Re: FW: GoSpace

[Martin Mueller <mueller@xxxxxxxxx>]

I did a rough estimation of number of legal positions many years ago. My
approach was to count the number of illegal positions and subtract them
from 3^(n*n). Every illegal position must have some stones without
liberties. The most frequent case is a single stone, surrounded by four
opponents in a ponnuki shape. Considering only these five points, there are
2 illegal states out of 3^5. Edge and corner are special cases. Using the
inclusion-exclusion principle, you can count the number of full board
positions containing at least one illegal ponnuki. It is tedious, but I
have done it at the time. If you want to persevere, you could then try
counting the states containing no illegal ponnuki but a pair of stones
without liberties, and so on.

	Martin