[Computer-go] Combinatorics of Go

[Álvaro Begué]

The people that think the number is low or high have bad intuitions,
that's all. Writing a program that generates random configurations and
checks whether they are valid is fairly trivial. If you don't trust
John's numbers, that's what you can do.

Alvaro.


On Saturday, January 1, 2011, Kahn Jonas <jonas.kahn at math.u-psud.fr> wrote:
>
> Intriguing!
>
> A position is obviously illegal if any point is occupied by a stone surrounded by opposite-colour stones.
> At the 4 corners, 25 out of 27 combinations will be legal. The proportion (25/27)^4 will survive.
> At the 68 edges, 79 out of 81: (79/81)^68 will survive.
> At the 289 interior points, 241 out of 243: (241/243)^289.
>
> Multiply those, I get 0.012321913.
>
> So presumably the number is on the high side, because this calculation only takes account of
> single stone blocks illegally on the board.
>
>
> I think it's rather (much) on the low side. The probabilities are not
> independent. And the correlations are positive: in particular, if a
> single point is legal, it may be that it is next to a free intersection,
> which immediately makes legal four (at the center of the board) other
> points.
>
> Jonas
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