Re: computer-go: Dobbelt moves

["Eric Boesch" <ericboesch@xxxxxxxxxxx>]

> 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).

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).

Now, do you want a total ordering?  I start with your 3 numbers +1 win, 0 
tie, -1 lose.  Then, I guess the strength of my opponent.  If I already know 
I will win, then I add the real number of points I expect to win by (as a 
humiliation bonus).  If I will lose or tie with perfect play, then I add a 
real number on [0,1) that estimates the probability of my being able to 
improve upon that result due to a blunder on my opponent's part.  Now I have 
a total ordering that allows me to play soundly (when gambling, I never 
consider moves that might turn a win into a tie, or a tie into a loss) and 
psychologically at the same time.

Finally, I have one more, good but imperfect, numeric move evaluation for 
you:  rate it +1 if it's the move Lee Chang-Ho would play, and 0 otherwise.

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