One upshot is that Schaeffer now possesses software that can play unbeatable checkers. Indeed, go to his Web site and you can play online yourself, providing you're prepared to lose again and again and again -- or maybe, just maybe, fight to a draw, assuming you, too, play with the crystalline perfection of a silicon brain.

Schaeffer did not solve checkers by replicating human intuition or game-playing ability. Rather, he employed what’s known as a “brute force” attack. He programmed a cluster of computers to play out every possible position involving 10 or fewer pieces. At the peak of his labors, he had 200 computers working around the clock on the problem, both in Alberta and down in California. (The data requirements were so high that for a while in the early '90s, more than 80 percent of the Internet traffic in western North America was checkers data being shipped between two research institutions.)

The brute-force method is slow, which is its big limit. Schaeffer says he suspects you couldn’t use it to solve chess, because that game -- with between 10 to the 40th and 10 to the 50th possible arrangements of pieces -- is far more complicated than checkers, which has 5 × 10 to the 20th positions. “Chess won't be solved in my lifetime,” he predicts. “We need some new breakthrough in technology to do that. CLIVE THOMPSON