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 avoid this "petty diplomacy" problem by determining the victor as the player who first delivers checkmate, with the third player losing in addition to the checkmated player. Other solutions have been tried as well. Some variants use a board with hexagonal cells. Usually three bishops per side are included, to cover all cells of the hex playing field. Pieces move usually as in one of the versions of hexagonal chess. Some variants use a hexagonal-shaped board with quadrilateral cells (see example in the photo). Some variants have used other board shapes with quadrilateral cells. Triangular cells not on the perimeter