Re: computer-go: Dobbelt moves

[William Harold Newman <william.newman@xxxxxxxxxxx>]

On Tue, Feb 27, 2001 at 11:00:05AM -0500, Eric Boesch wrote:
> >From: William Harold Newman <william.newman@xxxxxxxxxxxxxxxxx>
> >
> >The analysis and examples in _Mathematical Go_ (Berlekamp and Wolfe,
> >ISBN 1-56881-032-6) show that the importance of moves is only
> >partially ordered. Since real numbers are totally ordered, you will
> >get less-than-ideal results if you try to express the importance of a
> >move with a single real number. Trying your theory on the examples in
> >the book would probably demonstrate this.
> 
> No offense, but this "you can't convert a position into a number" assertion 
> is a common error.
> 
> The fact that the game positions are in a partial ordering does not mean 
> that NO total ordering is ideal.  It means that MANY total orderings are 
> ideal (that is, they win whenever a sure winning move is available, and they 
> tie whenever a sure tieing move is available).

The original poster was talking about sente and gote, and showed a
diagram and analysis where he was clearly trying to find a local
score, not a whole-board score. Therefore, he was talking about the
problem of breaking up a game into subgames; and I tried to answer in
the same vein. This is the same problem that is analyzed in
_Mathematical Go_, giving useful scores which are only partially
ordered. (Actually I forget the exact definition of partial ordering,
and I suspect now that the ordering properties of games like "*" may
mean that it's not even partially ordered. That's probably a common
error too.:-)

> Here's one "ideal" ordering using integers (it's not a total ordering, 
> though, because numbers are repeated).  Use the final score that will result 
                                          ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> with perfect play on both sides, or if that's too much detail for you, just 
  ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
> use one of 3 numbers (assuming a win is a win is a win):  +1 (I win), 0 
> (tie), and -1 (I lose).

I'm familiar with minimaxing, and probably the original poster is
also. Alas, once you break the game into subgames, where tenuki is
allowed, you can no longer determine a useful minimax value locally,
because globally optimal play includes local tenuki, and decisions
about where and when you tenuki are affected by other subgames. Your
other proposals for a integer score fail in this problem for analogous
reasons.

-- 
William Harold Newman <william.newman@xxxxxxxxxxxxxxxxx>
software consultant
PGP key fingerprint 85 CE 1C BA 79 8D 51 8C  B9 25 FB EE E0 C3 E5 7C