Dvoretsky’s Endgame Manual: FastTrack Edition: FastTrack Edition

By Mark Dvoretsky and Alex Fishbein

The FastTrack to Endgame Expertise!

Since it first appeared in 2003, Dvoretsky’s Endgame Manual has been acclaimed as the best single volume ever written on the endgame. With staggering depth and accuracy, it clearly reveals the secrets of this most important stage of the game.

One of the unique characteristics of the Endgame Manual has been the highlighting of text considered to be essential to the understanding of endgame theory. The late, great trainer Mark Dvoretsky carefully selected the text to be highlighted so that players at all levels could benefit from this monumental work.

Now in its fifth edition, the 440-page manual may seem somewhat intimidating to some readers. With that in mind, German grandmaster Karsten Müller and American grandmaster Alex Fishbein – both recognized endgame experts in their own right – have collected the highlighted text from the fifth edition and presented it so that the core concepts might be more readily available.

The result is Dvoretsky’s Endgame Manual: FastTrack Edition. As noted by Australian grandmaster Ian Rogers in his foreword:

I am very pleased that Dvoretsky’s Endgame Manual: FastTrack Edition has come along. It is eminently suitable to sit in an amateur player’s library as their only endgame book, and equally good at preparing a serious student for many other fine endgame books – not forgetting of course the storied father of this volume, Dvoretsky’s Endgame Manual.

If you are serious about studying endgames, have a limited amount of time, or are simply looking for a convenient way to improve your play in endgames, the FastTrack Edition may just be the book you have been looking for.

• Language: English
• Publisher: Russell Enterprises, Inc.
• Release date: Sep 7, 2021
• ISBN: 9781949859348

Mark Dvoretsky

The late Mark Dvoretsky (1947-2016) was considered the premier chess instructor and trainer of his era.

Book preview

Introduction

With the great success of Dvoretsky’s Endgame Manual, the question arose of how intermediate players should approach the book. Mark Dvoretsky’s original concept was that they should study only the text that is highlighted. This highlighted text has always served a dual purpose: to delineate the exact positions and practical techniques that the readers should try to remember, and to point the less advanced readers to the more accessible material.

But with the revolutionary changes in chess in the last twenty years, the lines became blurred. Faster time controls increased the number of precise positions to remember, as players often have only seconds to make a decision. Meanwhile, computer engines and tablebases have revealed more endgame secrets, making the theory larger and more difficult to master.

DEM-FastTrack brings a back-to-basics approach. We have started with just the text that was highlighted in gray in the fifth edition. Where necessary, we have retained practical examples of how to apply the theory. The overriding principle is accessibility to readers who have not yet reached master or expert level, or perhaps have only begun their chess journey.

We have included 60 exercises, as they form an integral part of Dvoretsky’s didactic concept. All of these came from the fifth edition of the Endgame Manual, where some were exercises and others were tragicomedies. We have graded all exercises with one, two or three stars, according to their difficulty. One-star exercises test how well you have learned the theory, but three-star positions can require a good amount of creativity. Of course, the difficulty level can be subjective, and it is good to remember that grandmasters have often made mistakes in these positions.

Some of the more difficult exercises are labeled as Play positions. They ask the solver to see not just the first move or two, but an entire variation. They will be easier to solve if you find a coach or friend to play out the position against you, using the solution in the back of the book. You play it move by move, with your friend playing the opponent’s response. If you play a different move than what is in the solution, you replace it with the correct move and continue from there.

The main line of the solution is always in bold print. Another way is to use paper to cover the moves of the solution, or better yet, ask someone (who does not need to be a chessplayer) to prepare a sheet of paper for each move, using the solution at the end of the book. It can also sometimes be useful to play out exercises, or other positions that you have mastered, against a computer engine or tablebase, with the clock ticking.

