Kramnik vs Nakamura: A Chess Scandal

TL;DR

This paper analyzes a controversy in chess involving allegations of cheating, using statistical methods to evaluate the probability of Nakamura's winning streak and discussing common fallacies in such analyses.

Contribution

It introduces a rigorous statistical framework to assess cheating allegations in chess, highlighting fallacies and providing a probabilistic estimate of Nakamura's innocence.

Findings

Nakamura has a 99.6% chance of not cheating based on streak analysis.

The Prosecutor's Fallacy is common in cheating accusations.

Cherry-picking and fallacies undermine the validity of some claims.

Abstract

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. Kramnik called into question Nakamura's 45.5 out of 46 win streak in an online blitz contest at chess.com. We assess the weight of evidence using a priori assessment of Viswanathan Anand and the streak evidence. Based on this evidence, we show that Nakamura has a 99.6 percent chance of not cheating. We study the statistical fallacies prevalent in both their analyses. On the one hand Kramnik bases his argument on the probability of such a streak is very small. This falls precisely into the Prosecutor's Fallacy. On the other hand, Nakamura tries to refute the argument using a cherry-picking argument. This violates the likelihood principle. We conclude with a discussion of the relevant statistical literature on the topic of fraud detection and the analysis of streaks in sports data.