You are obviously someone who understands chess, both the game and its larger context(s). I hope you will find the time to read the beginning of a several part "chess piece" that I'm working on:
The short answer is that it fails to take prior probabilities into account. If all we knew is that Nepo blundered away a few games and that super-GMs rarely blunder, then there might be an argument there. But given the extreme unlikelihood that Nepo would take a dive and that Carlsen would presumably pay him to do so, Nepo's blunders only raise the likelihood of a thrown match from infinitesimal to (maybe) visible-with-a-microscope.
Now for the long answer:
Here are a couple of examples to illustrate the general idea. First, a popular chestnut in books on thinking, especially ones dealing with Bayesian reasoning. Suppose there's a dread disease that strikes one person in 10,000. Bad luck: you test positive for it, and the test is 99% accurate (1% of the time it gives a false positive, and there are no false negatives). What is the probability that you have the disease?
Second, suppose you tell me that you hear scratching sounds in your attic every night, and I explain that it might be a Night Gremlin. "What's a Night Gremlin?", you ask. I inform you that it's a supernatural creature that enters some people's attics at night, then materializes and starts scratching the floorboards. No one has ever seen a Night Gremlin, and there's no indirect evidence for them either; there's just the hypothesis which, it must be admitted, fits the facts perfectly. Should we believe in Night Gremlins?
The answers to the questions ending the paragraphs are 1 in 101 and no, respectively. In the case of the dread disease, the easiest way to see why the likelihood that one has it if they take a positive test is this: suppose that everyone in a random population of 10,000 takes the test; how many positive results will there be? The answer: 101, of which 100 are false positives (1 in 100 scales up to 100 in 10,000) and one is a person who actually has the disease. So the odds are 100 out of 101 that your positive was a false positive, and 1 in 101 that you have the disease. As for the Night Gremlins case, it's obvious that we shouldn't believe in them, even though the hypothesis explains the phenomenon perfectly. The problem is that the prior probability that Night Gremlins exist is vanishingly small, as there is no physical evidence, or indeed evidence of any sort, for their existence. That doesn't mean that they don't exist, but there's no reason to believe in them, and given ample alternative explanations of a conventional sort, we're not forced to posit Night Gremlins to explain the scratching in the attic.
And so it is with the fradulent match hypothesis. Carlsen and Nepo have everything to lose if they get caught, there's no evidence in either player's career of having done anything of this sort nor any evidence that there was a fix. There's also no obvious motive for Carlsen to get Nepo to take a dive, given the insane risks. You offer Nepo's 4-1 lead in decisive games [in classical chess] going into the match, but that's entirely misleading. Two of Nepo's wins came when they were boys, and Nepo's third win came way back in 2011. The most recent decisive games were split: Nepo went up 4-0 in 2017, and Carlsen finally struck back in 2019. Additionally, Carlsen not only won the last decisive classical game between them, but also enjoyed a substantial plus when it came to rapid and blitz games, and of course enjoyed the considerably higher rating. Another problem is that if Carlsen was so gung-ho on keeping his title, why is he giving it up now without a fight?
So, it seems to me that this theory is rather like Night Gremlins and thinking it 99% likely that one has the disease: it's only plausible if one ignores all the relevant information that goes into the prior probability of the hypothesis, and massively implausible when that information is taken into account.
Finally, I'm aware that players of practically all levels, from low-rated amateurs to GMs have thrown games. That makes the thrown-match hypothesis a very tiny bit more likely than it would otherwise be, but still very, very exceptionally unlikely. Think about why games are thrown: money (but both players are already well off, and unless Nepo was given millions of dollars the money he loses by not becoming champion outweighs any potential bribe - not to mention the incalculable damage to his reputation and ability for further earnings if he's caught) and qualification (but they've already at the top - unless there are interplanetary chess championships I'm unaware of, there is no next step).
Ok, two more things. First, if blunders are really a tell-tale sign of chicanery, then couldn't they produce something more plausible? I mean, they're able to execute a leak-proof conspiracy to throw the match, but they can't create games and a match arc that looks more like what chess fans would expect? Second, I don't find Nepo's collapse and his repeated blunders *that* implausible. He already had a reputation for sometimes collapsing when things went badly, and game six is the sort of game that can be psychologically crushing.
And as for the blunders, I can speak from experience. Granted, I'm not a super-GM, but I am (or at least was) a decent player who has beaten and drawn plenty of IMs and GMs. When I lose to those guys, it's almost always because they grind me down in a long, tough game and not because I blunder or otherwise collapse. I've gone through years where I've been undefeated, and in some of those years that has included games with IMs and GMs. But there was one stretch of my tournament career, back in 1999 or 2000, where over the course of four or five tournaments over a stretch of several months it seemed that I blundered in every game. It was maddening, and it didn't seem to matter what I did: something would go wrong in practically every single game. I didn't lose all of them, thankfully, but it was a disaster. 60-70 rating points later, I quit playing in tournaments for the better part of a year, and then my mind started working normally again. Whether it's fatigue, bad sleep, discouragement, or just one's mind not working the way it's supposed to, blunders can happen. Snowballing failure happens all the time in sport.
I would prefer not to continue this thread, as the accusation at least borders on libel in the absence of genuine evidence. Also - and this obviously isn't your fault - I *strongly* prefer that comments are at least in something that's recognizably within the neighborhood of the post's material. I may create posts that are open for (more or less) free-for-all comments every now and then, so save up your topics for those posts.
