Think Like a Grandmaster E-Book

A.A. Kotov

• Herausgeber: Batsford
• Kategorie: Lebensstil
• Sprache: Englisch

Seitenzahl: 369

Veröffentlichungsjahr: 2012

Beschreibung

This is a well-established training manual which encourages the average player to understand how a grandmaster thinks, and even more important, how he works. Kotov tackles fundamental issues such as knowing how and when to analyze, the tree of analysis, a selection of candidate moves and the factors of success.

Leseprobe

First published in the USSR English translation © Batsford 1971 Fifth impression 1978 Reprinted 1980, 1982, 1984, 1985, 1986, 1988, 1990, 1994

First algebraic edition published in the United Kingdom in 1995 by Batsford 151 Freston Road London W10 6TH

An imprint of Anova Books Company Ltd

Copyright © Batsford

All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise, without the prior written permission of the copyright owner.

First eBook publication 2012 eBook ISBN: 9781849940535

Also available in paperback Paperback ISBN: 9780713478853

This book can be ordered direct from the publisher at the website:www.anovabooks.com, or try your local bookshop for the hardback

Contents

Symbols

Preface

Introduction: An Unusual Experiment

1 Analysis of Variations

Do you Know how to Analyse?

Historical Digression

The Tree of Analysis

Forced and Unforced Variations

Different Types of Tree

Bare Trunk

A ‘Coppice’

‘Thickets of Variations’

Selection of Candidate Moves

What is a Candidate Move?

‘Creeping Moves’

Gross Blunders

Dizziness due to Success

Conditioned Reflexes

The Blind Spot

Through the Eyes of a Patzer – Blumenfeld’s Rule

More Practical Advice

To Analyse or Not to Analyse?

Positions for Analysis or Judgement

Trust your Opponent or Not?

Time-trouble

Exercises

2 Positional Judgement

Open Lines and Diagonals

Modern Ideas on Open Lines

Pawn Structure and Weak Squares

Weak Squares

Passed Pawns

Pawn Islands

Weak Colour Complexes

The Position of the Pieces

Poor Position of a Number of Pieces

Space and the Centre

Exercises

An Experiment Continued

Imitate Botvinnik or Najdorf?

What is Concrete and What is General?

General Questions and Preparation

The Opening

Middlegame

The Ending

General Formulae and Concrete Analysis

3 Planning

A Single Plan

Planlessness Punished

Be Flexible

The Centre

Closed Centre

Open Centre

Mobile Centre

Fixed Centre

Tension in the Centre

Exercises

4 The Ending

5 A Player’s Knowledge

Opening Study

Is it Possible to Study the Middlegame?

Adjourned Games

Advice on Various Questions

Chess and Life

The Factors of Success

Know Your Opponent

Know Thyself!

Solutions to the Exercises

Index of Names

Symbols

+

Check

!

Good move

!!

Brilliant move

?

Bad move

??

Blunder

#

Mate

(D)

Diagram follows

Preface

An immense number of books have been written on chess. Some chess writers annotate recent games, others compile and bring up to date works on opening variations, but, strange as it may seem, no one has had the idea of describing the methods by which the leading players of our time have reached the peak of their playing strength. Yet a study of these methods would greatly facilitate the process of mastering the intricacies of the game.

In this book the author describes how Botvinnik, Tal, Smyslov, Petrosian, Keres, Bronstein and many other leading grandmasters studied chess theory, and trained themselves to understand the mysteries of chess strategy and tactics. They themselves have revealed some of their methods in articles and game annotations, while I have become acquainted with others from personal conversations with my fellow grandmasters.

The reader will also find an account of my own personal experience – my achievements in the field of chess are the result of immense hard work in studying theory, and I flatter myself that this experience will prove to be of interest to the reader.

Chess is a complex game, yet millions of enthusiasts are fascinated by it. Some of them reach the playing strength of a first or second category player, while others are satisfied to be known all their life as ‘a beginner’. Yet surely even a weak player would like to win a chess title and be known as master, or even grandmaster. If someone could only show them how to reach this goal, then many of these enthusiasts would be prepared to set off along the long and irksome road of tournament play with all its exciting and nerve-racking experiences.

How then does one become a grandmaster? Is it the case that a strong player’s abilities are purely natural, and that hard work cannot change anything? Naturally there must be some inherent ability, but as in other spheres of human endeavour the main factor is immense, unstinting effort to master the skills of chess strategy and tactics.

