I once played a team chess variant where each player could place pieces captured by their partner on their half of the board instead of moving. Made for some of the wackiest play lines since a piece materializing on the board could throw off your whole plan, but super fun from a strategy perspective, since board state could change dramatically between turns.

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Luckily, the range is limited by the fact that the square boundary lines follow great circles

I would have thought only a knight could do that, and only if the boards had a one-square gap between them. Other pieces have to travel through the intervening space, they don’t teleport. But Randal probably knows more about chess than me so I’ll accept this.

It’s only legal if you can build up enough speed to move to the parallel board in a single frame.

This is the premise of 5d chess with multiverse time travel

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