I haven't read the paper myself, but from a Wikipedia page that
references the paper: "Tromp and Farnebäck show that on a 19×19 board,
about 1.2% of board positions are legal (no stones without liberties
exist on the board) .....As the board gets larger, the percentage of the
positions that is legal decreases."
http://en.wikipedia.org/wiki/Go_and_mathematics#Legal_positions
As a side issue, the figures don't appear to include the 8 way symmetry
applicable to most board positions, so the true figure is probably
closer to 1/8th of that.
Raffles
On 01/01/2011 10:16, Ray Tayek wrote:
At 01:09 AM 1/1/2011, you wrote:
... If I understand correctly, they computed the State-space
complexity of 19x19 Go to be 2.08168199382· 10^170, which is really a
big number.
3^(19*19)=1.740896506590319E172 is all combinations of black, white
and vacant intersections on a 19 by 19 board. but some of these are
illegal. off the top of my head, that number seems a bit low as it
seems to be saying that only about 1.2 percent of the combinations are
legal board states.
thanks
---
co-chair http://ocjug.org/
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