Many of the chess variants use chess pieces, but are very different from original chess. Antichess, Racing Kings or Horde are the biggest examples, but 3-check, Crazyhouse or Atomic are still much different, in terms of strategy.

To me, it's interesting to see how chess would look like if the rules were changed just a little bit. Here (publication with cooperation DeepMind and Kramnik) there are some examples: arxiv.org/pdf/2009.04374.pdf. No Castling chess is one of them. Maybe we can try some of them. For me, the most intriguing seems "Self-capture", which allows taking the own pieces. "Stalemate=win" perhaps seems less spectacular, but it changes the theoretical result in many endings, implying different strategies in early endgame and in middle game as well.

There are more options, but these three (no-castling, self-capture, stalemate-win) seems quite natural - I can imagine someone defines chess in that way.

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Interesting! We'll take a look, and see how easy/worthwhile they are to add. It won't happen before the MSO Grand Prix however.

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There's also atomic960

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