Computer Program Can’t Lose at Checkers

Published 12:00 am Monday, December 26, 2005

WASHINGTON – Perhaps Chinook, the checker-playing computer program, should be renamed “King Me.” Canadian researchers report they have “solved” checkers, developing a program that cannot lose in a game popular with young and old alike for more than a thousand years.

“The program can achieve at least a draw against any opponent, playing either the black or white pieces,” the researchers say in this week’s online edition of the journal Science.

“Clearly … the world is not going to be revolutionized” by this, said Jonathan Schaeffer, chairman of the department of computing science at the University of Alberta.

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The important thing is the approach, he said. In the past, game-playing programs have used rules of thumb _ which are right most of the time, he said _ to make decisions.

“What we’ve done is show that you can take nontrivial problems, very large problems, and you can do the same kind of reasoning with perfection. There is no error in the Chinook result. … Every decision point is 100 percent.”

Schaeffer’s team started with the end of a game with just one checker on the board. Then the team looked at every possible position with two checkers, on up to 10 checkers on the board.

Every combination of 10 checkers offers 39 trillion positions for the endgame, he said. Chinook can calculate them all.

It does not matter how the players make it to 10 checkers left because from that point on, the computer cannot lose, Schaeffer said. For two players who never make a mistake, every game would be a draw, he said.

“‘Checkers is solved’ is an intriguing title for this wonderful and delightful article about another former human skill falling to the ubiquitous computer,” said Ernest L. Hall, director of the Center for Robotics at the University of Cincinnati.

That does not mean an end to people playing checkers, said Hall, who was not part of Schaeffer’s research team. Even though a computer beat the world chess champion, people still enjoy and play the that game.

“Anything we can do to encourage the further study of science and engineering, of developing problem solvers for the many known needs of the world, should be encouraged,” Hall said. “So I applaud Schaeffer for making a breakthrough in computer problem solving for the game of checkers. It may encourage others to solve the other games we encounter in life.”

Schaeffer’s proof is what is called a “weakly solved” result. It calculates the result from an initial position _ 10 pieces on the board _ rather than from the beginning of the game.

Could Schaeffer’s team produce a “strong solution” by calculating every position from the beginning of a game? Maybe, but there is not enough computer power available, he said. It took more than 18 years to get where they are now.

How about chess? Current chess computers still rely on rules of thumb rather than trying to study every possible position, Schaeffer noted.

“Checkers has roughly the square root of the number of positions in chess,” the researchers said. “Given the effort required to solve checkers, chess will remain unsolved for a long time, barring the invention of new technology.”

Next week, Polaris, a poker-playing computer program built by Schaeffer and his colleagues, will challenge two poker professionals in a $50,000 man versus machine poker game in Vancouver, British Columbia, as part of the annual conference for the Association for the Advancement of Artificial Intelligence.

The checkers research was supported by the Natural Sciences and Engineering Research Council of Canada, Alberta’s provincial technology organization iCORE, Canada Foundation for Innovation, Western Canada Research Grid and the University of Alberta.

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