# Suit Combinations - Deriving Optimum Suit Plays

Deriving Optimum Suit Plays

Within the simplified setting, declarer's optimal play of a suit combination may be derived using well-established game theory, namely the theory of two-person zero-sum games. Crowhurst generally covers two alternative objective functions for every suit combination in the catalog. One is the (maximum) expected number of tricks won, or tricks expectation. Another is the (maximum) probability of winning a salient specific number of tricks such as three for a combination with four cards in each hand.

This means that an objective function to be maximised is specified. For suit play purposes, this objective function (or goal) is usually taken to be the likelihood of making a specified minimum number of tricks.

Given this objective, all lines of play are checked against all possible defenses for each distribution of opponent's cards, and the objective function is determined for each of these cases. Each line of play combined with each distribution of opponent's cards can then be assigned a minimum value of the objective function resulting from the best defense for that layout. The optimum line of play is selected as the line that maximises the minimum value of the objective function averaged over all possible layouts. As a result, the optimum solution to the suit combination takes into account all lines of defense (including all forms of falsecarding), and guards against the best lines of defense, but is not necessarily optimal in terms of exploiting errors made by the defense.

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