On Sun, 2006-10-15 at 12:40 +0100, Jacques Basaldúa wrote: > >Another question is how many illegal board configurations are > there ... > >by assigning each point on the board a random state of > (white,black,empty) > > That does not represent real game positions. All positions have about > 7x7x2/3 = 33 stones. (A normal distribution assuming the state is > uniform)
I don't think this is correct. I don't want to represent "real" game positions, I want to take a random sample of ALL board configurations (all 3 ^ 25 if you are talking about 5x5 Go) and sample them in an unbiased way. Then I determine which of those are legal. I think my thought experiment does this. The point is that a flat array of 3^25 entries would be required to store all possible states but this kind of table has a lot of holes in it, namely the illegal states. So I am considering a much more flexible scheme that requires storing only LEGAL positions. It's nice to know in advance how many of those there are. I plan to further reduce it by storing only positions I can't calculate. (With bloom filters you are not actually "storing" positions, you are probabilistically representing their membership in a set in a very compact way.) The beauty of this scheme (if it works that is :-) is that I have complete control over the space/calculation trade off. And the amount of compromise that I must accept is a function of how good I make an evaluation function that returns tight bounds correctly. So it's a scheme that can be implemented, and continuously refined. I have 2 things to play with in a very flexible way - space and time, and a 3rd thing that can affect both, evaluation function quality. As it turns out, John Tromp has provided the answers on his web page, so I don't need to do statistical sampling, I can get the exact number. It's not necessary for me to know the number, it just helps me understand the magnitude of the problem better. - Don _______________________________________________ computer-go mailing list [email protected] http://www.computer-go.org/mailman/listinfo/computer-go/
