A mathematical proof shows that checkers always results in a draw when neither player makes a mistake. For computer-game aficionados, the game is now “solved.”

The computer proof took Jonathan Schaeffer, a computer-games expert at the University of Alberta in Canada, 10^14 calculations over 18 years to complete and is one of the longest running computations in history.

Schaeffer has also released online an updated version of a checkers-playing program called Chinook that cannot be beat.