Kramnik vs. Nakamura: A Chess Scandal

We provide a statistical analysis of the recent controversy between Vladimir Kramnik (ex-chess world champion) and Hikaru Nakamura. Hikaru Nakamura is a chess prodigy and a five-time United States Chess Champion and a top player in online blitz chess. Kramnik called into question Nakamura’s 45.5 out of 46 win streak in an online blitz contest at chess.com. We evaluate the weight of evidence using the a priori assessment of Viswanathan Anand and the observed streak. Using Bayesian analysis, we show that Nakamura has a 99.65% probability of not cheating given Anand’s prior that one in 10000 players cheats. We demonstrate that Kramnik’s argument falls into the Prosecutor’s Fallacy, a statistical reasoning error that confuses the probability of observing the evidence given innocence with the probability of innocence given the evidence. We conclude with a discussion of the relevant statistical literature on streak analysis in sports and fraud detection.