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A variation of loop chess wold probably work really well for 4 players. Instead of captured pieces going to your own "available pieces pool", they would go to your partner's pool. Typically, multi-player games are sequential. Player 1, then 2, then 3, then 4, etc. But with this variation, each individual game would go on as normal.
(kaŝi) Se vi volas trovi kontraŭulon kiu ludas simile lerte kiel vi, rigardu la paĝon 'Taksaro' kaj en ls subpaĝo de la dezirata ludtipo trovu ludanton kun simila BKR. (pauloaguia) (Montri ĉiujn konsilojn)