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This site unfortunately is getting out of date, it for example still links to my old d2d4.de page which doesn't exist anymore for years now. I have mailed months ago about this.
Bughouse is an excellent 4 player variant that can be played with a different number of players, or (as a Bughouse variant) even a greater number of boards & sets than just two, if desired. Fwiw, I've seen on internet chat sites talk that Bughouse is hard for engines, as there are two boards & sets + drops, multiplying the possibilites compared to standard chess. If ever one of the two boards has a player sitting (refusing to move), however, the computer may then have an advantage if playing against a human on the remaining board (provided that person doesn't already have a big advantage).
From the wiki entry on Bughouse: "A valuation system, first suggested by FICS-player Gnejs, often applied to bughouse is pawn=1, bishop=knight=rook=2 and queen=4."
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