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Sorry, I hadn't been listening. Apparently, anticheckmate chess might be a
new game.

It's precisely what I said: WKe8, BKe1, Kings may not capture, all else as
per rule zero except that if you ever make a move that ends with your K
not in check you win.

Clearly, 1. f2-f4???? Ke1-f2 is the shortest game. 1. e2-e4? Ke1-e2! is
also bad.

Reference Racing Kings.

This is such a simple idea I thought it must already have been taken; and
you can tell without playtesting that it works well, with a feel similar
to Racing K.

This is such an obvious idea.