>So a small error in the opening or middle game can literally be worth anything 
>by the time the game ends.

These are my estimates: human pros >= 24 points lost, and >= 5 game-losing 
errors against other human pros.

I relayed my experience of a comparable experiment with chess, and how those 
estimates proved to be loose lower bounds, and it would not surprise me if 
these estimates are also far from perfection.

I urge you to construct a model that you feel embodies important 
characteristics, and get back to us with your estimates.

-----Original Message-----
From: Computer-go [mailto:computer-go-boun...@computer-go.org] On Behalf Of 
Darren Cook
Sent: Monday, March 14, 2016 5:15 PM
To: computer-go@computer-go.org
Subject: Re: [Computer-go] AlphaGo & DCNN: Handling long-range dependency

> 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 was with you up to this point, but players (computer and strong
humans) play to win, not to maximize the score. So a small error in the opening 
or middle game can literally be worth anything by the time the game ends.

> I am certain that there is a vast gap between humans and perfect play. 
> Maybe 24 points? Four stones??

24pts would be about two stones (if each handicap stone is twice komi, e.g. see 
http://senseis.xmp.net/?topic=2464).

The old saying is that a pro would need to take 3 to 4 stones against god (i.e. 
perfect play).

Darren
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