Kramnik vs Nakamura: A Chess Scandal
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866910598819741696 |
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| author | Maharaj, Shiva Polson, Nick Sokolov, Vadim |
| author_facet | Maharaj, Shiva Polson, Nick Sokolov, Vadim |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_06739 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Kramnik vs Nakamura: A Chess Scandal Maharaj, Shiva Polson, Nick Sokolov, Vadim Applications 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. |
| title | Kramnik vs Nakamura: A Chess Scandal |
| topic | Applications |
| url | https://arxiv.org/abs/2409.06739 |