While the book was specially prepared with the general audience in mind, we do want to offer some remarks for the more advanced reader. We have retained some analysis in the rook ending section, particularly the Kantorovich-Steckner position (beginning on page 121), which is considerably more complicated than most of the text. However, it is part of endgame theory now, and your opponents might know it. We have also updated the famous Spielmann-Rubinstein endgame with the latest (and remarkable) discovery by Charles Sullivan already after the publication of the fifth edition. Finally, a few of the three-star exercises at the end (pages 201-203) feature some beautiful endgame studies.

If you like this FastTrack edition, you should of course consider getting the full book to deepen your understanding of this very important phase of the royal game. Finally, there is no better way to close than quoting grandmaster Artur Yusupov, considered by many to be Dvoretsky’s most successful student: I am sure that those who study this work carefully will not only play the endgame better, but overall their play will improve. One of the secrets of the Russian chess school is now before you, dear reader!

Karsten Müller, Hamburg

Alex Fishbein, New Jersey

April 2021

Foreword

In an era when tournament players are often required to make key endgame decisions at 30 seconds per move – and far less when playing online – knowledge of the endgame has become more important than ever before.

Knowledge of a wide variety of endings is now obligatory to survive in modern chess, since there will be no time during a game to work out if a particular technical position of, say, rook and pawn v rook is winning – and if so how to do it.

Dvoretsky’s Endgame Manual has, since it was first published in 2003, been the first point of call for many players. It occupies a deified position in the pantheon of endgame chess literature; a work combining accessibility with academic rigour which has helped thousands of chess students build up their knowledge base and master even the trickiest of endings.

Dvoretsky’s Endgame Manual was notable for the unique feature of distinguishing the essentials from the advanced material, using different printing colours to distinguish the two. Thus it was possible for a student new to endgames to concentrate on the basics and leave the more complex parts for later.

For such a reader, Dvoretsky’s Endgame Manual: FastTrack Edition is a boon. Müller and Fishbein have extracted all the highlighted sections from Dvoretsky’s Endgame Manual and created a slimmed-down version of the original, covering all the essentials without reducing the academic rigour of the late, great Mark Dvoretsky’s work.

The theoretical knowledge is leavened with practical examples, keeping the student’s eye on the multiple ways a complex position can be reduced, through suitable tactics, to the set of basic positions which have already been taught.

However, lazy players hoping for a quick fix for their endgame problems will be disappointed. As I read through Dvoretsky’s Endgame Manual – FastTrack Edition I realised basic is not synonymous with easy.

For example, a basic endgame which bugged me throughout my career, rook + h-pawn v bishop, is covered in a page and a half on pages 149-150. To understand why the generic endgame is drawn with the pawn on h5 but winning with the pawn on h4, and how to win by pushing the h pawn at exactly the right moment, is explained simply and well. However that explanation cannot be fully understood – at least with any hope of implementing the correct technique in practice – without following each and every sub-variation.

As you might have gathered, I am very pleased that Dvoretsky’s Endgame Manual: FastTrack Edition has come along. It is eminently suitable to sit in an amateur player’s library as their only endgame book, and equally good at preparing a serious student for many other fine endgame books – not forgetting of course the storied father of this volume, Dvoretsky’s Endgame Manual.

Ian Rogers

Sydney

April 2021

Signs and Symbols

Chapter 1

Pawn Endgames

Pawn endings are very concrete – even the tiniest change in the position generally alters the shape and outcome of the struggle. Here you can rarely get along on general principles – you must know how to calculate accurately.

The study of pawn endings chiefly boils down, not to the memorization of exact positions, but to the assimilation of standard techniques, which considerably eases our search for a solution and the calculation of variations.

Many pawn endings are clearly defined tempo-battles. In these endgames, speed is everything: which pawn will queen first, will the king come in time to stop the passed pawn or get to the other side of the board in time. And there are other pawn endings in which a maneuvering war predominates, and in which zugzwang assumes paramount importance.

Maneuvering endgames are generally more complex than rapid ones, but we shall begin with them anyway, in order to acquire the vital concept of corresponding squares. Then we shall switch to studying the ideas involved in rapid endgames, before returning once again to the maneuvering.

