Newsgroups: rec.games.go, rec.puzzles
Followup-To: rec.puzzles
From: hoey@zogwarg.etl.army.mil (Dan Hoey)
Date: 26 Feb 92 16:38:18 GMT
Subject: Re: Go-moku (renju) book.

In rec.games.go, w...@math.canterbury.ac.nz (Bill Taylor) writes about
the book

> FIVE-IN-A-ROW  (RENJU)
> For beginners to Advanced Players
> by  Goro Sakata 8-dan  and  Wataru Ikawa 5-dan
> Ishi Press  -   Tokyo  -  1981

and their attempt to demonstrate that unrestricted five-in-a-row is a
first player win on a 15 x 15 board.  I do not believe this has been
proven, even for an infinite board.

>OPEN CHALLENGE TO ISHI PRESS.
>If the authors have discovered a detailed proof of unrestricted black
>win, as they seem to claim, it should be possible to program it
>without too much difficulty.  Such a program could easily be emailed
>to western go/gomoku and computer people, for independent verification.

The challenge is too strong, for they could conceivably develop a
nonconstructive proof, or at least a proof that does not yield a
tractable algorithm for play.  I think this is the current status of
Hex, for example, or at least of Hex generalized to a large board.

The challenge is also too weak, for a program that no one knows how
to beat does not constitute a proof that it is unbeatable, or that an
unbeatable one exists.

Unfortunately, I doubt that the authors are interested in considering
the deficiencies of their demonstration from a mathematical
standpoint.  People who play games professionally tend to believe
they have demonstrated any number of things, and they are too used to
dealing with nonprofessionals who cannot fill in the trivial gaps of
a proof in their specialty to believe one who points out a nontrivial
gap.  It isn't restricted to the Japanese, either.  Try talking to a
chess master about the possibility that White is in zugzwang on move
1, and must lose with correct play.

Dan Hoey
Hoey@AIC.NRL.Navy.Mil