[eurozrap] no-castling Chess960

if Chess960 still does not offer enough variability, forbid castling on one side or both (i.e., forbid long castling, forbid short castling, or forbid both, equally for both players), resulting in 4*960 = 3840 total possibilities, a superset of Chess960.  the starting position can be specified by some extension of FEN for Chess960.

we could also add the additional 2*960 = 1920 (for a total of 5760) positions which permit castling only on opposite sides.  however, some of these might be very unbalanced (unfair).

incidentally, in orthodox chess (position 518), we can also set up a no-castling start position by moving knights, moving rooks, moving rooks back, moving knights back.  for which Chess960 positions can similar tricks achieve a no-castling or partial-castling initial position?

if castling is forbidden, we do not need to restrict starting positions to have the king between rooks.  if castling is only partially available, there only needs to be a rook on the castling side.  (if both rooks are on the same side, we will need to specify which rook is the castling rook).  there are 960*(4+3+3) = 9600 possible starting positions.  the factor of 4 counts the 2*2 possibilities of permitting or forbidding short and long castling if the arrangement is RKR.  the factors of 3 are for king not between rooks: which rook to castle with, or castling forbidden entirely.  adding initial positions permitting only opposite side castling increases the factor of 4 to 6, so 960*(6+3+3) = 11520 possible starting positions.

inspired by Kramnik's proposal for no-castling orthodox chess.