That great chess thinker Emanuel Lasker asserted that in the space of 100 hours he could produce a first-category player from a young man of average ability. Could one go further than that? Lasker never had occasion to prove the validity of his claim; the question naturally arises: could one by dint of careful study and hard work go as far as becoming a master or in the end a grandmaster?

My own experience tells me that such study and hard work do lead to immense improvements in one’s practical results. I would remind the reader that up to 1938 I had never managed to reach master standard, but my study of the game in the period 1936-37 led suddenly to a ‘great leap forward’. I gained the master title in 1938 and only one year later that of grandmaster. It follows that one can become a grandmaster by one’s own endeavours: one merely has to work hard at it. How exactly to go about it is contained in this book.

A few points are worth noting:

1) My desire to make the book as clear and helpful as possible has led me to employ new names for some strategic laws and concepts. This was not done in an attempt to try for an unnecessarily scientific approach, but merely to help the memorisation of important points.

2) The book makes use to a large extent of the games and advice of those Soviet grandmasters who belong to what is now called the older generation. The reason for this is that all my chess career I have rubbed shoulders with Botvinnik, Keres and Smyslov. The younger grandmasters, on the other hand, are busy with their current tournament battles and write less about their thought processes at the board, normally restricting themselves to giving concrete variations.

3) The book contains games by the author – again easily understandable as, in aiming to describe the secrets of the chess mind, I have naturally had to dig down deep into my own brain.

So, dear reader, forward into battle, to storm the heights of grandmaster chess!

Introduction: An Unusual Experiment

We shall now try to describe the complex process of thinking which takes place in a grandmaster’s mind during play. To explain his thought processes as clearly as possible let us try a little experiment that was suggested to me by the method of studying mechanics in high school. First of all one studies Statics – the effect of forces on a body at rest -and then Dynamics, in which the same phenomena are studied in motion. So, too, we shall first consider how to think about moves from the static point of view, and then later in the book from the dynamic.

Let us then imagine the room where a top-class tournament is being played. Let us go on to the stage and ask one of the players, for example Polugaevsky, to give up his seat to us. Let us now ask Smyslov to tell us straight away without any further consideration the course of his thoughts as he studies a position in which he, White, is to move.

I can be certain that his first reaction would be count how many pawns there are. As a rule a grandmaster can take in at a glance, without counting, how many pieces there are. However, he may at times also count the pieces. We now assume that Polugaevsky has not sacrificed anything and so material is level.

The next stage in Smyslov’s thinking will be to clarify the following points:

First, from which opening has this position arisen. If not many moves have been made, he will be able to ascertain this from the pawn configuration and the position of the pieces. If we are well into the middlegame then one has to work on the remnants of the pawn structure, on the open files and diagonals and outposts for the knights.

Then there follows the question: have I ever had this position before, or has it ever occurred in games by other grandmasters? This is an important point in clarifying matters, as if one can call to mind similar positions from earlier games, then it is easier to reach an assessment of how things stand, and to hit upon the correct plan or analyse variations. Such a use of accumulated knowledge is an excellent way of saving thinking time as well as avoiding errors or the wrong plan.

This period of thought, which we call the clarification period, is very important. Here the main role is played by the knowledge, experience and erudition of the grandmaster. Naturally the memory plays its part in helping to bring to mind the moves played in games of long ago. One can find remarkable examples of this technique in the games of Alekhine and Botvinnik, who were thereby helped to produce great works of art.

Armed with these preliminary soundings, the grandmaster then attempts to assess the position. He not only has to solve the basic problem of who stands better; he also has to discern the nature of the position down to its smallest details. He will note the presence and comparative value of various open lines, all the while bearing in mind the concrete tasks that lie before him: occupy this open file or diagonal, close that one, on this file neutralise the action of the enemy rooks. He will also work out which important outposts he should occupy with his knights, from which outposts he should drive out the enemy cavalry. It will become clear to him which of his pawns and those of the opponent are weak, where there are strong passed pawns. In a more subconscious than conscious way he will establish where there is co-operation and harmony between his pieces, and likewise for the opponent. He will say to himself mentally: this is what I have to put right; here is where I must regroup.

