Statistical evidence of fraud

Professor Ken Regan of SUNY Buffalo has written a detailed article about the recent allegations of fraud in a high-level chess tournament in Europe: The Crown Game Affair.

Regan describes the complexity of attempting to develop statistical evidence of fraud:

My report describes two main tests, which are partially independent. Presumably their combined confidence would be higher, though I have not yet worked out how to do this numerically. Several alternative specifications for the tests, such as using the player’s rating before rather than after the tournament as the main baseline, excluding one (or two) game(s) where public transmission of moves was switched off amid suspicion of him, and excluding moves after (say) move 70 in very long games when the time available to think might be too short for some cheating mechanisms, exhibit much higher deviations. Although the “Intrinsic Rating” component does not accompany a statement of odds, it indicates that the inherent quality of the moves, as judged by computers, was highly significantly beyond what goes with a 2700-level performance.

Although this is a challenge, Regan is confident that the results are definitive:

Here 2600 is a chess rating that usually distinguishes a “strong grandmaster,” while my own rating near 2400 is typical of the lesser title called “international master,” and Ivanov’s pre-tournament rating of 2227 is near the 2200 floor to be called any kind of master. Although Magnus Carlsen recently broke Garry Kasparov’s all-time rating record to reach 2861, my program for “Intrinsic Ratings” clocked Ivanov’s performance in the range 3089–3258 depending on which games and moves are counted according to supplementary information in the case, all higher than any by Carlsen and his two closest pursuers enumerated by me

The New York Times notes that statistical evidence may be the only evidence that exists in this case: A Quandary for the Game in a High-Tech Era.

A third-place finish at a tournament last month by a formerly obscure player was so startling that organizers searched his clothing and took apart his pen looking for evidence that he had outside help. They found nothing.

But the episode has again raised the question of how officials can monitor games in an era when technology is so advanced, and it set off concerns about how such suspicions will affect the game. If every out-of-the-ordinary performance is questioned, bad feelings could permanently mar the way professional players approach chess.

Chess, of course, is not the only sport that continually struggles with the problem of maintaining fair competition: just look to this week's cycling news for a much higher profile example, or to this fascinating story from last fall for a more intriguing example.

But chess is somewhat unique in the man-machine symbiosis aspect; indeed, a number of people have suggested that chess as a whole might benefit from a more open acceptance of computers, as in the recent development of Advanced Chess, also called Freestyle Chess, Cyborg Chess, and Centaur Chess.

Today, however, the humans had the day, as World Champion Vishy Anand played perhaps the most brilliant game of his decades-long spectacular career, a devastating annihilation of world #2 Levon Aronian, with the black pieces no less!.

The day of the computers draws ever closer, but Anand's scintillating performance today is one to treasure.