Been a while since I read it but feel like even after a couple of years of winning games and tracking his own performance, he had enough stats knowledge to realise that he didn't actually know if he was good or just lucky. The noise swamped the signal.
This feels relevant to many of these trading things where people start to believe their own BS.
If you've flipped a coin and it's came up heads 10 times in a row, why wouldn't you bet everything on it happening again? You're really good at getting heads when you flip. Humans aren't really built for that kind of thing.