It will not cause Smyslov much trouble to establish which side controls the centre, and what is the influence on the centre of this or that piece. Then he will assess the value of each side’s pawn chains, and find out where pawn advances are possible. After all this he will understand more clearly who has the better position, who has the initiative, who must attack, who will be forced to defend. He will decide where White must attack if Black merely defends, or instead tries to counter-attack on the flank. Or will Black try for a blow in the centre – a grandmaster knows full well that the best answer to a flank attack is a counter-blow in the centre.

Finally, if the position is even, Smyslov will decide that he must manoeuvre quietly so as to provoke weaknesses in the enemy camp.

This then is the way that a grandmaster in the tournament room goes about assessing a position. We cannot claim that he will deal with the elements of the position in this precise order. Much of what we have categorised he will probably entrust to his intuition, but in one way or another the various problems will be considered and solved.

How much time does this process take? Naturally this depends on the ability of the grandmaster and on the special features of each particular position. There is also the element of temperament. It is well known that with some players sober analysis plays the main part, while with others, intuition developed by analytical practice predominates. Assessing a position is very important and a lot of time is devoted to it.

Only when he has gone through this preparatory work will Smyslov start to draw up a plan. The direction of a player’s thoughts is governed principally by the features of a given position, but no small part belongs to the character of the player. Petrosian would most likely give first thought to how to defend his weaknesses, whereas Tal would probably start to look for the chance to prepare a sacrifice.

So in one way or another our grandmaster will decide the general plan of campaign, where to direct his pieces, what to attack, and in case of necessity how to defend. Along with this general plan, he will have a more concrete plan, which decides what his next few moves will be: occupy this square, exchange that pawn, etc. He will also see what his opponent’s plan is, and how he can cross it.

Up to this stage a grandmaster’s thoughts have been based on general ideas and strategic principles. Now, at long last, he will start looking for the best move. He will establish what moves are possible, and how they fit in with his plan. Then he will begin analysing many variations. For each of the moves he will examine, he will foresee the opponent’s reply, then his best answer and so on. Only after finishing this immense task, now purely analytical, will Smyslov move a piece and stop his clock. Thinking over, move made!

Our experiment has enabled us to examine the sequence of a grandmaster’s thoughts when he is choosing the best move in a given position. We have also learned from it that a real chess player must have the following qualities:

1) He must be well up in modern opening theory.

2) He must know and keep in his memory the principles behind typical middlegame positions learned both from his own games, and from those of other players. The more a player knows and remembers, the easier it is for him to find a ‘precedent’, i.e. a position that has occurred before and which is similar to his own present position. Naturally, it is not a question of mechanical memorising, but of knowing methods and possibly separate moves and combinations employed at some time or other and appropriately assessed in subsequent notes and analysis. We shall call these first two qualities with good reason ‘chess erudition’.

3) A grandmaster must be able to assess a position accurately and correctly.

4) No less important is the ability to hit upon the right plan, which must meet the demands of the given position.

5) A grandmaster must be able to calculate accurately and quickly all the significant variations that might arise in the subsequent course of play.

These then are the most important qualities which players should develop within themselves, mainly by practice, analysis and personal effort. We shall now examine all these qualities and show how they can be acquired by dint of hard work. To facilitate their treatment we shall deal with them in a different order.

1 Analysis of Variations

Do you Know how to Analyse?

Recently I was invited to the closing ceremony of a team tournament in which both candidate masters and first-category players were playing. I asked my audience what they would like me to talk to them about, and I was inundated with requests. Some players asked me to demonstrate an interesting combination, while others wanted to know how to play the Sicilian Defence correctly for Black.

‘But do you know how to analyse variations?’ I asked my listeners, and without giving them time to reply went on, ‘I will show you how to analyse variations and if I’m wrong, then stop me. Let us suppose that at one point in your game you have a choice between two moves, d1 or g5. Which should you play? You settle down comfortably in your chair and start your analysis by silently saying to yourself the possible moves. “All right, I could play d1 and he would probably play …b7, or he could take my a-pawn, which is now undefended. What then? Do I like the look of the position then?” You go one move further in your analysis and then you pull a long face – the rook move no longer appeals to you. Then you look at the knight move. “What if I go g5? He can drive it away by …h6, I go e4, he captures it with his bishop. I recapture and he attacks my queen with his rook. That doesn’t look very nice… so the knight move is no good. Let’s look at the rook move again. If he plays …b7 I can reply f3, but what if he captures my a-pawn. What can I play then? No, the rook move is no good. I must check the knight move again. So, g5, h6; e4, xe4; xe4, d4. No good! So I mustn’t move the knight. Try the rook move again. d1, xa2.” At this point you glance at the clock. “My goodness! Already 30 minutes gone on thinking whether to move the rook or the knight.” If it goes on like this you’ll really be in time trouble. And then suddenly you are struck by the happy idea – why move rook or knight? “What about b1?” And without any more ado, without any analysis at all you move the bishop, just like that, with hardly any consideration at all.’

