• The chess world was rattled in late 2022 when Magnus Carlsen, the current world champion, accused Hans Niemann, a 19-year-old U.S. chess grandmaster, of cheating using a chess-playing artificial intelligence (AI) system.
  • Niemann had defeated Carlsen, prompting Carlsen’s accusation; Niemann asserted that he had defeated Carlsen fairly even though he later admitted to having cheated twice in online chess games at the ages of 12 and 16.
  • A month later, a 72-page investigation report drafted by claimed that Niemann had “likely cheated” more than a hundred times while playing online chess.
  • But the report also said, “There is no direct evidence that proves Hans cheated at the September 4, 2022, game with Magnus.”

How can you tell when a player has cheated?

  • First, researchers build a statistical model using the database of millions of finished chess matches. Then they estimate the probability that a human player’s move will coincide with a move made by a chess engine using the fitted model.
  • By feeding records of Niemann’s games into chess engines, some experts discovered that Niemann had played a lengthy series of AI-recommended moves in tournament games and that his tactics were frequently similar to those of a computer. But some experts contended that the onboard movements in actual games of many players could resemble those of an AI, since human players’ training, preparation, and practices are now affected by these engines as well.
  • The Carlsen-Niemann dispute may finally be decided in court: Niemann has sued Carlsen, and chess prodigy Hikaru Nakamura, who also accused Niemann of cheating in online games, for $100 million for defamation.

How reliable is statistics?

  • An infamous criminal case from the U.K. involving a woman named Sally Clark is a prime example of how the use of false statistics resulted in an injustice.
  • Following the untimely deaths of two of her infant children from sudden infant death syndrome (SIDS) on separate occasions, Clark was accused of murder. A paediatrician said that the probability of a random SIDS death when the mother is older than 26, affluent, and a nonsmoker, is 1 in 8,543.
  • So the probability of two such deaths, the expert continued, was computed as 1/8,543^2, or 1 in 73 million. Clark was promptly convicted in 1999.
  • But the Royal Statistical Society disagreed and said there was “no statistical basis” for the paediatrician’s figure.
  • In fact, the paediatrician had committed the ‘prosecutor’s fallacy’ by wrongly considering the two deaths to be independent.
  • When Ray Hill, a mathematics professor at the University of Salford, examined additional data in 2002, he concluded that the chance of a second child dying of SIDS given that a first child had died of SIDS might be as high as only 1 in 60! Clark was thus released from jail in 2003.
  • Carlsen has expressed a belief that cheating is “an existential threat” to chess. It might be tempting, against this backdrop, to see the future of this 1,500-year-old game lying even in part in the hands of the Carlsen-Niemann case, specifically in the proper use of statistics and their interpretation. But there will be several ways to calculate and interpret them, just as the case itself can swing either way.
  • For example, according to analysis by an anonymous Chessbase user called gambit-man, Niemann has an unusually high number of games with near 100% engine correlation.
  • Niemann’s defence might be that his play is far less computer-like than Carlsen’s has been in the recent past.
  • There is a metric called centipawn loss: it measures how much worse a player’s moves were compared to the engine’s top choice. A lower value indicates a closer match to the engine’s choice.
  • There’s another metric called depth: the number of forthcoming moves by a single player that a chess engine tries to predict. Compared to the open-source chess engine Stockfish (v. 15) at depth 18, Niemann’s and Carlsen’s centipawn loss scores are 25.6 and 16.9, respectively.

So who wins the argument?

  • It’s hard to say. Perhaps we will never know for sure if Niemann really cheated because statistical analyses only suggest whether cheating may have occurred; they don’t provide absolute verdicts.
  • The only thing of which we can be reasonably certain is that whoever wins the case, an honest game of chess needn’t hang in the balance — but not for the reasons Carlsen is concerned about.


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