That is excellent analysis. Of course it's rather difficult to categorize errors like this but it gets the point across, the top players must be making "game changing" errors in virtually every game.
No doubt a lot of errors are not "game changing", for instance if you have a won game you can make an error that will make it "harder" to win or in more precise terms your win will be "smaller." So it's almost certainly the case that there are many more "small errors" (where the final score changes but not the result) than game changing errors. Of course this is not relevant to your analysis. Years ago I did a study with a very simple version of 6x6 checkers and the results surprised me. This was checkers on 6x6 and only a single jump allowed to make everything real simple. It was possible to search to great depths and I found that the program continued to improve with each additional ply of lookahead. Although draws became more and more common, it was clear that the programs were making errors even with enormous search depths. (This WAS a few years ago and I don't remember what I considered "enormous.") I think today it would be easy to re-write this program to play perfect checkers, but when you consider how simple 6x6 checkers is to 8x8 checkers, which is very simple compared to chess, which is very simple compared to GO, it should not be difficult to believe that humans play terrible go (from "God's" point of view.) On Tue, Oct 12, 2010 at 10:04 AM, Brian Sheppard <[email protected]> wrote: > (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 > > > > _______________________________________________ > Computer-go mailing list > [email protected] > http://dvandva.org/cgi-bin/mailman/listinfo/computer-go >
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