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Just as a Bishop is colourbound, a Rook is squarebound. A piece even less bound than the Rook would be a Bishop that can stop on the corners of the squares, preferably only a certain type of corner, e.g. the lower left corners of the squares, though for symmetry in a FIDE-like set-up, a toroidal 64 point grid is recommended. And, yes, even this piece is bound in some way, for it cannot access the edges of the squares.
In other words, if we have an empty 8x8 board and a white Chiral Marshall on the D1 square, this piece can move to B2, C3, D5, D6, D7, D8 (the four rook moves which must end on the opponent's side of the board), E3, and F2.
The same Chiral Marshall on D8 can move to A8, B8, C8, D8, E8, F8, G8, H8 (rook move), B7, C6 (knight moves), D7, D6, D5, D4 (rook move again), E6, and F7 (knight moves).
The black Chiral Marshall can only make a rook move ending on White's half of the board (A1-H4)
I like this because it encourages more aggressive play; by making the pieces more powerful on the opponent's side of the board, it makes passive play less fruitful and should make games more exciting.
- Sam
Knights have a little secret. And that secret is: they're almost doubly colourbound. A narrow Knight is, a wide Knight is, and a certain configuration of Knight moves is even bound to 1/5th of the board. Knights alternate 1/4 bindings whenever they move. Thus, I propose the Quadrant-Changing Rook. The Quadrant-Changing Rook is the same as a normal Rook, but it must change what quadrant of the board it resides. This piece is absolutely horrid in development, and awkward in the endgame. What is this piece's strength?
May I bring to the table what I call 'The Chiral Rook'. The Chiral Rook is the same as the normal Rook, but it can only access the left or right side of the board, which determined by its initial placement. This Rook can access only half of the board, and thus is similar to a Bishop, which is often called a colourbound Rook. What is the value of such a piece? How would it change when there is rotational symmetry?
A colourbound piece is defined as a piece whom may only access one colour of square on the board. Ralph Betza provides the more lenient definition of a piece that cannot access all of the board. A colourchanging piece is defined as a piece whom must change the colour of square it resides on when it moves. This thread is for the discussion of colour and boundness.
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