Bug House or "Siamese Chess" is a dynamic four player variant in which teams of two players compete across two simultaneous games, one pair of players per board.
Winning is achieved by traditional checkmate as in standard chess, or via chess clock flag, as often a position results in which one game would result in mate, thus the losing player would prefer to halt his play in hopes his partner will reign in his sibling game.
Each team is comprised of one player as black, one white, competing thus in an opposite-colored game mirrored by the opposing team. The game is dynamic in that any pieces captured by one player is thus available to his partner to inject (or "drop") into his own game at will, in lieu of a regular move.
Strong teams thus will communicate with each other as to which pieces are highly desirable to "feed" the leader game, or likewise to "starve" the opposing team by denying any material to be captured.
One major division in rules for this variant is whether dropped pieces may result in checking the King or not. As may be noted in Japanese shogi, dropped pieces cannot directly check the king, however in bughouse this certainly expedites the game and its energy level.
Likewise, in this manner, the Knight becomes a highly coveted piece as its checks cannot be blocked, and should be conserved for such play where its unique abilities are maximized.
Crazyhouse is a single board, two-player version of Bughouse. The chief distinction in the rules of Crazyhouse from those of Bughouse is that promoted pieces, if captured, revert back to pawns, whereas in Bughouse, captured promoted pieces remain the same. This difference significantly alters the learning and playing experience of each variant.
Note that in Crazyhouse games, when a piece is promoted, one should keep track of which piece(s) are promoted pawns to be aware of the results of capturing particular pieces.