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Dan Heisman

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Learning Endgames

Quote of the Month: Until you are master strength you don't have to know more than about two dozen exact endings.

The Quote of the Month is from GM Andy Soltis's book Studying Chess Made Easy, and can be found in his chapter "Overcoming Endgame Phobia." This chapter is full of good, practical advice, but the quote I selected is at the heart of Soltis's main point. In order to understand it, you need to know what Soltis's meant by "exact endgames." He defines these as endings with "only a few pieces and pawns. They are important because they can occur at the end of many other endgames and because their outcome is certain. Every exact endgame is either a forced win or a forced draw."

I gave examples of several important exact endgames in King and Pawn vs. King and K&P&? vs. K. Other exact endgames, but not necessarily needed by players wishing to achieve 2000, would be the famous rook and one pawn vs rook endgames Lucena and Philidor.

In 1972 I lost a trivial Philidor endgame to famous master E. Schuyler Jackson, and I had already been rated 2100 for a couple of years! At that time my rating put me in the upper two percent of USCF players, yet it was not until after losing that game did I learn the well-known draw. So, one can achieve a reasonably high level of play without memorizing a ton of book endgame knowledge.

Exact endgames are examples of chess knowledge. Many players are under the impression that to be a decent endgame player you only need to acquire as much of this type of knowledge as possible. But the Quote of the Month is closer to the truth: until you are a strong player, learning more than the rudimentary number of exact positions will probably just result in diminishing returns. Unfortunately, many fine endgame books are written for stronger players, and have a multitude of exact endgames whose understanding and solutions are not necessary for becoming a reasonable endgame player. So a main theme of Soltis's chapter is that you aren't likely going become a strong endgame player just by judiciously studying one or more of these fine works.

At the opposite end of the spectrum, you can study "practical" endgames and learn endgame principles in a more general manner by playing out positions in books like Capablanca's Best Endgames. This is possibly a more helpful approach, necessarily augmented by those two dozen exact endgames that yes, you should "memorize" or "understand" – preferably the latter.

There are many ways to pick up basic chess knowledge. Players rated under 2000 can choose among books such as Alburt and Krogius's Just the Facts or Averbach's Essential Chess Endgames. For additional level of detail Silman's Complete Endgame Course is excellent. For players in the expert-master range a very good "knowledge" book is de la Villa's 100 Endgames You Must Know.

If you prefer to pick up endgame knowledge via puzzles, rather than examples, I highly recommend Pandolfini's Endgame Course. A major problem with this work is the many typos. Bruce told me his publisher refused to allow these to be fixed, even in future printings! Therefore, before attempting the problems, fix the material via the errata list.

None of the material above will help you very much if you play mostly fifteen minute games and consistently take two to three minutes max on the entire endgame. Ditto if you play much longer time-control games, but play these quickly and don't take more than fifteen or twenty seconds on your moves during the endgame. Even if you have acquired the basic endgame knowledge, you are probably lucky if you can apply it in a meaningful manner at  fifteen or twenty seconds per move.

Similarly, even if you have the knowledge and don't take time to check and see if it applies in the current position, disaster can strike. My most well-known student, Howard Stern, learned a valuable lesson when he tried to apply the knowledge he learned from the following position:

Black to play

Novice Nook
[FEN "8/3k4/3P4/3K4/8/8/8/8"]

Here I showed Howard the basic endgame already featured in King and Pawn vs. King: In the state where the offensive king can't get in front of the pawn and the pawn reaches the sixth rank, then the defending king, whenever it is on the seventh rank blockading the pawn, must go straight back. Here 1...Kd8! 2.Ke6 Ke8 3.d7+ Kd8 draws, while 1...Ke8?? 2.Ke6 Kd8 3.d7 wins. The first few times you reach a similar position, if you are not sure if you remember this correctly – and possibly even if you do! – you should also still calculate it carefully, to corroborate your endgame knowledge.

But shortly thereafter, Howard arrived at the following position:

Black to play after 1.Kd5-Kc5

Novice Nook
[FEN "8/3k4/8/2K5/3P4/8/8/8"]

This position is also covered in King and Pawn vs. King but under the state "When the offensive king can get in front of the pawn", in the particular and famous "opposition" case with the king exactly one rank in front of the pawn. Here the rule (with the white king still on d5) is "Whoever is to move is at a disadvantage and the opponent has the opposition." White to play did not have the opposition and moved his king sideways from d5 to c5. It is important to understand that the offensive king is trying to make progress (he can't), while the defensive king is trying to maintain the opposition, which he can with 1...Kc7=.

