Results

This section contains the experimental results for the addition of the extra arc representing hand dependence as well as for hand refinement. Both the individual effect of each enhancement and their combined result are discussed.

Figure 4 shows the results of playing modified versions of BPP against the original version of BPP (which will be used as a baseline for comparison of the effectiveness of an enhancement). The horizontal axis shows the number of games played, while the vertical axis shows the cumulative winnings of the original BPP (negative winnings represents a win for the network implementing a newly developed feature).

  

Figure 4: Cumulative winnings of original BPP against players which are able to represent hand dependence and have refined hand classification.

The addition of the arc to the network alone did not appear to make any significant impact in the quality of play breaking practically even, losing $0.0031 \pm 0.0268$ units per game ( $t = -0.1151; p \le 0.025$).

The model featuring refined hand classes showed a significant improvement in play ( $t = 2.5240; p \le 0.025$), winning $0.0672 \pm 0.0266$ units per game most likely due it's ability to distinguish between common hand types.

Interestingly, when both enhancements are combined, it appears that the introduction of modeling the dependence between hands does improve playing performance significantly ( $t = 3.0672; p \le 0.025$). The combined improvements make a profit of $0.0842 \pm 0.0275$ units per game when played against the original network. This indicates that the two features are apparently highly dependent and only with significant refinement of hands does modeling the dependence of each players hands have any influence on performance. The lack of improvement when hand dependence was implemented alone can most probably be explained by the fact that most of the arcs effect takes place when both players are holding similar hands. (Eg. The arc reduces the likelihood of both players are holding a pair of queens). As this situation occurs mostly for paired hands, much of the extra knowledge introduced by the arc was being lost due to a large number of paired hands being lumped together. With the addition of the node refinement, the additional information provided by the introduction of the arc was used more effectively and a significant influence was being made to the posterior probability of winning.