[gzfwymvy] Castling

In Chess960, the end result of castling always looks like orthodox chess.  We can keep this constraint but relax some other assumptions about castling:

If we do not require the king to start in between the rooks, then there are 2880 start positions.  However, if the pieces start on castled positions, castling becomes a no-op, equivalent to passing, which we may or may not permit.

Remove the constraint that the neither the king nor the rook may have moved.  We can require they have returned to their original squares, or that only the king has returned to its initial square, or that merely that they both be on the 1st rank.  This also removes the unfortunate nit in orthodox chess of needing to keep track of "invisible" state of whether castling is permitted.  Mistakes have occurred in real games, including the same player castling twice or more.

Let the rook half of the move be optional.

Let the rook not necessarily need to be present.  This is seen rook handicap games.

The above three ideas have the story that the king always has available a special escape route.

Remove the constraint that the king cannot start nor travel through check.  This might be especially relevant in Chess960 where the king might travel many squares while castling, so it's "too" easy to prevent castling by attacking any one of those squares.

Let the player choose whether the end position looks like kingside or queenside castling, possibly mirrored.  This would destroy the designed lack of symmetry in Basque Chess960.

Let it be possible to castle with pieces other than the rook.  The general idea is to allow the king to get behind pawns without having to move those pawns.  One could have 3 or more pieces participating in castling.  RBBQK... -> ..KRBBQ.  Bishops might change parity.