However, a little knowledge is a dangerous thing and Howard mis-remembered this position as the one in the previous case, where the white king was not in front of the pawn! Therefore, he followed the nonexistent "rule" that he should move his king straight back! So he played 1...Kd8?? and, after 2.Kd6, his delighted opponent duly won.

After the game, Howard questioned me about his error and I explained that he had mixed up the two states – an easy and understandable mistake to make when you first acquire similar types of knowledge. The good news is that your capability for improvement often doesn't depends on how smart you are, but how many times you make the same mistakes, and Howard learned this one well. I don't think he ever made that error again.

Despite the fact that in this example Howard had reached an exact endgame and correct remembrance would have saved him, these 100% "knowledge" approaches to studying endgames don't begin to cover the entire gamut of endgame play. I think a great example of why this is so was covered in the first position in Analysis Insights, a "simple" endgame position where White had the choice of two captures:

White to play

Novice Nook
[FEN "8/5p2/5b2/4PK2/3k4/8/5P2/8"]

I am not going to repeat the analysis – if you haven't read the linked example, it's highly recommended. However, I will repeat the lesson learned: many students, when presented with this position, made the move based on general principles. This approach would be reasonable, if not necessary, when a position occurs early in the game and it is not possible to calculate exactly which moves win and which do not. However, these students chose to hand-wave even though it was a deep endgame and it was possible, with a little analysis, to prove which of the alternatives was winning and/or drawing. They simply did not do the analytical work.

Sometimes the reason for not doing the work was the student felt incapable of doing the analysis, but for others the distinction between using the kind of logic/principles that would apply early in the game vs doing the concrete analysis required in a deep endgame was completely unknown to them.

This discovery led me to the inescapable conclusion that many lower-rated players are weak in the endgame not because they don't know enough exact positions or have not studied the book Capablanca's Best Endgames. It is because they are either accustomed to playing time limits which are not conducive to careful endgame analysis or, worse, never learned to analyze any chess position carefully – endgame or not. This latter conjecture might sound harsh but it is true that many don't even realize that playing good chess requires a lot more than acquiring a bunch of knowledge.

This fact was driven home to me a couple of years ago when I was discussing the extensive use of Hand-Waving (Hand-Waving is Worse than Hope Chess) and Hope Chess in lieu of careful analysis via a set of tweets on Twitter. I received a very telling set of tweets from one gentleman, to the following effect:

Follower: Dan, I've been playing for a couple of years and I've raised my rating to about 1,500 by studying tactics, openings, and endgames. But after seeing your tweets and reading some of the material, I've come to the conclusion that if I want to get a lot better, I can't just rely on acquiring more knowledge. I've got to start to learn how to analyze.

Me: Yes, all that knowledge is very useful, pretty much necessary. But it's not sufficient. There are many tactical patterns and endgames that are not easily found in books but that must be carefully calculated. The number of possible reasonable patterns is much higher than the number of positions you can study in a lifetime. Therefore, to become a good player, you can't rely on knowledge alone, but have to be able to carefully analyze and calculate many types of positions, especially forcing/tactical positions and many endgame positions.

Follower: Yes, I've started to work on my analytical skills.

Me: Yes, I have many articles (and some books) on that subject. Good luck!

Follower: Thanks!

In his very advanced endgame books, famed instructor Mark Dvoretsky takes an approach that is not completely knowledge-driven. Dvoretsky often presents very challenging puzzles to the reader and, only after the reader has tried to analyze, does he offer the required knowledge – as well as some tips on how to approach the analysis. I think to some extent many endgame authors try to include some analytical tips (as opposed to just listing solutions and alternatives). Some, such as Silman, are willing to provide the expansive room and have the willingness to cut down on just providing tons of examples. Limiting the number of positions allows more analysis than does the encyclopedic approach. The latter, because of the voluminous amount of material, usually just allows room for solutions (and alternative lines).

Learning how to analyze at any phase of the game helps you learn how to analyze in the endgame. It's just that in the endgame it's much more obvious (as illustrated in the previous diagram) that analysis may be necessary, while in the earlier phases of the game inexperienced players can often get away with dangerous hand-waving.

