These numbers follow a well defined trend. It could be a very good mathematical research to try to derive the function describing this trend. Success in deriving this function could shed light on the topological properties of Go positions.
Daniel Liu
In a message dated 1/26/05 11:29:58 AM Pacific Standard Time, birk@xxxxxxxxxxxxxxxxx writes:
> The number of legal configurations can be estimated by computer simulations.
> Randomly generate a large number of configurations and count how many are
> legal.
I did this in 1999 and sent it this list:
Boardsize Legal Positions (sample size > 1e6)
3x3: 64.4%
5x5: 48.9%
7x7: 36.0%
9x9: 23.5%
11x11: 14.8%
13x13: 8.69%
15x15: 4.78%
17x17: 2.46%
19x19: 1.19%
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