Did Carlsen quit because he believed that Niemann cheated? A Reddit reading list.
Lots of speculation, but the burden of proof is very much on the accusers.
Magnus Carlsen’s loss to Hans Niemann in round 3 of the Sinquefield Cup was certainly a surprise, and Niemann’s examining precisely the very unusual line seen in the game that morning was odd as well. Does this mean that Niemann cheated, or that it’s at least more probable than not that he did, or even that it’s a reasonable hypothesis?
No.
When evaluating a hypothesis, it’s not enough to ask whether the evidence fits a hypothesis. One must also ask, for example, about the prior probability of that hypothesis. My carpet needs vacuuming, but from this I shouldn’t conclude that my home was visited by dust gnomes, who are indetectable creatures who subtly deposit dust on carpeted floors when a home’s occupant isn’t looking. My carpet looks just as one would expect, given the existence of those mischievous gnomes, but barring some independent reason to think these annoying dust-bearers exist we should stick to the belief that my carpet’s dust got there in the usual way. Likewise, the prior probability that Niemann would cheat is exceedingly low: there’s no actual evidence of his having done so, it’s an insanely risky thing to do as getting caught would ruin his career, he played a very good but not impeccable game, etc. It’s not impossible that Niemann cheated, but that’s not how these things work. It’s not impossible, as far as I know, that there are dust gnomes or that the moon landings were faked, but that doesn’t mean I have any reason whatsoever to accept those hypotheses.
Anyway, for those who want to read up on this sordid affair, you’ll find a well-curated list of sources on this Reddit page. The latest twist in the drama is Chess.com’s banning Niemann from their Global Chess Championship, which if justified undermines Niemann’s claims about his own integrity. (That wouldn’t prove that he cheated OTB against Carlsen, but it certainly wouldn’t help his credibility.)
Concise and well-stated. If the prior proability of the hypothesis is indeed low then we shouldn't blindly believe it.
However, I don't know the prior probability of him cheating in a major OTB tournament. Having previously cheated online, his motivation to do well and the importance of this tournament, the stakes involved, the danger of getting caught and the fact that he is confident (arrogant?) about his own chess abilities, I'd have said maybe in the range 1% to 10%. Are you willing to put forward an estimate?
Good luck with those priors! What's your prior, for example, of Carlsen walking out of a tournament for no good reason? I haven't checked this carefully, but I would bet my bottom dollar that the result of conditioning on the totality of evidence in this case is going to be acutely sensitive to the ratio of one very small number to another, the estimation of which is going to be more or less completely arbitrary.