On Game Space Size (Monte Carlo)

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

We've been talking about Monte Carlo quite intensively now but
a friend of mine who is not in Go at all pointed out to me that
we probably do not need to make the map !

Let's try to explain this.

If we want to calculate the Go-space from the distribution map we should (as pointed out before) multiply the number of possible states with the legal-state-density for every point on the map. Ultimately this means that the centre of the map is weighed far heavier than the sides because of the peak in Newtons Binomium.

Now, if we discard the map and just create a random board position we will most often create a board with the same number of black, white and empty points only at rare occasions a board position is created with only one stone. THIS IS ALLRIGHT ! because the even distribution of black white and empty stones should weigh heavier than the empty board situation !
The fact that the distribution over the board is not uniform is not important to Monte Carlo. It only means that we should not stop too early. But than again. Calculating the map probably takes much longer.

As a final note.
My computer is still calculating the 19x19 board-map because I think it contains interesting information nevertheless.
It is however of no importance to the Monte Carlo estimate.

Is there anyone who can verify the above for me ???

Greetz. Pieter