We just discovered a very interesting chess game played in curved spacetime
Notice that you cannot move diagonally over the center. Similarly a centered knight only has 6 potential locations to move to
Due to how the board is warped the queen can sometimes have more than one way of reaching the same 'square' which is relevant in the case of of those paths are blocked.
Same logic for movement applies to all pieces.
Pawn promotion
A pawn will be promoted to centaur, archbishop, chancellor or queen once it reaches the area with the pattern no piece for that player starts on.
Starting position
Since the bishops can change color we can have each player start with 3.

Notice that you cannot move diagonally over the center. Similarly a centered knight only has 6 potential locations to move to
Due to how the board is warped the queen can sometimes have more than one way of reaching the same 'square' which is relevant in the case of of those paths are blocked.
Same logic for movement applies to all pieces.
Pawn promotion
A pawn will be promoted to centaur, archbishop, chancellor or queen once it reaches the area with the pattern no piece for that player starts on.
Starting position
Since the bishops can change color we can have each player start with 3.
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