Maybe 10 years ago I extrapolated from the results of title matches to arrive at an estimate of perfect play. My memory is hazy about the conclusions (sorry), so I would love if someone is curious enough to build models and draw conclusions and share them.
The basis of the estimate is that Black wins 53% (or so) at 6.5 point komi, but White would win with a 7.5 points. So we estimate 7 as the value of the game, and Black should always win with perfect play. How often do the players have to make game-changing errors in order for Black to win only 53%? You can be sure, for example, that the players make more than one "losing move" per game. If they didn't, then Black would win an enormous percentage. Even 2, 3 or 4 errors (win/loss affecting!) per game per player don't match the observed outcome at all. I recall that you need 5 or 6 game-losing errors per player per game. (And note that game-losing errors have to alternate between the players, so they are always equal if Black wins and off-by-one if White wins.) You can also look at the score differentials. If the game is perfect, then the game ends up on 7 points every time. If players made one small error (2 points), then the distribution would be much narrower than it is. I recall estimating ~12 small errors per player per game. I am certain that there is a vast gap between humans and perfect play. Maybe 24 points? Four stones?? I don't know how that translates to Elo terms, but 600 point could be about right. I do want to acknowledge Robert's point that we don't know what the limit is. It is very hard to extrapolate from this distance. For comparison, I did the same calculation for chess in 1981 after the Korchnoi-Karpov rematch. I recall an estimate that perfect chess play was >= 3000 Elo, and it turns out that is a significant underestimate. Best, Brian -----Original Message----- From: Computer-go [mailto:computer-go-boun...@computer-go.org] On Behalf Of Robert Jasiek Sent: Monday, March 14, 2016 10:11 AM To: computer-go@computer-go.org Subject: Re: [Computer-go] AlphaGo & DCNN: Handling long-range dependency On 14.03.2016 09:33, Petri Pitkanen wrote: > And being 600 elo points above best human you are pretty close to > best possible play. You do not have any evidence for such a limit. -- robert jasiek _______________________________________________ Computer-go mailing list Computer-go@computer-go.org http://computer-go.org/mailman/listinfo/computer-go _______________________________________________ Computer-go mailing list Computer-go@computer-go.org http://computer-go.org/mailman/listinfo/computer-go
