A Planning Approach to Declarer Play in Contract Bridge

Abstract

Although game-tree search works well in perfect-information games, it is less suitable for imperfect-information games such as contract bridge. The lack of knowledge about the opponents' possible moves gives the game tree a very large branching factor, making it impossible to search a significant portion of this tree in a reasonable amount of time.<P>This paper describes our approach for overcoming this problem. We represent information about bridge in a task network that is extended to represent multi-agency and uncertainty. Our game-playing procedure uses this task network to generate game trees in which the set of alternative choices is determined not by the set of possible actions, but by the set of available tactical and strategic schemes.<P>We have tested this approach on declarer play in the game of bridge, in an implementation called Tignum 2. On 5,000 randomly generated no-trump deals, Tignum 2 beat the strongest commercially available program by 1394 to 1302, with 2304 ties. These results are statistically significant at the a = 0.05 level. Tignum 2 searched an average of only 8745.6 moves per deal in an average time of only 27.5 seconds per deal on a Sun SPARCstation 10. Further enhancements to Tignum 2 are currently underway.