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This variant I find very interesting. Additional idea: let the pieces make a non-capturing move laterally or backwards with demoting the piece to the next lower kind, e.g. in the order queen -> rook -> bishop -> knight -> pawn. This is buying more time, and also combinations may include the demotion of a piece to alter its way of moving. The king is maybe too vulnerable in these variants. A defended Queen on any of the three squares in front of the King mates, and also a defended rook directly in front of it. Three pawns can also mate. One might add the rule that the king may also move laterally or backwards when attacked. I think this does not lead to cycles, but if there are Rooks and Nightriders, a cycle is possible: white: King e2, Rook e1 black: King e5, Nightrider f7 1. Kd3+ Kd6+ 2. Ke2 Ke5
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