Key Squares

Key Squares are what we call those squares whose occupation by the king assures victory, regardless of whose turn it is to move. In other types of endgames, we may also speak of key squares for other pieces besides the king.

The d5-square on which the king now stands is not a key square – White to move does not win. The key squares are c6, d6 and e6. Black to move must retreat the king, allowing the enemy king onto one of the key squares. With White to move, the position is drawn, since he cannot move to any key square.

With the pawn on the fifth rank (see the next diagram), the key squares are not only a7, b7 and c7, but also the similar sixth-rank squares a6, b6, and c6. White wins, even if he is on move.

1 Ka6! Ka8 2 b6 Kb8 3 b7+–

Note that 1 Kc6?! is inaccurate in view of 1…Ka7!, when White has to return to the starting position with 2 Kc7 (2 b6+? Ka8! =) 2…Ka8 3 Kb6 (again, 3 b6?? is stalemate) 3…Kb8 4 Ka6!, etc.

The key squares are a6, b6 and c6. The sensible thing here is to head for the square farthest from the enemy king, since that will be the one hardest to defend.

1 Kc2! Ke7 2 Kb3 Kd6 3 Ka4 (3 Kc4? Kc6=) 3…Kc6 4 Ka5 ( 5 Ka6) 4…Kb7 5 Kb5 +–

Corresponding Squares

Corresponding squares are squares of reciprocal zugzwang. We may speak of corresponding squares for kings, for kings with pawns, and with other material, we may speak of correspondence between any pairs of pieces.

The most commonly seen cases of corresponding squares are: the opposition, mined squares, and triangulation.

Opposition

Opposition is the state of two kings standing on the same file with one square separating them (close opposition, three or five squares between them, is called distant opposition); the opposition may be vertical, horizontal, or diagonal.

To get the opposition means to achieve this standing of the kings one square apart with the opponent to move (that is, to place him in zugzwang); to fall into opposition means, conversely, to fall into zugzwang oneself.

Return to the very first diagram in this chapter, where we see the simplest case of the opposition (close, vertical). With White to move, there is no win: 1 Kc5 Kc7 ; or 1 Ke5 Ke7 . Black to move loses, because he must allow the enemy king onto one of the key squares: 1…Kc7 2 Ke6; or 1…Ke7 2 Kc6. Opposition is the main weapon in the fight for three connected key squares (in the first diagram in this chapter they are c6, d6 and e6).

When we are speaking of the opposition, it is usually not just one pair of squares, but several, which are under consideration: c5 and c7, d5 and d7, e5 and e7. The stronger side gets the opposition in order to execute an outflanking (where the enemy king retreats to one side, and our king then attacks the other way). The weaker side gets the opposition in order to prevent this outflanking.

White has the opposition, but it is not enough to win.

1…Kc7!

1…Ka7? is a mistake, in view of 2 a5! ba 3 Kxa5 (here, getting the opposition decides) 3…Kb7 4 Kb5 Kc7 5 Kc5 +–

2 Ka6

Since 2 c5 would be useless, the king starts an outflanking maneuver. Black replies by getting the horizontal opposition.

2…Kc6 3 Ka7 Kc7! 4 Ka8 Kc8!= (but not 4…Kc6? 5 Kb8 Kc5 6 Kb7+–).

If we moved the position one file to the right, White would win: 1…Kd7 is met by 2 d5!

White would also win if he had a reserve tempo at his disposal. Let’s move the a-pawn back to a3 – then, after 1…Kc7 2 Ka6 Kc6, he first recaptures the opposition by 3 a4!, and then performs the outflanking maneuver, 3…Kc7 4 Ka7 Kc6 5 Kb8! (outflanking!) 5…Kc5 6 Kb7+–

In the next diagram, White’s king cannot move forward: on 1 Kg3? there comes 1…Ke1! 2 Kg2 Ke2 3 Kg3 Kf1!–+

White would like to take the opposition, however 1 Kf1? is also a mistake. After 1…Kd2 2 Kf2 Kd3, the f3-square his king needs is occupied by his own pawn, and the opposition passes to his opponent: 3 Kf1(or g3) Ke3! 4 Kg2 Ke2, etc.

