Jose Carrillo wrote on Sat, Nov 27, 2010 04:16 AM UTC:
Agree with H.G.
Castling makes both positions different, and no symmetrical.
For instance, g-castling (O-O):
In 'B B R K R N N Q' g-castling is accomplished by the King jumping 3 squares, and the Rook moving once.
In 'Q N N R K R B B' g-castling is accomplished by just having the King jump over the f-rook, while the rook stays on the same spot.
Also, b-castling in one of the positions is not equivalent to g-castling on the other.
There is no symmetry because of castling.