On a four-sided backgammon table, two teams face each other; one team moves clockwise, the other counterclockwise. Otherwise, the rules follow standard backgammon pretty closely. A variant is supplied allowing four *individual* players.
A newer version from 2005, Quadrogammon, features a silk-screened roll-up board.
Though not the same game, another 4-player backgammon variant is Backgammon 4