Transcendental Chess of one side can be any of 4²×6!÷2² = 2880. There is no castling. On the first turn a player, instead of making a move, can transpose any of two pieces on the back row. In Chess960 the back rows are mirror images, but in Transcendental Chess the setup of black and white is different 2879 out of every 2880 times (there being a 1–in–2880 chance that both sides will draw the same setup). This can create inequalities in the position. One way to equalize these inequalities is to play a couplet: the players play two games, one each as
Three-player chess have three cells obliquely adjacent, and three cells adjacent at points. Circular boards have three- or four-sided cells, but not triangular or quadrilateral. Some variants incorporate fairy chess pieces in addition to standard chess pieces. The introduction of a third player drastically alters the style of play, even when standard pieces are used. Many chess openings are useless due to the extended board and third player. Each player must think twice as far ahead—anticipating the moves of both opponents, with the added complexity that the next player may move to attack either opponent. If a player trades off pieces with