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DanielLC comments on Polarized gamma rays and manifest infinity - Less Wrong Discussion
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I find this suspect. If someone who was only good enough at chess to make moves at random played against a chess master, the latter would win so often that if they play for any reasonable amount of time, the former could never tell if the latter is capable of losing.
Who says you have to test the chessmaster only on board positions you can reach by playing from the canonical opening position?
You should be able to ask the supposed chess-solver about whether and how to win from arbitrarily-chosen board positions.
He doesn't have to know how to do that. Any information he has regarding positions he'd never get in can be wrong and he'd still be unbeatable. This includes knowing whether or not it's a position he can get in. The only way to reach a contradiction is if you show that he can lose from a given position, and that he can get there from a starting position.
You could try working backward by checking every position that might lead to this one and see if he moves so it does, but there might be no way to get to it, or multiple. You'd have to follow the entire tree back to prove that it doesn't connect to the beginning. Worse, he isn't even guaranteed to play deterministically, and just because he didn't move to that position this time doesn't mean he can't.