titled The Chess Ending, King & Queen against King & Rook. 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. The third-rank defense is when the rook is on the third rank or from the edge of the board, his king is closer to the edge and the enemy king is on the other side (see the diagram). This defense is difficult for a human to defeat. For example, the winning move in the position shown is the counterintuitive withdrawal of the queen from the seventh rank to a more central location, 1. Qf4, so the queen can make checking maneuvers to win the rook with a fork if it moves along the third rank. If the black king emerges from the back rank, 1... Kd7, then 2. Qa4+ Kc7; 3. Qa7+ forces Black into a second-rank defense (defending king on an edge of the board and the rook on the adjacent rank or file) after 3... Rb7. This position is a standard win, as White heads for the Philidor position with a queen versus rook (in the next section). A possible continuation: 4. Qc5+ Kb8 5. Kd6 Rg7 6. Qe5 Rc7 7. Qf4 Kc8 8. Qf5+ Kb8 9. Qe5 Rb7 10. Kc6+ Ka8 11. Qd5 Kb8 12. Qa5 [Philidor—mate in 7]. Philidor position The Philidor position is a queen vs. rook position. If Black is to move in this position, he quickly loses his rook by a fork (or gets checkmated). For example, 1... Rb1 2. Qd8+ Ka7 3. Qd4+ Ka8 4. Qh8+ Ka7 5. Qh7+ thus forking the rook on b1. If, on the other hand, White is to move in this position, he would like to be in this position except with Black to move. This can be accomplished by triangulation: 1. Qe5+ Ka8 2. Qa1+ Kb8 3. Qa5 and now it is back to the same arrangement, but Black has to move and is in zugzwang. Nunn describes that with the pieces in the center of the board the queen ought to force the rook towards the Philidor position. Nunn describes the various retreat