[Computer-go] Combinatorics of Go

[Robert Finking]

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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