In late November, the latest official world chess championship match was staged in a large hall in the Olympic city of Sochi, Russia. The games were broadcast on the Internet with live commentary and followed by millions around the world. Vladimir Putin even spoke at the closing ceremony. The winner,Magnus Carlsen, has the highest chess rating ever and has been acclaimed by other grandmasters as the greatest player of all time. But perhaps a small asterisk should be attached to his records.

That’s because the two best chess...