Computer Bridge; a Big Win for AI Planning

Article excerpt

* A computer program that uses Al planning techniques is now the world champion computer program in the game of Contract Bridge. As reported in The New York Times and The Washington Post, this program--a new version of Great Game Products' BRIDGE BARON program--won the Baron Barclay World Bridge Computer Challenge, an international competition hosted in July 1997 by the American Contract Bridge League.

It is well known that the game tree search techniques used in computer programs for games such as Chess and Checkers work differently from how humans think about such games. In contrast, our new version of the BRIDGE BARON emulates the way in which a human might plan declarer play in Bridge by using an adaptation of hierarchical task network planning. This article gives an overview of the planning techniques that we have incorporated into the BRIDGE BARON and discusses what the program's victory signifies for research on Al planning and game playing.

One long-standing goal of Al research has been to build programs that play challenging games of strategy well. The classical approach used in Al programs for games of strategy is to do a game tree search using the well-known minimax formula (eq. 1) The minimax computation is basically a bruteforce search: If implemented as formulated here, it would examine every node in the game tree. In practical implementations of minimax game tree searching, a number of techniques are used to improve the efficiency of this computation: putting a bound on the depth of the search, using alpha-beta pruning, doing transposition-table lookup, and so on. However, even with enhancements such as these, minimax computations often involve examining huge numbers of nodes in the game tree. For example, in the recent match between DEEP BLUE and Kasparov, DEEP BLUE examined roughly 60 billion nodes for each move (IBM 1997). In contrast, humans examine, at most, a few dozen board positions before deciding on their next moves (Biermann 1978).

{our payoff at the node p if p is a terminal node minimax (p) = {max{minimax(q) q is a child of p} if it is our move at the

node p

{min{minimax(q) q is a child of p} if it is our opponent's move

at the node p

Equation 1. Minimax Formula.

Although computer programs have done well in games such as Chess and Checkers (table 1), they have not done as well in the game of Contract Bridge. Even the best Bridge programs can be beaten by the best players at many local Bridge clubs.

Table 1. Computer Programs in Games of Strategy. This is an updated and expanded version of similar tables from Schaeffer (1993) and Korf (1994).

Connect Four            Solved
Go-Moku                 Solved
Qubic                   Solved
Nine-Men's Morris       Solved
Othello                 Probably better than any human
Checkers                Better than any living human
Backgammon              Better than all but about 10 humans
Chess                   Better than all but about 250 humans,
                        possibly better
Scrabble                Worse than best humans
Go                      Worst than best human 9 year olds
Bridge                  Worse than the best players at many
                        local clubs

One reason why traditional game tree search techniques do not work well in Bridge is that Bridge is an imperfect-information game. Because Bridge players don't know what cards are in the other players' hands (except for, after the opening lead, what cards are in the dummy's hand), each player has only partial knowledge of the state of the world, the possible actions, and their effects. If we were to construct a game tree that included all the moves a player might be able to make, the size of this tree would vary depending on the particular Bridge deal--but it would include about 5. …

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