My words were interrupted by applause. The audience laughed, so accurate was my picture of their trials and tribulations.

When I revealed that I was writing a book to tell all that I knew about analysis, based on what I had learned from other grandmasters and what I had discovered myself, I was rewarded yet again by applause. Thus I came to realise that players even in high grades need such guidance. Then I said jokingly, ‘Botvinnik is working hard at trying to make a computer play chess as well as a human being, so let me teach human beings to analyse with the accuracy of a machine.’

The example I have described of incorrect, unsystematic thinking is quite common even with players of real ability and high gradings. They suddenly abandon their analysis and make a move which they haven’t examined properly at all. Let us consider one such case.

White’s attack on the kingside looks very threatening, and naturally the master who was White tried to find a concrete way to shatter the enemy king or to get some decisive advantage. It is not very difficult to see this concrete line must involve a sacrifice.

‘I have to sacrifice,’ the master told himself, ‘but which piece? There are several possibilities: 26 xh6, 26 xg6 or 26 g4 followed by 27 xh6+ Which then? Let us analyse 26 xg6 xg3 27 hxg3 fxg6 28 xe6 gxh5 29 xf6+ h7. The exchange down, the d-pawn weak, Black’s bishop is strong. No, that’s not it. What if 26 xh6? Let’s have a look. 26…gxh6 27 xh6 xe5 28 xe5 g7 29 e3 (29 xg6 xg6!) 29…d5 and here White has nothing concrete.

‘Possibly 26 g4 is stronger? Where will the black queen go? f5 is bad because of 27 xh6+ gxh6 28 xf5 exf5 29 xg6+ h7 30 xh6+ g7 31 h4. Two pawns up, White stands clearly better. Nor does 26…xd4 save him, since then 27 xh6+ gxh6 28 xg6+ or 28 xe6! and the black king cannot be defended.

‘So 26 g4 is good? But what if 26…h4? Then 27 xh6+ f8!. No, White cannot allow that; the queens are exchanged and all his pieces are en prise. So g4 doesn’t work. Let’s look at the other captures on h6 and g6 again.’

And once again his thoughts dwelt on the various ramifications of those two moves, and yet again the resulting positions did not appeal to the master. Once more he returned to consider 26 g4 and once again he did not find a win there. How many times he jumped from one variation to the other, how often he thought about this and that attempt to win, only he can tell. But now time-trouble came creeping up and the master decided to ‘play a safe move’ which did not demand any real analysis: 26 c3. Alas, this was almost the worst move he could have played. Black replied with the decisive 26…f4 and after 27 g4 h5 28 d1 h4 White was forced to resign. Note in passing that White was wrong to reject 26 g4. After 26…h4 27 xh6+ f8 28 xh4 xh4 29 xf7 xf7 30 xe6+ f8 31 g4 xg2 32 b4+ d6 33 xd6+ xd6 34 xc8 xe1 35 xb7 White would win.

Can you remember cases when this happened to you in tournament games? No doubt you can! So let us discuss how to learn to think about possible moves with the greatest efficiency.

Historical Digression

Practice has shown that only a few players have mastered the technique of analysis; even highly rated players are lacking in this respect.

In chess circles, where one hears many apt sayings, there is a common joke that no type of exercise can change a player’s playing strength. Wits like to quote the words of Ostap Bender (Translator’s note: One of the main characters in the well-known satirical novels by Ilf and Petrov, The Twelve Chairs and The Golden Calf. One of the jokes of the book was that Bender, who could not play chess, gave lectures and displays on the game!) who in his famous chess lecture said, ‘The blonde plays well and the brunette plays badly, and no lectures will change this state of affairs!’ However, the experience of many players of widely different playing strength shows that the opposite is true.

We shall be mentioning again the need for regular self-examination, for the need to summarise the lessons of the tournaments we have played in. It is by means of such self-criticism that we can best clarify the faults of our chess thinking. To give the reader a better idea of what I mean I shall tell you about the work I did myself in this field, work which gave much better results than I expected.

