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<blockquote>
'The only other rule I can think of is that if it's your move and the
other player is already in check, you cannot capture the King but you
can play any other legal move you choose'
</blockquote>
This also deals with the discovered check problem in multiplayer variants:
that is, when player A moves a piece that was blocking player B's piece,
so now player B's piece attacks player C's King, and the turn sequence is
A-B-C so player C never gets a chance to move out of check before being
captured.
I've played it and I agree with Ralph--the best way to introduce randomness into Chess. A checkmate rule I find satisfactory: If a player is mated by a single move, the game is over. If a player is mated by two consecutive moves, if taking two consecutive moves would relieve the mate, the mated player wins the next toss automatically and can play two moves. For stalemate the rule is the same.
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