H. Neustadtl 1890

The only thing that saves White is getting the distant opposition:

1 Kh1!! Kd2 (1…Ke1 2 Kg1=; 1…g4 2 Kg2! Kd2 3 fg=) 2 Kh2 Kd3 3 Kh3=

Now let’s examine the mechanism by which the stronger side can exploit the distant opposition. It is, in fact, quite simple, and consists of the conversion of the distant opposition into close opposition by means of outflanking. If outflanking is not possible, then possession of the distant opposition is worthless.

H. Mattison 1918*

The pawns are lost, after which Black’s king will control the key squares in front of the f7-pawn. But White has a tactical resource at hand: he moves both pawns forward to lure Black’s pawn nearer to his king allowing him to defend the new key squares.

1 g6! fg 2 f5!

2 Kg2? Kg4 3 f5 gf–+, and Black controls the opposition; also bad is 2 Kh2? Kg4 3 f5 Kxf5! 4 Kg3 Kg5–+

2…gf 3 Kg1

Black controls the distant opposition, but he cannot convert it into the close opposition. The problem is that after 3…Kg5 4 Kf1, outflanking with 4…Kh4 has no point. On 4…Kf4 (g4), it is White who takes the close opposition by 5 Kf2 (g2), and Black’s king cannot use the f5-square as it is blocked by its own pawn. If the king and the pawn could both occupy this square simultaneously, then on the next move the outflanking would be decisive; unfortunately, the rules of chess do not allow such a thing.

J. Drtina 1907

Taking the distant opposition with 1 Ke1? leads only to a draw. The opposition on the e-file is meaningless: 1…Ke8! 2 Ke2 Ke7 3 Ke3 Ke8 4 Ke4 Ke7, and White cannot get any closer, because the e5-square is off limits. And if the white king leaves the e-file, his opponent will take the opposition forever, e.g., 2 Kf2 Kf8! 3 Kg3 Kg7! 4 Kf3 Kf7!, etc.

In such situations there is usually a major line, through the middle of three connected key squares, in which is it vitally important to capture the opposition. And when the enemy king retreats from it, you must outflank it. In this instance, the key squares are e6, f6, and g6, the middle square is f6, and the major line is the f-file.

Imagine that Black’s king was on f7, and moved to one side. White must move to outflank, thus: 1 Kg2!

It is pointless to stay on the e-file: White’s king will reach the key square g6. So Black plays 1…Kf6

As we have already noted, on the f-file it is necessary to maintain the opposition; therefore, 2 Kf2!

What is Black to do now? Moving the king forward is useless: 2…Kf5 3 Kf3 Ke5 4 Ke3 Kf5 5 Kd4 and 6 c5. If we retreat the king to the right, White’s king advances left and takes over the key squares on the queenside: 2…Kg6 3 Ke3 Kf7 4 Kd4 (4 Kf3 is not bad, either) 4…Ke7 5 Kc3 Kd7 6 Kb4 Kc7 7 Ka5! (diagonal opposition!) 7…Kb7 8 Kb5 Kc7 9 Ka6+–

That leaves only 2…Ke7; but then comes the algorithm we already know: 3 Kg3! Kf7 4 Kf3! Ke7 5 Kg4 Kf8 6 Kf4! Ke7 7 Kg5! Kf7 8 Kf5+– The distant opposition has been successfully transformed into the close one.

Mined Squares

Sometimes, it is a single pair of squares that correspond; I refer to such squares as being mined. Do not be the first to step on a mined square, or you’ll be blown up – that is, fall into zugzwang. You must either first allow your opponent to step on the mined square, or move forward, accurately avoiding it.

