The queen versus rook endgame is a chess endgame where one player has just a king and queen, and the other player has just a king and rook. As no pawns are on the board, it is a pawnless chess endgame. The side with the queen wins with best play, except for a few rare positions where the queen is immediately lost, or because a draw by stalemate or perpetual check can be forced.[1] However, the win is difficult to achieve in practice,[2] especially against precise defense.[3]
Normally, the winning process involves first winning the rook with the queen via a fork and then checkmating with the king and queen, but forced checkmates with the rook still on the board are possible in some positions or against incorrect defense. With perfect play, in the worst winning position, the queen can win the rook or checkmate within 31 moves.[4]
This endgame was known to be won since the 18th century, but it was then thought to be an easier win than it actually is. Since this endgame only has four pieces, it was fully analysed by computers in 1978, and this revealed subtleties overlooked by earlier writers.[1]