In the period 1935-36 I had managed to take first prize in a number of first-category tournaments. I had played with success in two Moscow championships, but all the same I was not satisfied with my play. When I did a critical survey of my games I came to the conclusion that there were serious defects in my play. I am looking, as I write this, at the many exercise books that I filled in those days with notes to my games. Believe me, they are full of harsh self-critical comments. No splenetic annotator ever gave such angry assessments to my moves as I did. I once wrote in the press: ‘Most of all it became clear to me that my main trouble was not superficial knowledge of the openings or poor endgame technique, but my limited understanding of the middlegame. My worst fault was an inability to analyse variations. I would spend far too much time examining comparatively simple positions, which often resulted in time-trouble. Moreover, I often made serious blunders. Finally, after the game I would always find out that my opponent had seen much more at the board than I had. It became clear to me that I had a lot of hard work to do on mastering the technique of analysis.’

This was how I expressed it in public, but in my exercise books I put it much more strongly. ‘I had worked out the following variations at random, and was duly punished by my opponent. Such vague analysis is the main drawback in my play and I must make every effort to root it out.’ That was what I wrote in my notes to my game with A. Yeltsov. ‘A lack of desire really to go into concrete variations thoroughly, a vague wandering about, those are my characteristic mistakes in my play in the 1936 Moscow championship,’ was another gloomy summing-up.

I was particularly discouraged by my game with Panov (Black) which after a sharp opening reached the following position.

White’s attack on the queenside, so it seemed to me, was developing in a systematic and logical way. I judged that the ‘ugly’ formation of the black pieces was proof of his serious positional difficulties. In the game there now came 22 c5 g5! after which it suddenly became aobvious that Black had very dangerous threats. The main point, however, was that his kingside pieces which I had thought gave the impression of awkwardness and lack of co-operation were working together very well, whereas my ‘nicely placed’ pieces were unable to parry his nasty threats.

There now followed 23 fd1 f3 24 h4 xe4 25 xf3 xa2 26 xa2 c3 27 d2 f6 and Black has a winning game. The finish was just punishment for my ill-founded optimism: 28 g2 e4 29 bc1 xd1 30 xd1 c3 31 e3 f5 32 h1 xe3 and Black easily won the ending.

After the game we analysed several variations. Panov told me that after 22…g5! he thought White had no good defence. If 23 fe1 then 23…f3 24 f1 (24 h4 xe4 25 xe4 fxg2 with the terrible threats of 26…xd5, 26…d7 and 26…f5) 24…xh3! 25 xh3 xh3 26 xh3 g5 27 g4 e7 28 g3 f4+ 29 h3 h6+ 30 g3 h4+ 31 xf3 f8+ 32 g2 xf2+ wins the queen.

Black’s whole manoeuvre – his original plan and the unexpected sacrifice – are attractive. These possibilities which were hidden in the position remained a mystery for me to the end of the game. I had not examined a single one of the tactical operations given above. Here is what I wrote in my summary of the tournament about my misconceptions in this game: ‘I was not able to find a single one of the variations and combinations while I was at the board. I didn’t even suspect that there was a combination coming at move 24, and I was very surprised when Panov showed it to me. To what a laughable extent my thinking is based on general principles and plans.’

In passing I did the following summary of the thinking time I took in the games of the 1935 Moscow championship: ‘From the 17 games, I was in serious time-trouble in 7 games, in simple time-trouble (5 minutes for 8-10 moves) in 5 games, not in time-trouble in 5 games (in 3 of which the game did not last long enough for the time control to matter). In time-trouble I played badly, most of the time going on mixing up variations and general reflections.’ Well then, that’s pretty clear. Such severe self-criticism presupposes that the next step will be efforts to root out the faults, and I started to work.

Having examined the games of other players, particularly masters, and read the occasional comments on this point that appeared in game annotations, I became even more convinced that the ability to analyse clearly a sufficient number of variations so as to clarify the position was the basic condition for success. However, I also came to the conclusion that in their analysis some players make various mistakes. Some examine a few lines to a considerable depth, others analyse a large number of variations two or three moves deep. The correct solution is to find the golden mean, especially as one is playing against a time limit. It also became clear to me that the ability to orientate oneself in the labyrinth of possible variations is not only a natural gift, but also the result of serious and prolonged effort, and training.

