although this possibility would rarely occur in practical play. Endgame studies These endgame studies apply to both Gliński's and McCooey's variants: king + two knights can checkmate a lone king; king + rook beats king + knight (no fortress draws and a negligible number (0.0019%) of perpetual check draws); king + rook beats king + bishop (no fortress draws and no perpetual check draws); king + two bishops cannot checkmate a lone king, except for some very rare positions (0.17%); king + knight + bishop cannot checkmate a lone king, except for some very rare positions (0.5%); king + queen does not beat king + rook: 4.3% of the positions are perpetual check draws, and 37.2% are fortress draws; king + rook can checkmate a lone king. Starchess Starchess is a hexagonal variant invented by Hungarian chess teacher László Polgár. The board is a horizontally oriented regular hexagram, consisting of 37 numbered cells. Due to the small board, games typically finish quicker than in standard chess. Each player has five pawns, a king, knight, bishop, rook, and queen. The white pawns start at cells 5, 12, 18, 23, and 29; the black pawns at 9, 15, 20, 26, and 33. At the beginning of the game, the players place their other pieces alternately on the cells behind their pawns (White: 4, 11, 17, 22, 28; Black: 10, 16, 21, 27, 34). As a consequence, there are (5!)²=14400 possible setups. Pawns move one step vertically forward and capture one step orthogonally left-forward or right-forward, and have an initial double-step option (identical to Gliński's pawn); there is no en passant capture. The promotion zone for white pawns consists of Black's back rank (cells 10, 16, 21, 27, and 34), and for black pawns, White's back rank (cells 4, 11, 17, 22, and 28). A pawn that has lost its initial double-step option by making a capture is called a "limping pawn"; a pawn that ended up on cells 2, 3, 35, or 36 is called a "dead pawn"; a pawn on cells 1 or 37 is called a "mummy". The king moves one step in any orthogonal direction; there is no castling. The knight jumps, two steps in any orthogonal direction, followed by one step in a different direction (identical to Gliński's knight). The rook can move any number of steps, but only vertically; the bishop can move any number of steps,