I agree. The number one error made by people with statistical knowledge is to assume independence of events. Even very smart and very educated people tend to ma

I agree. The number one error made by people with statistical knowledge is to assume independence of events. Even very smart and very educated people tend to make this mistake rampantly. I hypothesize it is due to the education curriculum being very slanted in the direction of assuming independence everywhere because it makes the math easier, but I can't prove this. In the real world, true and full independence should be considered an exception rather than the norm. Saying that Neimann is a very good chess player is basically a restatement of the fact that his previous records are likely clean. Nobody was accusing him of constant cheating before. (Cheating once is relatively easy. Cheating continuously, in multiple different environments, and leaving no trace, is hard.) The entire question at hand is essentially "Is Neimann's probability of cheating correlated with playing Magnus Carlson?" (and a family of similar questions can be asked) and no amount of analysis of his games not played against Magnus Carlson will answer that. As for why the probability of cheating would be correlated with playing Magnus Carlson, again, no amount of consulting the statistics will be able to answer that question, but for anyone who is a human being with human foibles the answer is fairly obvious. Someone used to double checking premises will observe that there's not much in this question statement specific to Neimann. The fact that he's cheated before does raise his particular probability, but you could ask this about anyone. And my reply to that would be, yes, that is indeed how things work, and is exactly why these high stakes games are played with more formality and more security than a pick-up game in a city park. Neimann's prior cheating does raise the question with a bit more urgency, but we generally assume a priori that anyone might be interested in cheating in a game with Magnus Carlson, and high level play in general, and act accordingly. agarden in a sibling post suggests that the analysis itself goes deeper, which sounds more interesting. I am speaking only to what is in the linked article. It would be far from the first time a reported simplified a complex and nuanced argument into something useless, and I thought the point about independence is still worth posting.