How do you checkmate with a Rook and King versus King? Is there a good and fast method? Can you explain it in a good way? Thanks!
I know you're a FIDE Master :), so I suppose you're more interested in this question from a teaching perspective.
The simplest way to understand a checkmate with King and Rook vs King is the idea of the rectangle of the opposing king. Consider this position-
Here, the Black King is restricted by the White Rook in this giant rectangular area of the chessboard. For simplicity, I am not considering the area restricted by the White King, which would be like this -
A simple way (I'll deal with optimizations later) to checkmate is to ensure that this rectangle gets smaller and smaller, so that the Black King is pushed to a corner of the board (more visual representation below with diagrams).
[FEN "8/8/8/8/4k3/8/8/K6R w - - 0 1"] 1. Re1+ Kd4 2. Kb1 Kd3 3. Kc1 Kd4 4. Re2 Kd3 5. Kd1 Kd4 6. Kd2 Kc4 7. Re3 Kd4 8. Ke2 Kc4 9. Rd3 Kc5 10. Ke3 Kc4 11. Ke4 Kc5 12. Rd4 Kc6 13. Rd5 Kb6 14. Kd4 Kc6 15. Kc4 Kb6 16. Rc5 Kb7 17. Kb5 Ka7 18. Rc6 Kb7 19. Kc5 Ka7 20. Rb6 Ka8 21. Kc6 Ka7 22. Kc7 Ka8 23. Ra6# 1. Re1+ Kd4
2. Kb1 Kd3 3. Kc1 Kd4 4. Re2 Kd3 5. Kd1
5...Kd4 6. Kd2 Kc4 7. Re3 Kd4
8. Ke2 Kc4 9. Rd3
9...Kc5 10. Ke3 Kc4 11. Ke4 Kc5 12. Rd4
12...Kc6 13. Rd5
13...Kb6 14. Kd4 Kc6 15. Kc4 Kb6 16. Rc5
16...Kb7 17. Kb5 Ka7 18. Rc6
18...Kb7 19. Kc5 Ka7 20. Rb6
Ka8 21.Kc6 Ka7 22. Kc7 Ka8 23. Ra6# 1-0
Of course, with this method, the one mistake that White must avoid is stalemate -
- Rb7?? stalemate!
Optimizations and Tricks.
More experienced players can get to smaller rectangles quicker by looking further ahead.
One trick is to trap the king in a smaller rectangle if it comes too close to the rook. For this, White also has to use the king more actively.
[FEN "8/8/8/8/4k3/8/8/K6R w - - 0 1"] 1. Re1+ Kd4 2. Kb2 Kd3 3. Kb3! Kd2 4. Re4! Kd3 5. Rc4
Another trick is to give a rook check when the kings are in opposition.
[FEN "8/8/8/2k5/8/2K5/8/4R3 w - - 0 6"] 1. Re5+!? (1. Rd1!) Kd6 2.Kd4
This trick is not necessarily optimal. In the above example, White can actually mate faster with the move 1. Rd1!
[FEN "8/8/8/2k5/8/2K5/8/4R3 w - - 0 6"] 1. Rd1! Kb5 2. Rd5+! Kc6 3. Kc4
The above optimization is also made possible by the rook-waiting-move trick. If, in the above position, instead of going to c6, the Black king tries to escape via a4, then the following checkmate is possible.
[FEN "8/8/8/1k6/8/2K5/8/3R4 w - - 0 7"] 1. Rd5+ Ka4 2. Rc5! Ka3 3. Ra5#
One more idea is to use king-opposition (in combination with the rook) to push the enemy king behind.
[FEN "8/8/8/2k5/8/8/2K5/4R3 w - - 0 4"] 1. Kc3! (1...Kd5 2. Re3!) Kc6 2. Kc4! Kd6 3. Re4
Combining these different ideas, here are two of the most optimal mates possible from the starting position -
[FEN "8/8/8/8/4k3/8/8/K6R w - - 0 1"] 1. Re1+ (1. Kb2 Kf4 2. Kc3 Ke5 3. Re1+ Kf6 4. Kd4 Kf5 5. Re4 Kf6 6. Re5 Kg6 7. Ke4 Kf6 8. Kf4 Kg6 9. Re6+ Kg7 10. Kg5 Kf7 11. Re5 Kg7 12. Rf5 Kh7 13. Kf6! Kg8 14. Rh5 Kf8 15. Rh8#) 1... Kd4 2. Kb2 Kd3 3. Kb3! Kd4 4. Kb4 $3 Kd3 5. Kc5! Kd2 6. Re4 Kd3 7. Re5 Kc3 8. Rd5 Kb3 9. Rd3+ Kc2 10. Kc4 Kb2 11. Rd2+ Kc1 12. Kc3 Kb1 13. Kb3 Kc1 14. Rd3 Kb1 15. Rd1# *
I would teach the slow but safe and easy way first: The rook divides the board in two halves. Then the attacking king tries to get in opposition to the enemy king (sometimes the rook has to swap sides or needs to make a waiting move for this to happen). Then the rook gives a check, hence pushing the king one field closer to the edge of the board. The mate follows exactly the same pattern.
I would suggest -- Play this out with an opponent. That's the best way to get the feel of it. Otherwise just google and you will see lots of explanation -- with some nice graphics. www.chess.com and chesstempo.com even have some practice board where you can learn.
One link that covers good theory and explains slowly is http://www.chesscorner.com/tutorial/basic/r_k_mate/r_k_mate.htm
Rule of thumb for checkmate with Rook against lone king:
- Use the Rook to restrict the opponent's King.
- Support the Rook with the King.
- Confine the King to a box and make the box smaller if possible.
- If it is not possible to make the box smaller, move the King (a waiting move to force back the opponent's King.).
- Last but not least which leads to victory is
Force your opponent king to corner (
Rank - 1st or 8th or File - a or h).
Wes already gave a good answer from the teaching perspective for the OP. This answer is complementary to his answer. I am concentrating on the optimization and tricks still keeping beginners in mind (may not be useful to OP). If you haven't seen the basic technique read that form Wes's answer first, then read these tricks and finally go back to optimisation and tricks section of his answer.
The most basic tool in making it faster is flexibility
(eg: not sticking one method always whether it is king-in-opposition method or box-in-method)
Also, just to recall, our purpose is to confine the king to an edge, not to a corner. And we are not preoccupied with which edge it must be.
Though obvious, these fact helps to make it shorter.
Trick 1) When you use king-in-opposition, there is no need to go all the way to the end of the side.
So, instead of the following, you can make the check earlier if the king is confined enough (see the variation).
[FEN "8/8/8/4k3/R7/2K5/8/8 w - - 0 1"] 1.Kd3 Kf5 2.Ke3 Kg5 3.Kf3 ( 3.Ra5+ Kf6 ( 3...Kg4 4.Rb5 Kg3 5.Rg5+) 4.Ke4 Kg6 5.Ra6+ Kg5 6.Rb6 Kg4 7.Rg6+ )
5...Kh5 6.Kg3 Kg5 7.Ra5+ *
Trick 2) King can be inside the rectangle instead of outside
[FEN "8/8/1k6/8/2R5/1K6/8/8 w - - 0 3"] 3.Kb4 Kb7 ( 3...Ka6 4.Rc6+ Kb7 5.Kb5 ) 4.Kb5 Ka7 5.Rc7+ ( 5.Kc6 Kb8 6.Ra4 ) *