Xref: utzoo rec.games.go:946 comp.ai:3979 rec.games.board:2059
Path: utzoo!utgpu!attcan!uunet!lll-winken!ames!sun-arpa!male!pitstop!sun!hanami!landman
From: landman%hanami@Sun.COM (Howard A. Landman)
Newsgroups: rec.games.go,comp.ai,rec.games.board
Subject: Re: Computer Go Challenge
Keywords: go, computer games, ai
Message-ID: <100427@sun.Eng.Sun.COM>
Date: 21 Apr 89 19:08:54 GMT
References: <3724@sdsu.UUCP> <100234@sun.Eng.Sun.COM> <2089@bingvaxu.cc.binghamton.edu>
Sender: news@sun.Eng.Sun.COM
Reply-To: landman@sun.UUCP (Howard A. Landman)
Organization: Sun Microsystems, Mountain View
Lines: 58

>In article <100234@sun.Eng.Sun.COM> landman@sun.UUCP (Howard A. Landman) writes:
>>On the other hand, some studies of my pro game database indicate that pros
>>routinely make hundreds of points of errors per game; so the possibility
>>that a program might someday beat them is quite real.  And the exploding
>>development of a solid mathematical theory of the endgame, based on Conway
>>and Berlekamp's work, promises programs that play rapid and accurate yose.

In article <2089@bingvaxu.cc.binghamton.edu> vu0112@bingvaxu.cc.binghamton.edu.cc.binghamton.edu (Cliff Joslyn) writes:
>Fascinating, I thought as much!  Could you explicate on the above
>reference, and any theory you have about how to measure sente, point
>value vs. threat value, ko involvement, etc.

None of the above work is published.  I've been in email correspondence with
Berlekamp and a couple of other people, and I spent 6 hours at Berlekamp's
house one evening.  He's making progress at a tremendous rate - most of the
results are less than 3 months old.  Before talking to him, I was able to
apply Conway's theory to find the temperature of a move.  This is useful
because the simple greedy algorithm of playing the move with the highest
temperature can be proved to be asymptotically correct; that is, if you have
multiple copies of the game, and either player is allowed to play in any copy,
then the highest temperature move is best in the limit of a large number of
copies of the game.  However, on a single board, there can be situations
where there is a large gap in temperatures where the correct strategy
is to play so as to get the last large move.  For example, suppose
there are three large moves left: 100 points in gote (A, temperature 50),
49 points in reverse sente (B, temperature 49), and 96 points in gote
(C, temperature 48), plus a bunch of small moves (all temp <= 10).  Then
the correct strategy is not to grab the highest temperature move, because
that leads to you getting A, but your opponent grabs B in sente and then
takes C.  Instead, you should take B, your opponent takes A, and you take C.
This way you get 2 out of 3 big points instead of 1 out of 3.

This is what professionals mean when they talk about getting the last big
point in the opening.  And they do this kind of analysis all the time in
the endgame.

Note that the addition of another large gote move, say 94 points in gote
(D, temperature 47), means that A might be the best move again.  Please
work this out for yourself

My application of the theory gives a precise mathematical (and graphical!)
meaning to "sente", "gote", "double sente", and even vague concepts like
exactly when something "becomes" sente or double sente.  But the explanation
is rather complicated and requires an understanding of the basic theory in
On Numbers And Games or Winning Ways v.1.  I hope to publish something
eventually, but right now it's all I can do to keep up with Berlekamp's
progress, and try to look at how this applies in real games.

Berlekamp has gone beyond mere temperature, to expressing games as
"overheated" simpler games, and playing in the simpler games.  This
allows him to distinguish (for example) some temperature 1 moves as
being infinitesimally better than other temperature 1 moves.  He can
construct problems in which this difference is the margin between
winning and losing.  I think even pro 9 dans would have trouble solving
these problems.

	Howard A. Landman
	landman@hanami.sun.com