Sunday, October 05, 2008

Basic Endings: Rook vs Knight

Rook vs Knight

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.

16 comments:

likesforests said...

BDK, Phaedrus, and Tempo have been talking about chess mastery as a skill rather than knowledge.

Endgame master consists of knowing evaluations, precise positions, principles, and techniques.

Some aspects of this endgame can go into "procedural memory", and I attempt to maximize that with the selected exercises. But some aspects, such as the principles and evaluations, I can't help but feel are better stored as text.

That means an occasional refresh is needed. On the fortunate side, the general principles for endings can be reviewed fairly quickly.

chesstiger said...

Chess endgames is one of the aspects of chess that can be learned the most since it's mostly about little pieces on the board.

Its good to learn endgames since it are always good examples to see how pieces work together and this one can at a later stage also trying to implement in your middlegame and who knows even the opening.

likesforests said...

Yes! This drill definitely gives one a better feel for the pieces. I see, for example, that although a knight on the rim is dim, a knight on b2, b7, g2, or g7 is dimmer. And certain "trapping patterns" are emerging... such as the king, knight, and rook lined up on a diagonal each two squares apart... or the king in front of the knight with the rook off to the side.

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Temposchlucker said...

It's fairly simple. Everything that remains of this position after a break of 4 months will be your habits. Either good or bad. Habits crystallized in the way you scan the board. Those habits are stored in procedural memory and are available immediately after the break. All the subtle reflexions and knowledge you have now will then be evaporated.

There is a way knowledge can survive such break period though. With what remains of your knowledge after 4 months you can reconstruct some of your knowledge by using logic reasoning. But that is a highly inefficient and slow process and prone to error. That is the main method how amateurs play chess, by the way.

The flaw of DLM's method for habitforming lies in the fact that it invites you to mechanically repeat the examples. That is not how habits are formed.

Troyis otoh provides you with positions that are slightly different each time, so passive anticipation on the answer is impossible. That keeps your attention active and you form your habits in no time.

Phaedrus said...

Hello Likesforests,

After your kind and generous participation to my exercise, I nevertheless hesitated to give a comment on this post.

And if I sound a bit critical about the subject of this post, please forgive me. I can assure you that is not because I do not appreciate this excelent piece of analyses and writing. I just want to make clear why I have chosen another path to improve, than studying these kind of endgames.

I have have skipped analyzing endgames with no pawns.

First of all I have noticed that endgames with no pawns occur very seldom. Secondly in most of them it is not hard to defend most of them, if you are behind in material.

Just to give you two examples:

If you are defending K VS K,B,N, the only thing you have to know is to stay away as long as possible from the corner square that has the same color as the bishop. Of course you will lose this against best play, but this is the only knowledge one needs as a defender.
Winning this endgame takes skill. But I occurs so rarely that even if it would take only one hour to learn it for a lifetime, it is hardly worth the effort.

Same here with K,R VS K,N. It does not occur very frequently (I only had it on the board twice in 30 years of competitive chess), and the main principles are very easy to remember. If you have the rook, try to separate King and Night. And if you have the night, keep or bring it close to the king. In 90% of its occurrence in games, this is adequate. The sophisticated technique that is required for the other 10% is hard to learn.

So I do not believe that giving this a lot of time and effort is a good investment for someone who wants to improve his rating. He can use this time better for other exercises in themes that occur more often.
Of course things are different if you want to improve your endgame skills as such.

Rolling Pawns said...

phaedrus - I had Lucena position only once in 3000 games online and never rated OTB ( I played 25 games in a year ). So, looks like it's not worth learning. That's what I thought even after drawing that online game instead of winning. Nevertheless, after losing one OTB R+Ps vs. R+Ps endgame I decided to learn rook endgames and started with Lucena and Philidor. So, this Sunday I play OTB and I get Lucena (I have a pawn). I am getting the feeling, that studying any endgame is much more useful, than for example playing a few blitz games ( which help to develop your tactical skills, train openings, etc. - that's what I thought until my rating hit a plateau ).

likesforests said...

tempo, "Everything that remains of this position after a break of 4 months will be your habits. Those habits are stored in procedural memory and are available immediately after the break."