How should one go about this training? Where was there a description of how to train and discipline one’s thought? There were no books on the subject, and it did not seem possible to get help from anyone else, so I had to fend for myself. I chose a method which seemed to me the most rational, and fortunately it was the right one. Ever since that time I have considered it the most effective method to get good results.

I selected from tournament books those games in which great complications had arisen. Then I played them through on a board but when I reached the crucial point where there were the greatest complications and the largest number of possible variations I stopped reading the notes. I either put aside the book or covered the page with a sheet of paper and set myself the task of thinking long and hard so as to analyse all the possible variations. All the time I tried to work myself into the frame of mind that I was sitting at the board in the tournament room.

Having spent between half an hour and an hour on this task I would sometimes (especially in very complex positions) write down the variations I had examined and then I would compare them with those of the annotator. At first there was a big discrepancy in favour of the latter, but then I learned how to widen my scope and delineate each variation with considerable exactitude. Naturally I analysed without moving the pieces so as to make it just like a tournament game.

In this fashion I examined a large number of very tricky and complicated positions. I remember one of them in particular. I think the reader will be interested to study the many variations which are the product both of the players themselves and of many annotators.

This position arose after Black’s 23rd move in the game Flohr-Fine, Hastings 1935/6. The tension has reached its peak and the outcome can be resolved by the slightest inaccuracy. Grandmaster Flohr did in fact commit such an inaccuracy by playing the obvious 24 d8?, which was convincingly refuted by Fine. He retreated his queen to c7, after which he simply won the knight and all White’s attempts to attack g7 came to nothing.

Annotators the whole world over analysed this position. A win for White found in one country was quickly refuted in articles published in another. A practically invisible finesse spotted by one analyst was soon shown to be an error on further examination. Finally the English master Winter found the one and only way to win. I had worked out the same line in my own analysis.

Look at the variations which arise after the winning pawn advance 24 b5!. The idea behind the move is not immediately apparent. It is to open the a3-f8 diagonal for the white queen to attack the enemy king. The win after the forced reply 24…xb5 25 xg7 is proved by the following variations:

1) 25…xg7 26 g4+ when none of the various replies saves Black:

1a) 26…f8 27 b4+.

1b) 26…h6 27 eg5! and Black cannot meet the two threats of 28 e5 and 28 e1.

1c) 26…h8 27 xb5 g8 28 xg8+ xg8 29 g5+ h8! 30 f5 g7 31 g4 and White must win, though not without technical difficulties.

1d) 26…xg4 27 g5+ f8 28 g7+ e7 29 xf7+ d6 30 f4+ with a decisive attack.

2) 25…xc4 26 f5!. This strong move creates mating threats as well as the threat of a family check on e7. Black has various defensive tries but they are all unsatisfactory:

2a) 26…c7 27 g4+ h8 28 e8+.

2b) 26…h8 27 xc4 followed by e8+.

2c) 26…c7 27 g4+ h8 28 xc4 and 29 e8+.

2d) 26…a4 (to prevent a queen check on the a3-f8 diagonal) 27 e8+ xe8 28 g4+ f8 29 xf6 and after Black has run out of checks he has no defence against g8+.

Training exercises of this sort gradually led to an improvement in the accuracy of my analysis, and I was able to penetrate more deeply into the secrets of very complicated positions. Finally I set up a personal record by analysing a possible variation from the fourth game of the Chigorin-Tarrasch match 24 moves deep. I confess I was very proud of this, though it is now clear to me that I was helped by the exceptional ‘straight line’ nature of the variation, which had comparatively few sidelines. Here is the position.

Chigorin went wrong by 48 gxf6 and after 48…xf6 49 h3 a3 50 xf6 xf6 51 g6 a2 52 xf6+ gxf6 soon lost. After looking at the position many times, I found a win by 48 h3!. I give the main variation and omit the subsidiary ones: 48…a3 49 h8 fxg5 50 f6 xf6 51 xg5 a2 52 h7+ f7 53 hxf6 xf6 54 h6+ e6 55 xf6+ gxf6 56 g8+ d7 57 g7+ e7 (57…c6 58 a8+ and mate in two) 58 d5+! c8! (58…e8 59 g8+ f8 60 f7+ wins) 59 a8+ d7 60 b7+ c7 61 xe7+ xe7 62 xc7+ e6. Now despite his material advantage White’s win is not simple. He forces it by the following fine manoeuvre: 63 c8+ e7 (or 63…d6 64 f5#) 64 f5+ f7 65 d7+ g6 66 g7+ h5 67 h6+ g4 68 h4+ f3 69 g3+ e2 70 g2+ xd3 71 xb2.

