King and Queen vs. King and Rook
Concepts
While this is technically a win for the superior side, it can be very subtle. If you are unaware of the basic ideas, you'll end up chasing the rook around for 50 moves and you'll snatch a draw from the jaws of victory.
There are a few things you will want to remember if you're found looking over the board at this position:
- Do not forget that the object of the game is to checkmate the enemy king. Many people try to chase the rook around in order to capture it, but sometimes the forest is missed for the trees as you try to pin down the rook. You have fifty moves (at most) from the start of this ending before it draws. Don't waste them needlessly if your opponent gives you the opportunity to mate.
- With rule one in mind, whenever possible, move your king so that it is closing in on the enemy king. This is the basic idea of this ending. In order to checkmate, you will need to pin your opponent's king to the wall.
- Avoid forks. This should go without saying, but as I've seen a number of such positions end in draws from carelessness, I'll say it anyway. Avoid situations where the rook can both put you in check and threaten your queen as often this will result in either a stalemate or a trade of pieces, which is also a draw. The goal is to win.
- When truly in doubt, check.In this ending a check means that either the king must move, or the rook must block the check. You must remember, though, to force an arrangement that is useful to you, so don't just check willy-nilly.
- Triangulate.This is where the subtletly comes in. You need to move your queen in such a fashion that you are going to either mate the king or remove the rook or both. Always move with that in mind.
Annotated Example
+---+---+---+---+---+---+---+---+
|BK | | | | | | | | 8
+---+---+---+---+---+---+---+---+
| | | | | | | | | 7
+---+---+---+---+---+---+---+---+
| | | | | | | |WQ | 6
+---+---+---+---+---+---+---+---+
| | | | | | | | | 5
+---+---+---+---+---+---+---+---+
| | | | | | | | | 4
+---+---+---+---+---+---+---+---+
| | | | | | | | | 3
+---+---+---+---+---+---+---+---+
| |BR | |WK | | | | | 2
+---+---+---+---+---+---+---+---+
| | | | | | | | | 1
+---+---+---+---+---+---+---+---+
A B C D E F G H
1. Kc3
Notice that the while your king has few choices, the choice he made was to move toward the enemy king while also threatening the rook and forcing it to move, which keeps the black king out of the way for the moment.
1. ... Rb6
This move may look odd, but if 2. Qxc6, the black king would have been unable to move and the game would have ended in stalemate.
2. Qg7 Rc6+ 3. Kb4
Still homing in on the king, and having severely reduced the enemy's mobility by blocking it off on the eighth rank.
3. ... Rc7
Again threatening stalemate if 4. Qxc7. Fortunately the queen is not so foolish.
4. Qg6 Kb7
The black king attempts vainly to get a breath of fresh air.
5. Kb5 Kc8
White's king gains the opposition, so black decides to hide.
6. Qe8+ Kb7 7. Qe4+
White maneuvers the queen to control mating squares along the seventh rank.
7. ... Kc8 8. Kb6 Kd8
Black avoids Qe8#.
9. Qa8+ Rc8 10. Qa3 Kd7 11. Qh3+ Kd8 12. Qf5 Rc7 13. Qg5+ Kd7
Triangulating on the king/rook pair while keeping the king from escaping to the center, where you'd have to start this process all over.
14. Qd5+ Kc8 15. Qe6+ Kd8 16. Qd6+ Ke8
The moment of truth! Both the king and the queen are adjacent to the enemy rook and the king is in check. The rook falls.
17. Qxc7 Kf8
The remainder is a textbook queen mate.
18. Qh7 Ke8 19. Kc6 Kf8 20. Kd6 Ke8 21. Qe7# 1-0