That would work for all positions regardless of legality, which are in 1-1 correspondence to {0,1,2}^(19*19). The count above is for legal positions only, i.e.

That would work for all positions regardless of legality, which are in 1-1 correspondence to {0,1,2}^(19*19). The count above is for legal positions only, i.e. those where every connected group of stones is adjacent to an empty point.