It's not arbitrary, GP stated it was a 3 bit counter. In GGP (or something, not sure how far down in the thread we are), they were referring to a 32 bit int counter until overflow. If you bin each number from 0 to 2^32 - 1 by mod 3, you don't get 3 bins of equal sizes, 1 bin always comes out smaller.
Smaller by a single number at most, it's effectively insignificant. Not sure where the 3-bit counter assumption came from as the original post said 32bit signed int.