On 6-dec-07, at 19:29, Don Dailey wrote:
Here is an example of why this works so well and why your greedy
approach is so wrong:
Consider a position where there are 2 groups left that are being
fought over. One of these groups is very large and the other is quite
small. The computer must win one of these groups or it will lose
the
game - but if it wins either group it wins the game. The computer
estimates that attacking the huge group will result in an
impressive win
with 80% confidence, but attacking the small group will result in a
"tiny" win with 85% confidence.
Don, what I think they are trying to say is the following: in your
scenario there may be a third group that is currently 'evaluated' as
dead which is bigger than your small group. This evaluation may be
wrong with probability X. In this case, killing the big group will
give you 80% chance of winning where killing the smaller group gives
you 85% times X, the chance the other group was evaluated wrongly.
That may turn out to be far less then 80% in total because X needs to
be >95%.
So size makes up for some loss of confidence. The question is how to
quantify it.
Of course 'evaluation' in MC is completely counterintuitive. It
doesn't evaluate groups separately at all. It makes it hard to think
about ways to improve it. But I'm absolutely convinced that MC
programs will play better if they find a way to adjust confidence for
the size of the win. The correct way just hasn't been found yet. And
it may not be easy at all.
Mark
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