Thank you. But now, I'm sure you're missing part of the equation.

Committing every aspect of every endgame to procedural memory would take a very, very long time. And it would be unnecessary, at least to reach the NM or IM level.

"There is a way knowledge can survive such break period though. With what remains of your knowledge after 4 months you can reconstruct some of your knowledge by using logic reasoning. But that is a highly inefficient and slow process and prone to error. That is the main method how amateurs play chess, by the way."

What is the capital of France, and what is the capital of Spain?

I doubt it took you more than 3 seconds to answer each question, or that you logically constructed the answers. But this knowledge is not part of a procedure. They're facts. They're stored in semantic memory.

When BDK failed to solve a tactic a week ago, I knew the answer because material-up pawn endgames are easier to win than material-up rook endgames. That wasn't a procedure, or an intuition, just a fact I knew well.

If the 1700 and 2000 in this example had memorized, "Keep the N near the K, and keep both out of the corner." they would have played significantly better... maybe 2200-level. And there are better ways to state the rules.

Dvoretsky--he's a master and a coach of masters--feels endgame mastery requires knowing precise positions, techniques, principles, and evaluations.

The more I think about it, his explanation is genius in that it acknowledges that one needs a mix of semantic and procedural knowledge to master an endgame.

"The flaw of DLM's method for habitforming lies in the fact that it invites you to mechanically repeat the examples. Troyis otoh provides you with positions that are slightly different each time, so passive anticipation on the answer is impossible. That keeps your attention active and you form your habits in no time."

Now this is a gem on an idea! Tempo, you're the master of procedural memory. But do not forget that the human mind has evolved other forms of memory. And perhaps these other forms have much to do with our evolution.

Conclusion--to master an endgame:

(1) memorize the principles and evaluations. Perhaps write them on a sheet and review them every month or three (spaced repetition: you can gradually reduce how often you review them.)

(2) Practice the key technique(s) many times on different positions until they're stored in your procedural memory. This type of memory has the amazing attribute that it doesn't require review to stay fresh.

(3) Precise positions - One only needs to separately memorize the few precise positions that are important and also an exception to the principles, evaluations, and techniques already learned.

Thoughts?

likesforests said...

"If you have the rook, try to separate King and Night. And if you have the night, keep or bring it close to the king. In 90% of its occurrence in games, this is adequate. The sophisticated technique that is required for the other 10% is hard to learn."

Phaedrus, I agree. If one learns the principles in part I, which are illustrated in part II, that is probably enough to be able to play R vs N (pawnless) well enough in at least 80% of cases.

But the intuitive feel I'm getting for a knight's best squares and how to dominate a knight, will surely help in other situations. I just reviewed the R v N (with pawns) endings in my stored games and I'm choosing better moves now.

It is hard to gauge the benefit of a better feel for the pieces, no? I have a similar problem gauging the benefits from my Troyis stint.

likesforests said...

rolling pawns - Yes, I've noticed that effect many times!!

I rarely encounter a particular ending. Then I learn how to win it. Then I encounter it 2x to 3x as often. Maybe it's because now it is a "win condition" that we aim for. :)

Blue Devil Knight said...

Very interesting topic.

Likeforests points to something important, which I tried to convince tempo of almost two years ago (wow). I said:
"I was speculating that chess isn't as simple as playing a piano. For one, semantic/declarative memory isn't always slow and effortful. For instance, what is the English word for a female dog? Most English speakers will immediately think of the word 'bitch', which is in semantic memory (a form of declarative memory).

"Perhaps, with chess, there is a similar rapid mostly unconscious access to semantic memory, and this guides our saccades to relevant locations on the board."

