07.20.07
Rats! Checkers has been solved
A computer program named Chinook vanquished its human competitors at tournaments more than a decade ago. But now, in an article published Thursday on the Web site of the journal Science, the scientists at the University of Alberta who developed the program report that they have rigorously proved that Chinook, in a slightly improved version, cannot ever lose. Any opponent, human or computer, no matter how skilled, can at best achieve a draw.
In essence, that reduces checkers to the level of tic-tac-toe, for which the ideal game-playing strategy has been codified into an immutable strategy. But checkers — or draughts, as it is known in Britain — is the most complex game that has been solved to date, with some 500 billion billion possible board positions, compared with the 765 possibilities in tic-tac-toe.
Even with the advances in computers over the past two decades, it is still impossible, in practical terms, to compute moves for all 500 billion billion board positions. So, the researchers took the usual starting position and looked only at the positions that occurred during play.
“It’s a computational proof,” said Jonathan Schaeffer, a professor of computer science at the University of Alberta who led the effort. “It’s certainly not a formal mathematical proof.” That means it is impossible for anyone to check every calculation the computer has performed.
Because of the vast calculations, the researchers had to keep painstaking track of the data. Miscopying a single bit — a glitch that did occur every few months — could render their result incorrect if not caught and corrected. When an error was caught, calculations had to be restarted from that point. A checkers hobbyist has independently verified major components of the proof with another computer program.
Dr. Schaeffer began his quest in 1989, aiming to write software that could compete with top checkers players in the world. In April, 18 years later, he and his colleagues finished their computations.
“From my point of view, thank God it’s over,” Dr. Schaeffer said.
For an exercise in futility, anyone can play a game against the perfect Chinook at http://www.cs.ualberta.ca/~chinook/play/. (It is limited to 24 games at a time.)


