There are many approaches to games with more than one king. They're either all Royal (checkmating one king is enough,) or Half-Royal (capture all but one and checkmate the last.)
Wild/9, and Kings use a totally different approach. It's more like adding a Guard next to the King than having two Royal Kings. The Guard is not exactly Royal, and is a very useful midgame and endgame piece. But it also have the exotic power of saving the King from an inevitable checkmate by taking over the throne himself.
Another approach, and quite a fun one, is what Fergus Deniho used in Symposium Chess, which I liked best of his variants.
'King and Queen are initially replaced by hermaphroditic Monarchs. As soon as one makes a move that can be made by only a King (castling) or only a Queen (moving further than one space), the two pieces differentiate into King and Queen, with the piece that moved turning into what it moved as. If one Monarch is captured before they differentiate into King and Queen, the remaining Monarch becomes King. The object is to checkmate the King.'
It can't be said that all these approaches create the same game.
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Derek,
Actually, Kings is quite different from Mirror West Chess. In Kings, you only have one king to attack (naturally, capturing the other king makes the job easier and more like normal chess.)
As I am told, Wild/9 experts play it simply as Chess (with a capital C) with an extra piece. (Actually, the highest rated player in ICC in wild/9 is an IM.) Of course removing the Queen alters opening play considerably. But Kings is still basically chess.
Kings, in essence, is asymmetric. Because the Royalty, so to speak, is always oriented to one side of the board. Technically, there's only ONE Royal King. Checkmating the Royal King wins the game regardless of how many other kings the player has.
Also, in Mirror West Chess no promotion to a King is allowed. Which I honestly found absurd about Wild/9. Mirror West deals with the two kings with a totally different approach, hence it's logical to disallow promotion to Kings.
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'How about a variant based on the theme that the closest piece to a given square is royal no matter what that piece is.'
This might be the craziest idea I ever read on the site, and I like it !! It even fits perfectly with any Diagonal Chess setup where the King is placed on the corner (so he gets to be the Royal piece in the beginning of the game, but you can always sac your king to give the opponent a hard time!)
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It might be fun if Kings was played with Losers Chess rules. You have to either be checkmated, stalemated, or lose ALL your pieces, probably including the other King. Capturing is obligatory (Losers Chess is different from Suicide in that you have to respond to checks. Escaping from a check takes priority to a capture, and if you can escape check WITH a capture you must do that.)