RE: computer-go: Dobbelt moves

[Jean-Pierre Vesinet <jpvesinet@xxxxxxxxxx>]

More comments added to Eric's post:

> >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.

It is only true if you compare local subgames, not moves.
The relation of comparison between local subgames (even simple subgames,
without ko) is not transitive.
For example consider three ideally separated subgames A, B and C, perfect
play assumed.
If you have only A and B on the board you would rather play in B than in A.
If you have only B and C on the board you would rather play in C than in B.
But it is possible that if you have only A and C on the board you would
rather play in A than in C.
In short you can have A < B and B < C but A > C.

Total ordering for moves exists.