I think there is something important here. Learning chess is much like learning a language, and word meanings (almost by definition) are stored in semantic memory. But I don't struggle to use English. It isn't slow or effortful. This is probably what it is like for kids that play a lot of chess.

The two memory systems seem to interact in ways I frankly can't fathom. Principles and practice lead to skills. I have skills with the English language, don't require all that much effort to come up with a good word for something.

I remember when I used to TA logic in grad school. I became a total bad-ass at doing proofs on the fly. I would just see the right way to get the answer, without much conscious access to how I did it. It was a skill that relied on semantic memory.

OTOH, I'm not sure how much chess is like this. I could be persuaded that logic and chess are nothing alike, or that they are pretty much identical in principle (note I'm not saying chess is logic, but that the psychology of chess skill, language skill, and logic skills are of the same kind).

As a neuroscientist, I have a huge background knowledge of basic facts that I don't even really remember. When someone says something like "neurons transmit information using sound waves" (as some physicists recently published) my red "bullshit" light went off, and it actually took me a little conscious deliberation time to articulate why it was bullshit (i.e., all the basic facts about why we think they communicate using electrochemical signals).

I'm sure many reading this have an area of expertise where they have this experience.

This is much like a GM who sees a move and a little light goes off that it is bad, but it may take him some time to explain to you why, but if he asks you to play it against him he will destroy you.

OTOH, we know that simply reading about chess is not sufficient to be a good chess player, so that suggests at the very least that my above claim is right: principles and practice are important. The problem with adults is perhaps that they often get too focused on principles.

Ironically, one of my favorite posts of Tempos is where he lays out tons of endgame principles before a tournament (it is here.

Funny thing is sometimes the principles are simply memorized, internalized, act as unconscious triggers for bullshit detectors, but are just flat-out wrong (this would be an example of a cognitive bias as Rowson talks about). In programming, from day one I learned not to use global variables, but it is to the point now where I don't even consider using them, even if it would actually be the smart thing to do. Unfortunately when I program I can't fire up Fritz to check my ideas :)

Temposchlucker said...

You reveals the flaws in my pseudo scientific reasoning quite well. I was already aware of it, but somewhat subconscious. I use scientific language while I have unsufficient knowledge of it. The problem is that I have no alternative. I don't have another framework of terminolgy I can use. So I'm using a defective vehicle to transport me. I treat the retrieval of "Paris" as the capital of France as a motorskill. Which is scientificly wrong, I belief. The reason I do this, is that there is a similarity between the speed, the lack of effort and the unconsciousness with which Paris is retrieved and a bike is ridden. Motorskill is the wrong word. But what is the right word to express this similarity?

It is probably best that I devote another post to this subject.

Temposchlucker said...

Blue, I will get back to that.

likesforests said...

I've spent oodles of time solving complex endgame positions and learning techniques and patterns for solving them, but I don't ever recall trying to memorize a list of principles and evaluations.

I just wrote out 111 evaluations I want to commit to memory. Simple but very specific, like in Bs of Opps: B+2P vs B: "With a- and d-pawns (or h- and e-pawns) it is impossible to win against a normal defensive setup" and "Two bishop's pawns (c- and f-files) win unless the position belongs to the third draw scenario."

Let's see how this works out. :)

Blue Devil Knight said...

Tempo: that seems reasonable. There is definitely a difference between the slow, conscious, deliberative thought, and the quick effortless (non)thought of using language or solving simple math/programming problems.

tanc(happyhippo) said...

Hello,

Thanks for the refresher on NvR endings. :)

There are indeed certain basic endings that is important.

The nice thing about learning endgames is that you know when you can get the draw and when you can go from middlegame to a winning endgame.

I definitely agree with your that it's definitely not easy committed endgame techniques to "procedural memory" but constant refreshers are a must unfortunately. :(

cheers and thanks