Basic Endings: Rook vs Knight

vs

This is one of the 100 endgame you must know, says GM Jesus de la Villa. It was also the subject of the first recorded chess endgame study by Al-Aldi in 842 AD.

I. Evaluation & Principles

• 71% draws.
• Usually won if the knight ventures away from his king's protection.
  
• Usually won if the knight's in a corrner (red zone).
  
• Winning chances with a knight on the rim (yellow zone¹).

[08-Oct-2008 update: Added b4, b5, d2, d7, e2, e7, g4, and g5 to the yellow zone.]

II. Technique

While the above will help you determine whether to enter a rook vs knight endgame, you need to know more to actually play it well. Read on to learn more. :)

Trapping a Separated Knight

[FEN "7R/k7/8/1K6/8/1n6/8/8 w - - 0 3"]
3. Rd8 Nc1 4. Rd2 Nb3 5. Rd1

1.Rd8! confines the knight, the first step towards winning it. Finishing off the knight is straight-forward: 1...Nc1 2.Rd2 Nb3 3.Rd1 or 1...Na1 2.Rd2 Nb3 3.Rd1.²

Surviving on the Rim

[FEN "3KN3/7r/8/3k4/8/8/8/8 b - - 0 5"]
5... Ke6 6. Nc7+ Kd6 7. Ne8+ Kc6 8. Kc8 Rh8 9. Kd8 Rh7 10. Kc8 Ra7 11. Kd8

White's knight prevents the Black king from occupying d6, e6, or f6. If the rook attacks on the eighth rank, White can survive by escaping via the e7 flight square.

More Complicated Cases

These examples may mislead you into believing this ending is simple. Nothing could be further from the truth. Even super-GMs can goof, and amateur games are often comedies of errors.

rn-pos-3.pgn

As you play over the above game, can you spot all the mistakes? Every ?? indicates one side blundered so badly the result changed from won to drawn or vice-versa.

III. Mastery

"This time, let go your conscious self and act on instinct." -- Obi-Wan Kenobi

When your clock is down to 5 seconds/move, it's not enough to know the winning technique. You must be able to play on instinct, as smoothly as you swim or ride a bike. Once you reach this level of mastery, you never forget. You've never forgotten how to swim, have you? ³

GM Yasser Seirawan learned this endgame by playing a simple game. He put only a white rook, white king, and black knight on the board. He then moved the White pieces and Black pieces in turn (Black is allowed to pass!) and saw how quickly he could hunt down the knight.

Play this for a few minutes a day for the next month. :)

Footnotes

¹ - Specifically, if the knight's in the red zone it can be immediately trapped by either the king or rook. If the knight's in the yellow zone it can be trapped by the king and rook together. I find this a useful way to gauge the relative danger of squares.

² - This position arises in a line from the Al-Aldi 842 AD endgame study.

³ - For the scientifically inclined, It's stored in your procedural memory. Experimental evidence proves this knowledge even survives many forms of amnesia.

dktransformation's ending

 


View Article

This is an exciting ending played by my friend dktransformation. I think it's practical and it contains interesting positions, mistakes, and nuggets of wisdom that we can learn from.

Queen vs Knight

 


View Article

Queen vs Knight is a simple win, but when you reach it you may be tired and in time trouble. You also must watch out for forks! See how a strong master goofed it up, then learn a simple trick that makes disappointments unlikely.

B+N+P vs B+2P

 


View Annotated Game

This ending is a great example of how a bishop, knight, and king can work together. It's shamelessly stolen from "Analysis on The ENDGAME" by ugralitan, but his article didn't cover these lines. I hope you will find this annotated game enjoyable and educational. :)

loomis, 28.Aug.2006

White to move. I'm a thief, and I'll admit it. Loomis posted this excellent position in his blog entry a year ago, and now I'm covering it here (with permission).


First, the easy part. White can blockade the queenside pawns with his knight via the maneuver Nf6, Ne4, Nc3, Na2. Then we're left with a symmetrical king and pawns position on the kingside. White's kingside pawns are further advanced, and he can generate extra tempi by shuffling his knight. But is that enough to win?


