Re: On Game Space Size

[Robert Jasiek <jasiek@xxxxxxxxxxxxxxx>]

Henrik Rydberg wrote:
> Several people have during the last week or so been interested
> in the question of how many legal states there are in Go space.
> I guess the answer has been around for a long time, even.

If history is considered, then the used ko rules might
influence the number of reachable positions / situations.
However, if passes are part of the rules, then the following
holds:

Proposition:
If a position can be legally reached, then it can be reached by a 
move-sequence without any removal.

Proof:
Assume P is a position that can be legally reached. Now we can
construct a move-sequence without any removal that creates P:
Let black occupy the black intersections of P while white passes, (*)
then let white occupy the white intersections of P while black passes.
During this any white stone has and keeps a liberty since it also has a
liberty in P; no black string is removed for the same reason. QED.

Corollary:
An additional pass creates remaining situations for the same positions.

Note:
Hence the set of legal situations is independent from ko rules.

Question:
What about no pass rules?

-- 
robert jasiek
http://www.snafu.de/~jasiek/korules.html
(*) The last white pass is omitted if white plays at least one
stone afterwards:)