(Was 19x19 gets interesting.)
Mark Boon commented that he believes that top pros make "a few dozen" errors per game. I concur, and I think that we can construct a model of Go competitions that supports that belief. with a 6.5 komi, the game is probably a forced win for Black. (It could be White, or even a draw by repetition, but that doesn't affect what follows.) So a perfect player would win 100% as Black, and also win as White unless his opponent plays perfectly. When top-ranked pros play head-to-head (e.g., in title matches) what we observe is closer to 53% wins for Black. Imagine an opponent that made an error on 1% of his turns. His probability of playing a complete game (say 130 moves) without an error is around 27%. It should be clear that such a player would win a lot more than 53% as Black. Maybe it isn't so clear. We are counting errors in point differential, so Black would win if he plays perfectly or if White makes errors that balance. If White had the same error rate as Black, then Black would win roughly 63%. So top pro error rates must exceed 1%. If the error rate were 2% then Black would still win much too often. I believe that top pros must have error rates around 9% in order to have a 53% win rate for Black. That implies a dozen errors per game per player. I am not sure what this means for dan ranking. But if 1 stone = 6 points, and 1 error = 2 points, then perfect players are about 4 stones better than top human pros. Here, "top" doesn't mean 9p; "top" means title holders. Brian
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