Just for fun, there is another possible complication. It's possible
that some LEGAL positions cannot be reached in a real game from an
empty board. I don't really know, but if that is the case, someone on
this list may be able to construct an example of a legal positions
that cannot be reached in a real game.
This is a good question. Are there any legal positions that cannot
be reached in a real game? It seems to me that there are not. If a
position is legal then it seems to me that the individual stones in
that position could be played legally in any order. Kos would not
pose a problem, because there need not be any capturing in this game.
If one side had many more stones than the other, the other side could
pass. There are surely many positions no two sane human players
would ever reach, but I think all legal positions should be
attainable.
P.S. If someone could come up with a practical way to "map out"
illegal positions, then it might also be possible to throw out
huge classes of positions that are legal, but can be proved to
be irrelevant (for instance, easy to "prove" it's a big win for
one side or the other.) I'm skeptical, but it's an idea to
think about.
I would think there would be a way of proving that broad classes of
positions are equivalent or worse to others. This wouldn't show that
a player playing an ideal game would never reach those inferior
positions (since early in the game the stone that looks detrimental
may have helped get to that position), but it could be a quick way of
eliminating from consideration all the moves going from one position
to a demonstrably worse one. For example, it is ever a good move to
fill in an eye? Or, similarly, to fill in (or attack) very secure
territory?