[Position after 1. Nf6 a5 2. Ne4 a4 3. Nc3 a3 4. Na2 Ke7 5. Kf3 Ke6 6. Ke4]

No, because Black's king can shuffle between d6 and e6. And a pawn advance is no help. Eg, 6...Kd6 7.f5 gxf5 Kxf5 is drawn.


So we return to the original position and try something else. What if White's king stops the queenside pawns, and his knight stops the kingside pawns?

[Position after 1. Kf3 a5 2.Ke4 a4 3. Kd4 a3 4. Kc3 a2 5. Kb2 Ke7]

If only the g-pawns, the knight, and Black's king were on the kingside this would be an easy win, but Black's f7-pawn complicates things.

Therefore, the winning strategy is to eliminate the f7-pawn! 6.Nf6 Ke6 7.Ng4 Kf5 (7...f5? or 7...f6? => 8.gxf6!) 8.Nh6+ Kxf4 9.Nxf7 wins.


What a funny-looking winning position! Material is almost equal, but Black is completely lost. White's king will capture the a-pawns, then help his g-pawn promote.

Knight vs Blocked Pawns II

To master an endgame, you must learn the general rules and you must practice them. We did the first step in Knight vs Blocked Pawns. Now we tackle the second step.


White to move. Dvoretsky, 2000. With our newfound knowledge, this position is too simple. Both 1.Nb5 and 1.Nd5 place our knight in the ideal defensive position and therefore win.


Black to move. Lugovoi-Skatchkov, St. Petersburg 1999. This position is almost as easy. Black's knight needs two moves to reach his ideal defensive square e4, and White's king needs two moves to attack the pawn. The fastest win is 1...Kb2 2.Kd5 Nd2! 3.Ke6 Ne4!


Black to move. Santurbano-Vittimberga, Imperia 2001. White's king will be able to capture the Black pawn in three moves, so Black's knight must act quickly to reach c2 in time. Both N -> f3, e1, c2 and N -> f3, d4, c2 win. Nf3 is powerful because it threatens two different wins!

Valeria Vittemberga apparently didn't know this rule, so she played 63...Nf5?? trying to centralize her knight, and blundering away the win.

You may have noticed these positions didn't have any rook pawns. Rook pawns are exceptions, and lead to a draw more often than other types of pawns.

Knight vs Blocked Pawns

loomis recently noticed that my Seven Rules of Knight Endings was missing the important situation of blocked pawns. This post corrects that.

Knights should defend passed pawns from behind, as that often makes them immune from capture by the enemy king.


This is easy to grasp visually. The f5 knight defends the pawn, and Black can't capture the knight without leaving the square of the pawn. White wins!


Add a pawn to d7 and the position changes completely. The pawn can't advance when Black captures the knight. Black to move wins!

How should a knight defend a blocked pawn?


The surprising answer is, from in front. Black would love to play Kd7, forking White's knight and pawn to secure a draw, but his own pawn gets in the way. He could try to draw by threatening the knight.


But 1... Kd5 2. Kg2 Kc6 3. Kf3 Kb7 4. Ne7! gets Black nowhere. The knight is happy to hop between c8 and e7 until the White king arrives.


1... Kf7 2. Kg2 Ke8 3. Kf3 Kd8 4. Ne7! is equally fruitless. The White king will soon arrive to queen the pawn no matter what Black tries.

Our new insight is:

Knights should defend passed pawns from behind, and blocked pawns from in front (on an adjacent file) so they're immune to capture by the enemy king.

Knight vs Pawn, by request.

 
"My nephew and I were looking over this position and wondering if it was a draw. It seems like it to me. If it is, I wonder if with a little variation it would be winable by white?"


White to move. wizzifnab, 2007.

It's a draw. Black's knight blockades the a-pawn, while Black's king protects his f-pawns and prevents infilitration by the enemy king.