Ironically, much of endgame play for lower-rated players is not how to take advantage of subtle advantages, as covered in most endgame books, but rather how to mundanely win won games, which we call technique. There are very few books that cover technique at a basic level. The following is a good example:

White to play

Novice Nook
[FEN "8/8/8/3p1k2/3P4/4K3/5B2/8"]

This is the type of positions where strong players resign against other strong players; for them it's too easy and it's too basic for them to put in a book. Yet it's also the type of position where weak players – not just absolute beginners - often struggle, winning more by accident than design. In fact, I have had more than one player, when asked to evaluate a similar position, tell me they think it's a draw! If you play it out, you will find that multiple zugzwangs are the key to victory, as is the case in many "easily won" positions.

Learning to win these "easy" endgames is far more important to players in the Under-1500 range than knowing how to win a subtle theoretical rook and pawn endgame. Again, it all begins with learning how to practice analyzing carefully, rather than memorizing a ton of "exact" endgames.


As I was writing this column, GM Soltis came out with his new book 100 Chess Master Trade Secrets. This was serendipitous, since one of the main purposes of the book was to address the "missing" endgame information he hinted at in his previous works Studying Chess Made Easy and What it Takes to Become a Chess Master, which is material that helped initiate our discussion. Specifically, he includes two chapters entitled

  • "Twenty Five Must-Know Endgame Techniques"
  • "Twenty Five Exact Endgames"

The idea is that if you are to become a master, these fifty endgame ideas should be requisite knowledge. However, I should warn potential purchasers that this is a fairly advanced book – you should not be learning "master-level" endgame information if you haven't mastered the basics. In other words, if you are 1800+ and an aspiring master, it's very helpful material. However, if you are 1200-1400 and hoping to skip right to master by studying this material, then it not only won't achieve your desired aim, but you probably will get greatly diminishing returns from trying to study this mostly advanced material "out-of-sequence."


Question Why is a rating so important, I thought we play chess for the fun of it and tactics training I don't understand, because they don't play my way?

Answer Thanks for writing. By looking past the rating system, your heart is in the right place. I have written two articles on my concerns about players' over-zealousness about ratings which you might enjoy:


Question I was reading your article on material value based on the evaluation of Mr. Kaufman. Maybe I was interpreting the "computer values" with changing piece values based on the number of pawns wrongly but I cannot make sense of it when it comes to the value of the exchange. I started an almost completely unnoticed forum topic. I would be delighted if you could have a look on it and share your opinion to my interpretation of and questions regarding the value of the exchange.

Answer The "pawns" from GM Larry Kaufman's equations are the number of pawns that side has remaining on the board. That's why knights gain in value when there are many pawns blocking the board and rooks gain in value when the board is relatively empty. In the "average" position, about 5 pawns, Larry has a rook worth about 5.25 [from his latest books] and a piece (B or N) at about 3.5, so the average value of the exchange when you have 5 pawns on the board, is 1.75. But if there are no pawns on the board, then the rook is more powerful and the exchange is worth more. If there are 8 pawns on the board as in the start of the game, then the knight gains in power relative to the rook and at the start of the game the exchange is worth less than its average of 1.75.


Question Very big fan, adult, 1600 in Canada, playing slow chess for three years now. Your teaching style is great for me, and I have read as many Novice Nooks as I can, finished 'Elements of positional evaluation' and now reading 'Improving chess thinker'. Just an observation, it seems like a large majority of those doing the de Groot exercise seek to justify the first move that occurs to them. Rather than objectively choosing between the options, I think subconsciously most seem to want to play their first idea and they tailor their analysis to convince themselves that it's a reasonable move. It would be interesting to examine what percentage go on to play the first move they suggest, regardless of how bad it is. Perhaps this brings up the point 'resist the urge to play the first thing that catches your eye unless it's the best move you can find in time allotted''? In any case, thanks for the logical, structured teaching approach. Together with my local teacher, it has helped me reach 1600 from 1200 over past couple years.

Answer Thanks, much appreciated. Yes, you are correct. I think it was deGroot who observed that lower players try to prove their move is reasonable while stronger players first use negative logic to show their move is good (assume I make this; how would my opponent beat it?) and then try to figure out what would happen with each of their major candidate moves and compare outcomes to see which one they like best (using a method he calls progressive deepening, which I talk about in my book, too).


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