RE: On game space size

[Pieter Cuijpers <P.J.L.Cuijpers@xxxxxxxxxxx>]

I've been reading the posts on Game Space Size carefully and
my computer is extremely busy calculating some Monte Carlo
now.
These are my findings so far:

1. You cannot leave out situations in which the number of black stones and the number of white stones differ. This is simply because black may have actually captured 25 white stones while there is also a 25-stone dead black group on the board. It happens (rather often) in real games.

2. You need a Monte Carlo Search (MCS) split up over the different combinations of any number of white and any number of black stones because the probability distribution is definitly not uniform.

3. I have run MCS on 1x1 2x2 ... 10x10 Go boards.
I visualise the search by putting the number of black stones on the x-axis and the number of white stones on the y-axis. I calculate the probability of each point and assign a colour.
After doing this "higher order circles" appear of the form:

black^p + white^p = size^2p

These circles visualise the chance that a boardposition on a "size"-square board with "black" black stones and "white" white stones is legal. The number of total boardpositions is not included yet. (We'll need Newtons Binomium for that.)

I can sent you the .gif file of the picture but I didn't want to
attach it right away.
If anyone is interested let me know.

Ofcourse if anyone is interested in the Matlab code this is also available.
My computer is now halfway calculating the 11x11 board.
I expect that 19x19 will take a loooooooooong time so maybe
I quit before then...

Greetz. Pieter (Pagode) Cuijpers