White's king can't penetrate along the h-file because 1.Kg3 Kh6 2.Kh4 Kg6 and Black's king can shuttle back and forth between g6 and h6, but White only has the one h4-square. White king also can't cross over to the queenside for a couple reasons:  (a) The knight will then find a way to fork the king and a-pawn (b) Black's king will have time to reach h4 and thus win White's f-pawn if the White king wanders too far away.

1. a5 Nc5 2. Kg3 Kh6 3. Kh4 Kg6 4. Kg3 Kh5 5. Kh3 Kg6 =

Remove either of Black's pawns and it's still drawn, but remove both and it's a win.

Seven Rules of Knight Endings

1. Botvinnik's Rule: Knight Endings are Pawn Endings - The techniques that win in a pawn ending (breakthroughs, shouldering, zugzwang, outside pawns) also work in knight endings. Imagine the knights gone and ask what the winning plan is--80% of the time that's correct.

2. If a Knight occupies any square in a pawn's promotion path, except a corner square, he can stop the pawn from promoting. If he even threatens such a square, 90% of the time he can stop the pawn from promoting.

3. Knight endings are extremely tactical. Keep an eye out for forks, checking moves, moves with more than one purpose, and knight sacrifices.

4. The king best shoulders a knight along a diagonal when they're one square distant, and along a rank or file when they're two squares distant.

5. If there are pawns on both wings, centralize your king and knight to increase their mobility. Knights have trouble protecting the rook-file.

6. Knights should defend passed pawns from behind, and blocked pawns from in front (on an adjacent file) so they're immune to capture by the enemy king.

7. "All Knight Endings Are Drawn But Tricky". Knight endings are drawm more often than rook endings, but they require more precise play.

Szabo-Groszpeter, 1984

 

This is an interesting and very instructive knight endgame. It highlights several themes you will find useful in your own games. First, remember Botvinnik's Rule. If the knights were gone, how would White play this position?


1.a5! bxa5 2.a6! and White's b-pawn is the first to queen. This is a basic pawn breakthrough. Moves like 1.Kxb6? are too slow to win a race.


Returning to our position with knights on-board, we would like to do the same thing, but Black's pesky knight on c4 prevents a5. We would like to trade knights, but we can't force it.

So we use a common tool in knight endings--the deflective knight sacrifice!


[Position after 1.Nd2!? Nxd2]

Before you play a crazy sacrifice, calculate as deeply as you can:

2.a5 bxa5 3.b6 Nc4 4.b7 Ne5. And not 5.b8=Q? Nc6+! -/+, but instead shouldering out the knight with the king should lead to = or +/-.

2.a5 bxa5 3.b6! a4? or 3...h4? +/- ... White's pawn is closer to the finish like and can promote before the other pawns.

2.a5 Nc4!? 3.a6 Nd6 4.Kxb6 should be = or +/-.

1...Ne5?! Kxb6 +/-

You may be able to calculate more or less deeply, or fewer or more variations, but the point is to calculate as deeply as you can. If White doesn't break through soon, he'll lose anyway, so a calculated gamble makes sense.


[Position after 2.a5 bxa5 3.b6 Nf3 4.b7 Ne5]

5.b8=Q?? Nc6+! obviously loses.

5.Ka8 Nc6! 6.b8=Q Nxb8 loses.

5.Ka6 Nc6! 6.Kb6 Nb8 and general rules tell us Black can at least force a draw, so we should pursue other lines.

5.Kb6 Nd7+ 6.Kc7 (to prevent Nb8) 7.Nc5 b8=Q 8.Na6+! and Black wins. If on the other hand White allows 6...Nb8, Black can at least force a draw, so we should pursue other lines.

6.Kb8! Nc6+ 7.Kc7 Nb4 8.Kb6 +/-
6.Kb8! Nd7+ 7.Kc8 Nb6 8.Kc7 Nc4 9.b8=Q +/-
6.Kb8! a4 7.Kc7 a3 8.b8=Q +/-


[Position after 6.Kb8! Nd7+ 7.Kc8 Nb6 8.Kc7 Nc4 9.b8=Q +/-]

A winning position.

