[hnvuegbc] Chess 6561

For a randomized chess initial position, one can advance each pawn a random number of spaces, mirroring both sides.  Advance zero or one space for 256 possibilities, zero, one, or two spaces for 3^8 = 6561 possibilities.  Scramble the first and eighth ranks like chess960 to achieve 6,298,560 total setups.  Should any of them be excluded because they give too much of an advantage?

Also consider upside down chess.