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"2)Make promotion cycled! Kings do turn back to pawns. However, kings still can't move into check (but thereafter became none-royal again)." In theory the king should be allowed to move at check with this rule (but can't stay into check). The idea of check is to make impossible to some player make some mistake move that will end the game. If the king will turn into a non royal piece, then by making the moving and puting this non royal piece into check, he will not end the game and lose by a mistake.
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A third subvariant: Player who win earn points according to how many kings the winner have + 1 (number of kings that the loser have is not relevant), and then add another + 1 if you win by checkmate instead of stale mate. Therefore player with more king earn more points, but only if you win; if you lose, then it is worthless. You can then also allow kings castling with any rooks horizontal/vertically away (even disregarding the other FIDE rules of castling), which does not changes the pieces; this might be a useful move in a few cases.