Starting formation would have to be a square placed at opposite poles. Each side gets 2 sets of pawns and pieces. Maybe you have to mate both kings of your opponent for a full win.
Yet another chess variant???
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You might as well just play Byzantine Circular Chess. Notice the pieces don't go 8 out because they would be touching each other allowing for Rxa8 or Rxh8 first move. N could take a7 or h7.
Interesting idea. Looked it up on Wikipedia. They say (the board is) "topologically equivalent to playing on the surface of a cylinder". However, this has already been institutionalized, with a World Champinoship dating back to 1996. But I don't like the way the rules are structured (no en passant and no castling) so I think I'll pass. Thanks for the comment and photo anyway.
Another chess variant waiting to happen: Chess played on a board that's not actually a board, but a globe. Would this lead to more, or fewer, back-rank mates? And what about the draws from not being able to promote a-pawns or h-pawns?