Applying Equivalence Class Methods in Contract Bridge

One of the challenges in analyzing the strategies in contract bridge stems from the fact that it is a Bayesian game with a very large type space, and that players’ action sets depend on their type. This results in a the strategy space being of a size where brute force methods of analysis are not practical. We present a general approach to simplifying this strategy space through the use of equivalence clases over types. The equivalence classes are chosen in such a way that the strategy needs to conditions on less information, thereby reducing the effective size and richness of the strategy. A common subproblem in bridge, the finesse play, is used as an example in applying this approach. Several types of finesses are described and modelled formally, along with the corresponding equivalence classe. The reduction in the strategy space as a result of the equivalence class representation is demonstrated on these examples. We then discuss possible methods of improving or extending this approach to larger subproblems in bridge.