Yeah, I'm surprised more comments aren't pointing this out. To spell it out further: > the number of valid positions [of a game on a 19 x 19 board] is 19 x 19

Yeah, I'm surprised more comments aren't pointing this out. To spell it out further: > the number of valid positions [of a game on a 19 x 19 board] is 19 x 19 in base 3 This statement is true when replacing 19 with any number, since the number of legal and illegal configurations is exactly 3^(n*n).