Here are two quite typical examples of mined squares.

Here we have what I call "untouchable pawns." White’s king shuttles between b3, c3 and d3, while the black king goes from c7 to b7 to a7, neither of them able to attack the pawn – the squares c4 and b6 are mined.

Here, kings at e6 and c5 result in reciprocal zugzwang. White wins by forcing his opponent to go to the mined square first.

1 Kf6! Kb5

Passive defense is hopeless too: 1…Kc7 2 Ke7 Kc8 3 Kxd6 – the king captures the d6-pawn while simultaneously occupying a key square for the d5-pawn.

2 Ke7! Kc5 3 Ke6! +–

Black to move plays 1…Kb5! White, however, is better off than his opponent in that the loss of a pawn does not mean the loss of the game: he replies 2 Ke4 (but not 2 Kf6? Kc4! 3 Ke6 Kc5–+) 2…Kc4 3 Ke3 Kxd5 4 Kd3, with a draw.

Triangulation

Triangulation refers to a king maneuver which aims to lose a tempo, and leave the opponent with the move.

The d5- and d7-squares are in correspondence. The mobility of Black’s king is restricted: he must watch for the c5-c6 break, and also avoid being pressed to the edge of the board. It is not surprising, therefore, that White can easily lose a tempo and place his opponent in zugzwang.

1 Ke5!

1 c6+? is mistaken here, in view of 1…Kc8! (but not 1…bc+? 2 Kc5 Kd8 3 Kd6! Kc8 4 Kxc6 Kb8 5 b7+–) 2 Kd6 Kb8! 3 Kd7 bc=

1…Kc6 (1…Ke7 2 c6) 2 Kd4 Kd7 3 Kd5

White has achieved his aim, by describing a triangle with his king. The rest is simple.

3…Kc8 4 Ke6! (diagonal opposition) 4…Kd8 5 Kd6 (and now, vertical) 5…Kc8 6 Ke7 Kb8 7 Kd7 Ka8 8 c6+–

The following position is very important, both for itself and as an illustration of the characteristic logic of analyzing corresponding squares.

Fahrni – Alapin 1912

The kings were on d5 and c8 here; but we shall not place them on the board just yet – let’s deal with the squares of correspondence first.

Two pairs of squares of reciprocal zugzwang are obvious right off: d6/d8, and c5/c7. The squares d6 and c5 border on d5; and for Black, the corresponding squares d8 and c7 border on c8. Thus, a standard means of identifying a new correspondence: that of the d5- and c8-squares.

Along with d5 and c5, White has two equally important squares: c4 and d4. Black also has two corresponding squares, b8 and d8, but they are not connected, while c4 and d4 are connected. With Black’s king on d8, White makes a waiting move with his king, from c4 to d4 (or the reverse). Black’s king will be forced onto c7 or c8, when White occupies the corresponding square and wins.

1 Kc4(d4)! Kd8 2 Kd4(c4)! Kc8 3 Kd5! Kd8 (3…Kc7 4 Kc5 and 5 Kb6) 4 Kd6 Kc8 5 c7

When the pawn structure changes, the system of key squares associated with the position generally changes too, just as with the system of corresponding squares.

For example, if the pawns in the last position were on a6 and a7, then White could not win by triangulation because b6 would not be a key square.

Also, if the pawns were on a5 and a7, then the system of correspondence would change to where the black king should cede the opposition by going to d8. We shall examine that structure in more detail later in this chapter.

Other Cases of Correspondence

Situations with corresponding squares come in all shapes and sizes – from the most elementary to cases so complex that most of the unoccupied squares on the board turn out to be squares of reciprocal zugzwang.

How is the correspondence between squares determined? There is no special formula. The sensible way is to find key squares, examine the possible plans for both sides, and calculate the simplest variations. This preliminary analysis may uncover some reciprocal zugzwang situations; from there, you may go on to define an entire network of corresponding