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?
For me, 2% is at the high end and I'm inclined to think it's below 1%...but that's based on my quite possibly outdated knowledge of possible methods of cheating. The players were wanded and there were no spectators (or were there?) because of Covid concerns, so how would he have done it? A Houston Astros fan banging a garbage can outside the building a certain number of times? Cheating online is easy (which is not to say that one will get away with it) - unless there are cameras on a player, and of course there aren't for ordinary games, which is the context of Niemann's self-confessed cheating three years ago. A player simply runs a second computer and judiciously decides to cheat at this spot or that, and not necessarily with the very best move. It's also a relatively low-stakes environment, so unless the cheating is egregious, who's going to investigate or even care very much? As long as you don't trip the cheating-detection software, you're home free. (At least that's the theory.) And if you are caught, well, it's embarrassing, but there are other servers and, most importantly, there's still real life (i.e. rated over-the-board chess).
If you cheat in real life, you don't have a career. That jacks up the risk-reward stakes tremendously. Of course, people do it anyway - even some GMs - but Niemann would have to be incredibly foolish to do so given how much he has to lose and how well things are going for him. He could be that foolish, but I assign it a low probability, especially given that he has been caught twice before in earlier years and knows that (a) he can be caught and (b) may not receive the benefit of any doubt.
So, low priors for me, but based on skepticism about the feasibility of cheating. If it is considerably easier than I'm assuming, then my priors will get jacked up.
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.
Given Carlsen's willingness to surrender his title without playing and his remark near the end of the Crypto Cup that he hasn't been motivated in a long time, and his being fabulously wealthy and the most important figure in chess by a colossal margin, and...I could add other things...that prior isn't going to be infinitesimal.
But I think "for no good reason" is ambiguous, between an objective and a subjective interpretation. (We're assuming that the reason or reasons in question have to do with something untoward happening in the context of his game vs. Niemann.) Assuming that there's nothing concrete that Carlsen knows and that we don't (and if there was, wouldn't Carlsen have proclaimed it?), there doesn't seem to be any objectively good reason - at least none that seems to me (and many world-class players) anywhere near good enough.
But subjectively, he may have a good reason. It's a commonplace for someone in the throes of a situation to evaluate what's happening one way, while those on the outside see it very differently, even with access to the same data set. Sometimes the insider perspective proves correct, and often it doesn't. Regardless, it makes a difference, and Carlsen has not exactly shown himself to be a Stoic sage over the years.
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?
For me, 2% is at the high end and I'm inclined to think it's below 1%...but that's based on my quite possibly outdated knowledge of possible methods of cheating. The players were wanded and there were no spectators (or were there?) because of Covid concerns, so how would he have done it? A Houston Astros fan banging a garbage can outside the building a certain number of times? Cheating online is easy (which is not to say that one will get away with it) - unless there are cameras on a player, and of course there aren't for ordinary games, which is the context of Niemann's self-confessed cheating three years ago. A player simply runs a second computer and judiciously decides to cheat at this spot or that, and not necessarily with the very best move. It's also a relatively low-stakes environment, so unless the cheating is egregious, who's going to investigate or even care very much? As long as you don't trip the cheating-detection software, you're home free. (At least that's the theory.) And if you are caught, well, it's embarrassing, but there are other servers and, most importantly, there's still real life (i.e. rated over-the-board chess).
If you cheat in real life, you don't have a career. That jacks up the risk-reward stakes tremendously. Of course, people do it anyway - even some GMs - but Niemann would have to be incredibly foolish to do so given how much he has to lose and how well things are going for him. He could be that foolish, but I assign it a low probability, especially given that he has been caught twice before in earlier years and knows that (a) he can be caught and (b) may not receive the benefit of any doubt.
So, low priors for me, but based on skepticism about the feasibility of cheating. If it is considerably easier than I'm assuming, then my priors will get jacked up.
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.
Given Carlsen's willingness to surrender his title without playing and his remark near the end of the Crypto Cup that he hasn't been motivated in a long time, and his being fabulously wealthy and the most important figure in chess by a colossal margin, and...I could add other things...that prior isn't going to be infinitesimal.
But I think "for no good reason" is ambiguous, between an objective and a subjective interpretation. (We're assuming that the reason or reasons in question have to do with something untoward happening in the context of his game vs. Niemann.) Assuming that there's nothing concrete that Carlsen knows and that we don't (and if there was, wouldn't Carlsen have proclaimed it?), there doesn't seem to be any objectively good reason - at least none that seems to me (and many world-class players) anywhere near good enough.
But subjectively, he may have a good reason. It's a commonplace for someone in the throes of a situation to evaluate what's happening one way, while those on the outside see it very differently, even with access to the same data set. Sometimes the insider perspective proves correct, and often it doesn't. Regardless, it makes a difference, and Carlsen has not exactly shown himself to be a Stoic sage over the years.