After further examination of the position I found a quicker win for White, but this is not important. Such exercises, involving analysing and covering up the page with the grandmaster’s notes, are very beneficial in perfecting the technique of analysis. If the reader will try it for himself, he will soon realise how effectively it helps him to improve. However, one must not restrict oneself to this method as there are others. Great help can be obtained by solving studies from a diagram without setting up the position on the board. One can read chess books ‘blind’ without using a set, there is analysis of positions where the task is given ‘White to play and force a win’ and so on. Every player who spends some time on such methods will soon notice an increase in his playing strength.

So I was able to discover for myself an excellent method for training in analysis. Subsequently I shared this discovery with a number of candidate masters and first-grade players who studied under me for several years in a Moscow chess club. They liked it, and I feel it played a part in improving their playing ability.

Later on I formulated for myself and also borrowed from other sources certain recommendations which one must know in analysing, particularly the concept of the ‘tree of analysis’, which I shall deal with a little later.

I soon realised that it is not enough for a master simply to analyse variations scrupulously just like an accountant. He must learn to work out which particular moves he should consider and then examine just as many variations as necessary – no more and no less. With superficial analysis one cannot get down to all the fine points of a position, but to get carried away by a large number of possible variations can lead to awkward consequences. I know players who consider an immense number of possibilities, then regularly get into time-trouble and so lose all the fruits of their labours.

In order to avoid this I tried to analyse the maximum number of variations, wrote them down, and then tried to establish which of them were worthy of consideration within the demanding conditions of tournament play, and which could be left out so as to save time. Normally a master decides this by intuition, but you have to develop your intuition. I managed to develop mine by the method described below and then I successfully tried out the same method in study groups of second- and third-category players.

(I shall deal later in detail with the question of choosing moves and variations. Here I describe the one example with which I began all my research.)

I once analysed in detail the apparently simple, but in fact very tricky position of the diagram. Then I asked the people in the group to study it and in the course of half an hour write down all the variations which they thought should be examined. They were not allowed to move the pieces. Then we examined the position together and so exhausted all the possibilities it contained. It turned out that it was far from simple to discover all the special features of the position. This can be shown by the fact that one strong master in his notes wrote that White would win by 1 e8 and gave the beautiful variation 1…xe8 2 xg7+ xg7 3 xe8+ f8 4 xf8#. He also took account of the cunning reply 1…g1+ which fails to 2 h3 f5+ 3 h4. However, he failed to find the excellent rejoinder 1…d2+! and Black draws. Taking the rook is bad – 2 xd2 xe8 3 xe8 c6+ and 4…xe8.2 f3 (or f1) loses to the reply 2…f5+, while after 2 h1 there comes 2…d1+ with perpetual. Black has a very fine win after 2 h3 viz. 2…f5+ 3 g4 f1+ 4 h4 xh2+ 5 g5 c5+ 6 (either!)e5 f6#.

That is the way to work on the second important factor in developing analytical ability – the ability to find the really important lines.

A third factor which must be considered in this respect is speed of analysis, so important in practical play. Anyone who has ever been in time-trouble will not need convincing of that – he will know the value of the odd minute saved here and there.

I practised the following method: I would set up a complicated position and give myself the task of working out all the possible variations in the space of 20-30 minutes. Then I would write them down and check how well I had worked out all the hidden secrets. Gradually, I reduced the amount of time, and each time checked how well I had done. Soon I managed to get rid of superficiality and speed up my thinking.

If the reader finds that he often gets into time-trouble and just omits key variations when he tries to save time, then there is something wrong in his thought processes. Current tournament rules give a near to optimum thinking time for moves – on average about four minutes a move (Editor’s note: Most events are now played at three minutes per move, but Kotov’s argument is just as relevant – in tournament play, time is at a premium and inefficient analysis often proves costly near the end of the session).

This is quite adequate when you bear in mind that it is increased by quick play in the opening where well-known series of moves are normally played. If this time is not enough and your games are decided in time-trouble with its inevitable errors, then you must devote a lot of attention to mastering the technique of analysis.

Three factors guarantee finding the right move. They are: an accurate analysis of all variations that can be logically considered, confidence that you have taken account of all the best moves and strict economy in thinking time.

