Re: computer-go: A problem with understanding lookahead

[Dave Dyer <ddyer@xxxxxxxxxxx>]

>
>Exactly.   Evaluations are all about probabilities,  a point I haven't
>been able to get across very well.  

Evaluations are not about probabilities, they are about estimates, which
is quite a different thing.  Search compares various estimates and
alpha-beta optimizes search by reducing the number of estimates that
have to be made.  Search (with or without alpha-beta) only works if
the estimates are resonably accurate and comparable to one another.

case A: 
Suppose you have an evaluator which is 90% accurate, defined as the
estimated value is withing 10% of the true value 100% of the time.
Search will work quite well; better or worse depending on the nature
of the deviations from the correct value.

case B:
Suppose you have an evaluator which is 90% accurate defined as the
estimated value if 100% accurate 90% of the time, but has the sign wrong
the other 10% of the time.   (search reports you are 100 points ahead,
you are actually 100 points behind).  This evaluator will not work at all.
When things are going badly, it will choose the WORST among the 10%
favorable outcomes rather than the least bad among the 90% unfavorable.


Traditional search techniques assume case A, but estimates of 
life and death in Go closely resemble case B, so searching based 
on these estimates will make things worse rather than better, even
if you could do it.

So, clearly, Go evaluators have to be based on probabilistic calculations
where each group has a range of possible life and death values.  When the
game is over, these values must converge to certainty, but during
the interesting part of the game, they are all in flux.

-- The bad news is that the mathematical framework for dealing
with this kind of reasoning doesn't exist.