BRIBIP: A Bridge Bidding Program

capable of making decisions in an environment of imperfect information. It is frequently necessary that such decisions be made in real life-as, for example, the decisions made in the day-today running of a firm. As a paradigm of such situations, the game of Contract bridge (3) was chosen, for several reasons: 1) Despite being a game of imperfect information, it is well-defined: in particular, tne scoring systems give a way of assessing the strength of any resulting program. 2) Although for any one player in the game, there is an environment of imperfect information, the four players between them have total knowledge of any situation. This leads naturally to a program based on explicit reasoning about why the other players react as tney do, rather than a probablistic approacn. This can be contrasted with games sucn as poker, where not all the cards are dealt, and thus a probablistic approach is necessary, even for humans. In fact, an earlier program (11), based on a probablistic approach, was written, and found to be unsatisfactory because the resulting data-structures were not subtle enough to reflect the logical processes needed to play a good game, and because the probablistic approach severely underestimated the need for a detailed plan. In view of these difficuties the current program, which can make explicit deductions in a Conniver-like fashion, has been built. 3) Tnere is a great deal of literature on the theory of bridge, and hence a wealth of suggestions as to how the program should work. Many of these suggestions are not in an immediately useful form-for example "When it is hoped to add the possibility of a pseudo-squeeze to the other chances, one should first casn the winners in the suit where the length is visible in dummy"-but they can be modified to suit our needs. However, many are in an immediately useful format, and can be straightway represented in the program-for example "Open on 12 or more points and at least four of the suit", etc. 4) The author is interested in bridge to the extent of representing Essex University in club competitions. The last two reasons are closely connected, and reflect a thesis which underlies this research: that the best way to produce an intelligent program is to code into it expert knowledge. This has been seen to be true of chess (2), and of checkers, where Samuel (9, 10) cooperated with …