Using dynamic programming to determine an optimal strategy in a contract bridge tournament

Abstract

One form of contract bridge tournament comprises several rounds of matches in which players compete as pairs for ‘masterpoints’ awarded for each match won or drawn and for being highly placed at the end of the tournament. In the second and subsequent rounds, pairs are matched against other pairs that have been approximately equally successful so far. There has been vague discussion among bridge players of the possible advantages of ‘throwing’, that is, deliberately losing a match in round r so as to obtain a lower ranking and face an easier opponent in round r+1. This paper uses dynamic programming and data from one tournament to identify an optimal strategy (either ‘throw’ or ‘play to win’). The optimal strategy is a function of a pair's ability, its placing after each round, the relative rewards for winning a match and finishing high, the opponent's skill, and the round. For example, we find that a very weak pair should ‘throw’ and ‘play to win’ in alternate rounds.

Keywords:

• dynamic programming
• sports
• recreation
• optimization
• contract bridge
• deliberately losing

Acknowledgements

The author gratefully acknowledges the incisive comments of many colleagues and referees.