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H. G. Muller wrote on Wed, Sep 20, 2023 05:39 AM UTC in reply to Bob Greenwade from Tue Sep 19 08:39 PM:

Well, the symmetry parameter primarily controls how the black pieces are placed in the initial setup, in relation to the white pieces, so you only have to specify the locations of the latter. Usually the only move with left-right asymmetry is castling, because on boards with an even width the King necessarily is placed asymmetrically, and some variants desire a symmetric result. Unlike rotating the board, mirroring it swaps the notion of left and right, which are concepts defined relative to forward and backward (which are the two directions that are really swapped). So an asymmetric piece that moves, say, diagonally inward from h1 and h8 would move fl for white, and fr for black if l&r was defined from the player POV. So they would then need to be different piece types, which then spoils the mirror symmetry of the placement. In a rotated setup the corresponding black piece would be on a1, and diagonally inward would still be fl. So there the problem does't exist. So far I have seen such asymmetric pieces only in Shogi variants, (e.g. Left and Right Chariot, or Quail), which tend to have rotation symmetry of the initial setup, so that it wasn't really a problem.


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