I recently played a blitz game, where for the first time ever I got this ending. I had pretty remote idea how to win, pursued his knight (ignoring the draw offer) for 48 moves until he blundered. Of course I wasn’t quite satisfied, so I decided to learn this ending.
Dvoretsky says that it is usually drawn, but there are several exceptions:
1. If the knight separated from the king, often it can be caught.
2. If the knight is in the corner, it can be taken because of zugzwang.
3. The squares g7/b7 are not good for the knight.
So, I looked at my game and found the moment (mostly my opponent played right), when I could separate his knight and king. Winning is not easy and even Fritz had a problem, so I used Endgame Nalimov Tablebases Online. Here is the position after Nf5-e3?:

1. Rf7 Ke8 2. Rf4 Kd7 3. Kd4

3. … Nc2+ 4. Kd5 Ne3+ 5. Kc5 Kc7 6. Rf7+

6. … Kd8 7. Kd4 Nc2+ 8. Ke5 Na3 9. Rb7

9. … Nc4+ 10. Ke6 Kc8 11. Rb5 Ne3 12. Rb2

12. … Ng4 13. Rc2+ Kb7 14. Re2 Ka6 15. Kf7

15. … Nh6+ 16. Kg6 Ng8 17. Re8 Nh6

Though this ending is rare, it shows very well the relative strength of the rook and knight. Also you can learn the typical ways of attacking/restricting the knight, for example putting the rook nearby on the same vertical/horisontal which should be useful for the regular R vs. N endgame (with pawns).
September 23, 2009 at 4:45 am
I spent a few hours once on that ending.
What I took away is basically that if the king is on the side of the board, and the knight is not completely and hopelessly left out to dry somewhere in Timbuktu, it’s probably a draw. In your game, it looks like the knight found it’s way to Timbuktu. Very hard to win, so congrats!
September 23, 2009 at 5:33 am
This was a blitz game wow.
I would have been so nervous of getting forked by the knight, i would have kept my king and rook on different colour square.
I think i would have been a coward and taken the draw.I know in this position you shpuld play on,as black can only draw but the clock ticks away.
But that would not have lead to your instructional ending.
Endings are a necessary evil you have to study them,but most games finish before the ending.
Perhaps thats the main reason most players study openings much greater than endings.
September 23, 2009 at 8:28 am
That was neat how you both cut-off the knight and kept the opponent’s king at bay. I particularly liked the Rf7-f4 maneuver, and how you finished it off.
I would have blitzed out 10…Na5, expecting to draw, which I think it should.
September 23, 2009 at 10:53 am
linuxguy – you are right about Timbuktu and about hard to win too. There are positions where you can win faster, for example if you put the knight on d3 instead of e3, the win is: 1. Kd6 Ke8 2. Rh3 Nf2 3. Re3+ Kd8 4. Re2 Ng4 5. Ke6 Kc7 6. Kf5 Nh6+ 7. Kg6 Ng8 8. Re8 Nh6 9. Kxh6
You see, even if it takes you 3 times more than Nalimov says, it’s still fine as long as it’s under 50 moves, you just have to play on.
Thanks for the praise, it’s actually Nalimov, not me
. By the way, it says that 9….Na5 loses due to 10. Rb5 Nc6 11. Kd6 Na7 12. Rb8+ Nc8+ 13. Kc6 Ke7 14. Rxc8
After initial Ne3 it’s a win no matter how Black plays.
chessx – my clock was OK, I played with increment. Yeah, different colour squares could help since it’s blitz.
You know, every time I study some ending, I actually like it. The thing is to force yourself to do it systematically.
Yes in the last tourney 3 games were finished before endgame, and 1 endgame was just lost before it started, but you never know. I got Lucena with the guy rated 250 lower than me, and looking at the bishop endings found that in one of my OTB games I had a wrong idea and should have lost, luckily for me my opponent made a mistake and it was a draw. Since getting Philidor position once in 5000 blitz games (remember my post?) you know what happened? I got 2 more in another 1000!. I drew both of them, knowing what to do.
Actually I think openings are evil, because we spend so much time on them neglecting other components of the game. Yeah, they give you a short-term gain. Calculation training and studying endgames are maybe annoying, but they can give you a long-term advantage. Knowledge can save you from embarrassment of not winning Q vs R endgame for example (which I won just by time recently and again studied it right away).