Nikolic-Vaganian, 2006

After 23...Kxf8 you'll find the main attraction--a knight vs knight endgame between two super-GMs. Botvinnik's Rule indicates a draw is likely.

24.Kf1 - Centralizing his king.

24...Ne4! - There's a tactical threat here! If White doesn't respond accurately, 25...Nc3! 26.a3 Nb1! 27.a4 Nc3! 28.a5 Na2! wins a pawn and likely the game. It's the same tactic we learned in Chekhover, 1938.

25.a3! - Accurate.

25...Ke7 26.Ke2 - More centralization.

26...c5 27.bxc5 Nxc5 - This swap slightly favors Black, because he's closer to creating a passed pawn on the queenside.

28.Nd4 g6 29.f3 a6 - Nd4 wasn't particularly threatening, but both sides decide to minimize counterplay. Now White's knight has no potential penetration points, and the Black's knight only option is the silly a4.

29.g4 Kd6 30.h4 Kd5 31.Kd2 - While White attempts to create a passer on the kingside, Black centralizes his king. Soon Black's king is superior and White's on the defensive.

31...Ne6! 32. Nb3! Offering a knight exchange. Black's king is superior to White's king, and knight endings are easier to draw than pawn endings. Don't get too hung up on Botvinnik's Rule! White wisely declines the offer.

33...f5 34.gxf5 gxf5 35.Kc3 b5?! - This seems like a mistake. It moves Black's pawns closer to White's king. White will easily penetrate on the queenside, but Black will have trouble penetrating on the kingside. f4? is met by e4! I think Black had winning chances before this.

36.Kb4 Nd8!? - This seems odd when a simple Nc7 defends the pawns, but Nc7 is too passive, and there's an idea behind this move we'll soon see.

37.Ka5 Kc4 38.Nd4 f4 - Good timing! Now e4 and fxe4 are impossible.

39. Nf5 fxe3 40. Nxe3+ Kd3 41. Nf5 Nc6+ 42. Kxa6 b4! 43. axb4 Nxb4+ - White's a pawn up, but Black's king is more active. Botvinnik forecasts a draw.

44. Kb5 Nc2 45. Kc5 Ke2 46. Nxh6 Kxf3 - Finally! Knight & Pawn vs Knight. Now Botvinnik's Rule again forecasts a win, but concrete calculation shows it's only a draw. White's own knight tragically slows his own pawn's advance.

47. h5 Kf4 48. Nf7 Kf5 49. Kd6 Kf6 50. Ne5 Kg5 1/2-1/2

An interesting game. Certainly not a boring "Grandmaster Draw".   :)

Chekhover, 1938

Vitaly Chekhover was a master on knight endings. He once wrote an entire book on the subject with the help of Yuri Averbakh.


Black to move. In this composition, immediately pushing the f- or h-pawns obviously leads to failure. What's less obvious is that the king cannot travel to the kingside to help his pawns.

  1...Kc3 2.Ne4+! {forks the king and f-pawn} =
  1...Kc5 2.Ne4+! {forks the king and f-pawn} =
  1...Kc4 2.Ne4! {threatens Nxf6} f5 3.Nd6+! =


Since the c3, c4, and c5 squares are mined, Black must find another path to the kingside pawns if he wishes to win. Kb3 and Kb5 are tempting.

If 1...Kb3, White has a brilliant refutation:   2.Ne4! f5 3.Ng3! f4 4.Ne2! f3 5.Nd4+! =. I suggest playing these moves out. Once you've seen the solution, I think you'll find it's more intuitive than the long list of moves suggests.


If 1.Kb5 then Ne4! 2.f5 Nd6+! =


What does that leave? Well, there's the counter-intuitive Ka5-Kb6 maneuver. Black could then cross the c-file on c6, c7, or c8. Let's play forward a few moves and reach that position: 1... Ka5 2. Ka2 Kb6 3. Kxa3.

