What is the least common move?

Probably something like gxh8=B#.
That should be about right. For a second I wondered if it was even legally possible.

wait i dont think Kh8# isnt legally posibble too
Hmm... that's actually pretty interesting. I think your're right - Kh8# isn't possible - but I'm not 100% sure.

Some en passant move might compete.
I wonder,
can anybody find a way that O-O++ or O-O-O++ is legal?
Or prove that it is not?
0-0-0 with double check is almost certainly impossible, as it would require a piece on the back rank to reveal a check from a piece behind it...

Which is impossible since double check involves a discovery, and castling cannot be a discovery since it is on the edge of the board and therefore there cannot be a piece behind the king/rook to give a discovered check when the king/rook moves.
What is the least common move?