You are obviously someone who understands chess, both the game and its larger context(s). I hope you will find the time to read the beginning of a several part "chess piece" that I'm working on:
https://jtbernini.substack.com/p/how-not-to-play-championship-chess
Let me know what you think.
The short answer is that it fails to take prior probabilities into account. If all we knew is that Nepo blundered away a few games and that super-GMs rarely blunder, then there might be an argument there. But given the extreme unlikelihood that Nepo would take a dive and that Carlsen would presumably pay him to do so, Nepo's blunders only raise the likelihood of a thrown match from infinitesimal to (maybe) visible-with-a-microscope.
Now for the long answer:
Here are a couple of examples to illustrate the general idea. First, a popular chestnut in books on thinking, especially ones dealing with Bayesian reasoning. Suppose there's a dread disease that strikes one person in 10,000. Bad luck: you test positive for it, and the test is 99% accurate (1% of the time it gives a false positive, and there are no false negatives). What is the probability that you have the disease?
Second, suppose you tell me that you hear scratching sounds in your attic every night, and I explain that it might be a Night Gremlin. "What's a Night Gremlin?", you ask. I inform you that it's a supernatural creature that enters some people's attics at night, then materializes and starts scratching the floorboards. No one has ever seen a Night Gremlin, and there's no indirect evidence for them either; there's just the hypothesis which, it must be admitted, fits the facts perfectly. Should we believe in Night Gremlins?
The answers to the questions ending the paragraphs are 1 in 101 and no, respectively. In the case of the dread disease, the easiest way to see why the likelihood that one has it if they take a positive test is this: suppose that everyone in a random population of 10,000 takes the test; how many positive results will there be? The answer: 101, of which 100 are false positives (1 in 100 scales up to 100 in 10,000) and one is a person who actually has the disease. So the odds are 100 out of 101 that your positive was a false positive, and 1 in 101 that you have the disease. As for the Night Gremlins case, it's obvious that we shouldn't believe in them, even though the hypothesis explains the phenomenon perfectly. The problem is that the prior probability that Night Gremlins exist is vanishingly small, as there is no physical evidence, or indeed evidence of any sort, for their existence. That doesn't mean that they don't exist, but there's no reason to believe in them, and given ample alternative explanations of a conventional sort, we're not forced to posit Night Gremlins to explain the scratching in the attic.
And so it is with the fradulent match hypothesis. Carlsen and Nepo have everything to lose if they get caught, there's no evidence in either player's career of having done anything of this sort nor any evidence that there was a fix. There's also no obvious motive for Carlsen to get Nepo to take a dive, given the insane risks. You offer Nepo's 4-1 lead in decisive games [in classical chess] going into the match, but that's entirely misleading. Two of Nepo's wins came when they were boys, and Nepo's third win came way back in 2011. The most recent decisive games were split: Nepo went up 4-0 in 2017, and Carlsen finally struck back in 2019. Additionally, Carlsen not only won the last decisive classical game between them, but also enjoyed a substantial plus when it came to rapid and blitz games, and of course enjoyed the considerably higher rating. Another problem is that if Carlsen was so gung-ho on keeping his title, why is he giving it up now without a fight?
So, it seems to me that this theory is rather like Night Gremlins and thinking it 99% likely that one has the disease: it's only plausible if one ignores all the relevant information that goes into the prior probability of the hypothesis, and massively implausible when that information is taken into account.
Finally, I'm aware that players of practically all levels, from low-rated amateurs to GMs have thrown games. That makes the thrown-match hypothesis a very tiny bit more likely than it would otherwise be, but still very, very exceptionally unlikely. Think about why games are thrown: money (but both players are already well off, and unless Nepo was given millions of dollars the money he loses by not becoming champion outweighs any potential bribe - not to mention the incalculable damage to his reputation and ability for further earnings if he's caught) and qualification (but they've already at the top - unless there are interplanetary chess championships I'm unaware of, there is no next step).
Ok, two more things. First, if blunders are really a tell-tale sign of chicanery, then couldn't they produce something more plausible? I mean, they're able to execute a leak-proof conspiracy to throw the match, but they can't create games and a match arc that looks more like what chess fans would expect? Second, I don't find Nepo's collapse and his repeated blunders *that* implausible. He already had a reputation for sometimes collapsing when things went badly, and game six is the sort of game that can be psychologically crushing.
And as for the blunders, I can speak from experience. Granted, I'm not a super-GM, but I am (or at least was) a decent player who has beaten and drawn plenty of IMs and GMs. When I lose to those guys, it's almost always because they grind me down in a long, tough game and not because I blunder or otherwise collapse. I've gone through years where I've been undefeated, and in some of those years that has included games with IMs and GMs. But there was one stretch of my tournament career, back in 1999 or 2000, where over the course of four or five tournaments over a stretch of several months it seemed that I blundered in every game. It was maddening, and it didn't seem to matter what I did: something would go wrong in practically every single game. I didn't lose all of them, thankfully, but it was a disaster. 60-70 rating points later, I quit playing in tournaments for the better part of a year, and then my mind started working normally again. Whether it's fatigue, bad sleep, discouragement, or just one's mind not working the way it's supposed to, blunders can happen. Snowballing failure happens all the time in sport.
I would prefer not to continue this thread, as the accusation at least borders on libel in the absence of genuine evidence. Also - and this obviously isn't your fault - I *strongly* prefer that comments are at least in something that's recognizably within the neighborhood of the post's material. I may create posts that are open for (more or less) free-for-all comments every now and then, so save up your topics for those posts.