3...Kc6 2.Ne4! f5 3.Ng3! f4 4.Ne2! f3 5.Nd4+! Yes, it's the same brilliant maneuver that White used in answer to Kc4.

3...Kc7 4.Nh5! f5 5.Ng7! f4 6.Ne6+! In a similar manner, White again wins the f-pawn. So no matter what, White can draw using knight forks!

If the king were on c8, then 4.Ne4 f5 5.Nd6+! would win.

---

We've already seen how White can draw using tactical shots, but let's consider what would happen if we missed one so 3...Kc7 4.Kb4 Kd7 5.Nf5 h5:

White's knight creates a barrier that the Black king can't penetrate. Black made progress with his h-pawn, but now he's forced back the way he came.

6.Kc5!


White's king increases the size of the barrier. How can Black make progress? If 6...Kc7 7.Ng7! h4 8.Ne8+! All other moves result in the loss of the queenside pawn. So now we've seen how useful creating barriers in knight endings can be, and how easily they can be setup.

I hope you enjoyed this wonderfully instructive composition from Chekhover. The missed-tactic game is below in PGN format, for your convenience.

[Event "Chekhover, 1938"]
[Result "1/2-1/2"]
[SetUp "1"]
[FEN "8/8/p4p1p/8/1k6/p5N1/8/K7 b - - 0 1"]
[PlyCount "32"]

1... Ka5 2. Ka2 Kb6 3. Kxa3 Kc7 4. Kb4 Kd7 5. Nf5 h5 6. Kc5 Kd8 
7. Kb6 Kd7 8. Kxa6 Kc6 9. Nh4 Kd6 10. Kb6 Ke5 11. Kc5 Ke4 12. Kc4 f5 
13. Kc3 f4 14. Kd2 f3 15. Ke1 Ke3 16. Nxf3 Kxf3 17. Kf1 1/2-1/2

Knight vs Pawn

If the knight is able to occupy or threaten any square in the pawn's path, except a corner square, he can force a draw.

Generally, these endings play themselves, but sometimes they require brutal calculation. Let's look at positions where the players goofed so that we might learn from them.


White to play. Morant Sampol-Hallerod, Calvia 2006. The obvious drawing moves are Na2 and Nc2 which occupy or threaten squares in the pawn's path. White played 51.Na6?? and soon lost the game, despite being a piece up.


White to play. Vlkovic-Arpa, Slovakia 1998. The knight is only threatening a corner square, but after 60.Ke6?? Nf8+, it threatened h7 and forced a draw. White should have secured the win by protecting the f8 square with 60.Ke8.


White to move. Appel-Liepold, Kaufbeuren 1998. Quick! Can you spot White's winning move? Appel played 65.h5? Ng4! and drew, but much better was the seemingly counter-intuitive 65.Kf5!, which stops the knight from reaching g4 and wins.


White to move. Petraki-Papadimitrou, Nikea 2005. White played 66.Nc1+ and lost. What?! You're about to say, "But his move followed our rule!" and you're perfectly correct. This just happens to be a rare exception.

White actually had two choices: Nb4 (drawing) and Nc1 (losing). Remember the maxim, "A Knight on the Rim is Dim" and you'll make the right move, even if you encounter one of these mysterious exceptions in your games.


Black to play. Ikonnikov-Verlan, France 2004. Black must calculate deeply to find the draw. Nd8? accomplishes nothing, for after that where does the knight go? The White king is defending c6. Instead, 67...Nh6!! 58.a5 Nf5 59.a6 Ne7+ and the White king can't protect both c6 and c8 so it's a draw.

If you couldn't solve this position, no worries. Sergei Verlan couldn't solve this position over the board, and his FIDE rating was 2285. However, you should have realized that Nd8 led nowhere, as he was able to do.

I hope you found these positions interesting and instructive.   :)

Capablanca-Corzo, 1901

I recently acquired "Capablanca's Best Chess Endings". Over the coming week, I plan to share some of these games with you.


