As he worked to create a chess computer, he realized that the approach he had previously used — trying to get a computer to use logic — was never going to be as effective as brute force, having the computer analyze as many moves as possible. The problem was that the number of possible moves in a chess game is estimated to rival the number of atoms in the universe. How could a computer tackle such a task?

He looked for a solution by programming a computer to play what he thought was a simpler game: backgammon. But that was also extremely complex: There were about 60 possible moves at any one time, and 21 possible results from the roll of the dice.

He designed a program that played backgammon well up to a point, but something would almost invariably go wrong. He analyzed the problem and discovered that the computer made mistakes when the situation in the game began to change — for example, when the computer went from having a clearly better position to one in which the outcome was in doubt — and the program failed to adjust its strategy. He applied fuzzy set theory to allow the program to make estimates of possible outcomes, and that worked.

In July 1979, the newly redesigned program, called BKG 9.8, played and won a match, 7-1, against Luigi Villa, the reigning world backgammon champion. Mr. Berliner’s program thus became the first to defeat a world champion at any board game, though he acknowledged that the program had better dice rolls than Mr. Villa throughout the match.

Mr. Berliner returned to building a chess computer, working with some of his students, including Mr. Ebeling, who went on to become one of the country’s best-known computer experts, and Murray Campbell, who was later part of the team that designed and built Deep Blue, the computer that beat Garry Kasparov, the reigning champion, in 1997.

In spring 1985, the new computer, HiTech, made its debut. It quickly ascended to the rank of master and then to senior master, becoming the world’s strongest chess computer. In 1988, it became the first computer to beat a grandmaster in a match, defeating Arnold Denker, 3.5 to 0.5, though Mr. Denker was well past his prime.