or be dealt in future).
To introduce this dependence to the network, an arc was added connecting the final hands of both players allowing the knowledge of one hand to be employed in determining the unknown cards of the other as can be seen in Figure 3. The conditional probabilities for each type of final hand for BPP, given that the final hand type of the opponent is of a certain kind, were then estimated by dealing out 10,000,000 pairs of hands.