The first game was a let down, because Corzo blundered away the Cuban Championship by playing 29...Nf5. After 30.Kxg4 and 31.Bxf5 or 31.Bxg4 White's playing an endgame that even I can evaluate as won (a passed pawn with pawns on both wings).

Then I played out the position against Rybka, and I didn't win! Perhaps this tells me something about Capablanca. He didn't show endgame genius in this game, but he did demonstrate superb technique we should seek to emulate.

It also tells me I need to spend more time studying bishop vs knight endgames!

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Bishop & Pawn vs Knight

This is the most common minor piece ending, so it's definitely good to know.

The attacker often must force his opponent into zugzwang in order to win. That's because bishops can "lose a move" much easier than knights can.

1.Kc7 Kc5 2.Bc6 (zugzwang). If Black moves his king, he loses his knight. If Black moves his knight, White's pawn can queen.


Sometimes, the attacker can corral the enemy knight, restricting its movement. If the knight becomes immobilized, the attacker wins easily.


The defender draws if he can get in front of the pawn or protect his knight.

1...Be6 2.Ne3 Bd7 3.Ng2 Bh3 4.Ne3 =

Bishop & Pawn vs Knight is drawn roughly 70% of the time. Even if the attacker promotes, they still have to win another endgame--Queen vs Knight.

Knight Endgames II

I wanted a chance to apply Botvinnik's maxim that knight endgames are pawn endgames, and I remembered that takchess had recently played a long knight endgame to a draw, so what better an opportunity to try this new theory?

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To my surprise, the theory is actually true!

The key is to realize that you have a passed pawn on the d-file, and on the a/b files a pawn majority which could very easily be converted into a second passed pawn. Once you have two passed pawns, Black will have a nightmarish time trying to defend both threats. Even a top chess engine didn't last very long--and I imagine a human would lose even quicker.

Knight Endgames

Knight endings are quite simple to evaluate:

1. Botvinnik's Rule:  Knight endgames are pawn endgames.

In other words, imagine that the knights were not there and then evaluate the position. The evaluation rarely changes with the knights present.

2. Knights have a hard time stopping rook's pawns.

As a knight approaches the edge of the board, fewer squares are available for it to move on, and thus it has a harder time moving about.

Tips for winning:

    A. Watch for knight forks.
    B. Remember that knights can't "lose a tempo" to avoid zugzwang.
    C. Make flexible moves that aim for two goals at once.

Does this seem oversimplified? Well, it is! I want to focus most of my energy on rook and pawn endings. Simple rules can guide me for the rest.

9/2007 Update: I've published a more sophisticated set of seven rules.

Bishop & Knight Mate

Emboldened by a blog entry and a lecture from chesslectures.com, I relearned the Bishop & Knight vs King mate.

The steps to this mate are simple:
  1. Push the enemy king to the edge of the board.
  2. Force him to the correct corner.
  3. Mate him.

You must force the enemy king into the corner that's the same color as your bishop to mate him. Mostly, you simply take away his safe squares one by one.

The scary part is, to force him into the corner, you must allow the enemy king to leave the edge of the board for a few moves, risking escape! Watch moves 8-12 carefully.





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[Event "Bishop & Knight Mate"]
[Date "2007.08.10"]
[White "likesforests"]
[Black "Nalimov"]
[Result "1-0"]
[FEN "1k6/8/1K1N4/6B1/8/8/8/8 w - - 0 1"]
1. Kc6 Ka7 2.Nb5+ Kb8 3. Nc7 Kc8 4. Be3 Kb8 5. Bd4 Kc8 6. Ba7 Kd8 7. Nd5 Ke8 8. Bd4 Kf7 9.Nf4 Ke7 10. Kc7 Ke8 11. Bf6 Kf7 12. Bg5 Ke8 13. Kd6 Kf7 14. Kd7 Kf8 15. Ke6 Ke8 16. Nh5 Kf8 17. Be7+ Kg8 18. Kf6 Kh7 19. Bf8 Kg8 20. Ke7 Kh7 21. Kf7 Kh8 22. Bg7+ Kh7 23. Nf6#