How Computers Play Bridge
by Jason Rosenfeld and Stephen Smith

      Bridge-playing computer programs have become significantly better in the last few years as programming techniques improve and computer speeds increase. How do programmers teach computers to play such a difficult game? Every bridge program has its own secret techniques, but here are the general approaches that the top programs use.

      Computer programs have extensive agreements about all the details of their bidding systems that go far beyond the limits of a convention card. When the same program is playing for both players in a partnership, it knows exactly what partner’s 3 bid means in the auction Pass-Pass - 1 - Dbl - 1 - 1 - Pass - 2 - 3 - 3. A program never has a bidding misunderstanding with another copy of itself.

      However, even these very extensive agreements cannot cover all possible bidding situations. When a program encounters a situation that isn’t covered by its agreements, it uses a technique called “simulation.” The program imagines possible hands that partner and the opponents might have, based on the bidding so far, and constructs dozens of possible complete deals. Then, for each of these deals, the program projects the hypothetical result of playing out the deal, depending on which bid the program makes next. The program then makes the bid that has the best chance of leading to the best result on these dozens of deals.

      Programs even use this simulation technique in situations covered by their bidding agreements. For example, let’s say the auction so far is:

West	North	East	South
		1	1
2	2	4	?

      A program is trying to decide on its bid as South. Even though the program has agreements on what 4, Double, or Pass would show, it is generally better for the program to simulate whether the best probable result would come from South declaring 4, from East declaring 4, or from East declaring 4 doubled. Just as a human would realize that a hand including a heart holding of 92 would worsen on this auction, the computer would discover from its simulation that a hand including a heart holding of 92 would tend not to take as many tricks.

      Programs also use this simulation technique throughout the play of the cards. When deciding which card to play as declarer, the program imagines dozens of possible hands for the defenders, based not only on the auction, but also on the cards played so far. Similarly, when deciding which card to play as a defender, the program imagines dozens of possible hands for declarer and partner. For each pair of possible hands, the program then projects the hypothetical result of playing out the deal, depending on which card the program plays next. The program then plays the card that is most likely to result in the best score. If the program is a defender, it pays careful attention to its partnership’s signaling agreements.

            This simulation technique has proven to be far better than depending totally on rules like “cover an honor with an honor.” However, simulation does need a few rules of bridge logic to help it along. For example, consider this situation:

	Q 4 2
	A Q 6 4
	A 4
	A K J 3
			5 3
			9 7 3 2
			K 9 7 5 2
			Q 2

West	North	East	South
	1	Pass	1
Pass	4	All	Pass

      Partner leads the A, K, and a third round of spades, and the program ruffs. Now if the program ignores all rules of bridge logic and just simulates an omniscient declarer, the program might lead the Q! Why? Well, the program knows that an omniscient declarer would play the A and K to drop the Q from the program’s hand. But with a few rules of bridge logic, the program realizes that declarer is not omniscient and might finesse the J, losing to the Q; thus, the program plays a different card.

      The hardest card play problem for a program is the opening lead. For the opening lead, the program must imagine dozens of possibilities for three unseen hands: partner’s and declarer’s hands, which will be unseen through the rest of the play, as well as dummy’s hand, which will not.

      No one knows for sure when computers will be better bridge players than human experts, if ever. But as computers become stronger and stronger, they become more challenging opponents for people, as well as more capable partners—partners that never criticize and never tire. We hope that bridge programs can help players practice and enjoy this game that we love.

The authors are Bridge Baron programmers.