We shall deal with all three in turn and dissect the most complex and incomprehensible caprices affecting a player’s thinking. We shall thus endeavour to give as accurate a picture as possible of the complicated process that takes place when a chess player tries to find the best move.

The Tree of Analysis

The course of a player’s thoughts when considering his move is best shown by a concrete example. The position in the diagram arose in Boleslavsky-Flohr, 18th USSR Ch (Moscow) 1950.

The game had begun thus: 1 e4 c6 2 f3 d5 3 3 g4 4 h3 xf3 5 xf3 e6 6 d4 f6 7 d3 dxe4 8 xe4 xd4 9 e3 d8 10 0-0-0 bd7 11 c4 a5 12 d2 b6 13 he1 xe4 14 xe4 f6 15 xe6 fxe6 16 xe6+

Now Flohr did not play 16…?f7, but tried 16…e7 and lost in the end. What interests us is how the game would have gone if Black had moved his king to f7, and how Boleslavsky would have worked out what to play in that event. We cannot be sure that the course of his thoughts was exactly as we describe it, but the general trend was bound to be as follows:

‘How did I intend to play if he moved the king when I sacrificed the bishop?’ is Boleslavsky’s first thought and he instantly remembers. ‘Yes, 17 xf6+. I remember thinking that I had a certain draw, while Black’s king would have to move about in the centre being harassed by all my pieces. Could there be a win there? So 17 xf6+ gxf6, and now what? I am a rook down, I must check or play some other forcing move. Only one move comes to mind: 18 h5+, otherwise Black will find a way to get his queen over to defend. What do I get from my queen check? Is it a good move! I must work it out, the position isn’t very complicated, I can analyse it right to the end. Let’s analyse. I have enough time and the whole game is now in the balance. If I can find a mate then it’s worth spending a few minutes on it. So, analyse!

‘But do I need to sacrifice the rook at all? Could there be a simple way to exploit my initiative without a further sacrifice? How?’ For a minute or so he examines the position with this in mind – is it essential to sacrifice? He quickly decides that he must. If 18 de1 Black has many defences, such as 18…b5 or even 18…d8. It follows that the exchange sacrifice on f6 is not only the obvious move, but also the only winning attempt, while all the time White has a guaranteed draw.

So the grandmaster settles down comfortably in his chair and starts analysing. ‘I play 17 xf6+ gxf6 18 h5+. Where can his king go? A lot of squares are possible – e7, e6, g7, g8. Four defences. Let me see if I can force mate or get a decisive advantage … Start with e7 and e6 and leave the others till the end. They are more complicated … So we have four candidate moves.

‘1) 18…e7 19 e1+ leaves Black in a bad way: 19…d6 20 f4+ d7 21 f7+ intending 22 e8+, 19…d8 20 e8+ c7 21 f4+ d6 22 e7#, or 19…d7 20 f7+ d6 21 f4+ c5 22 e3+. So, that’s all right.

‘2) 18…e6 19 e1+. This is also all right. Everything as in the first variation.

‘3) 18…g7. I have perpetual check by 19 g4+ f7 20 h5+. What else is there? Aha, the bishop check wins out of hand. 19 h6+ g8 20 g4+ f7 21 d7+ e7 22 g7+. Right, it’s going well, but what about g8? Analyse carefully!

‘4) 18…g8 19 g4+. Quiet moves are no use; I’m a rook down. Now two defences: 19…g7 and 19…f7.

4a) 19…g7. What is there to think about? 20 h6 c7 21 d7 wins. No, stop! The rook move is a gross blunder. He gives up his queen by 21…xd7! 22 xd7 xh6+ and I’m the one to resign. No, it’s not so simple. How do I meet 19…g7?’ And after further thought Boleslavsky finds two candidate moves, 20 e6+ and 20 c4+, which give him attacking chances, and he considers each in turn. ‘20 e6+ f8 21 f4 d8 22 xd8+ xd8 23 d6+ xd6 24 xd6+ and White must win; or 20 c4+ f8 21 b4+ and Black must give up his queen. So that makes the first variation clear. Now for the second.

‘4b) 19…f7 20 c4+. This is strong. I’m not going to repeat moves. Then 20…g7 or 20…g6. Clearly not e8, right into the crossfire of all my pieces. But if he does? Maybe the few pieces I have left don’t frighten him? To be sure let’s check it.

‘4b1) 20…e8 21 e1+ (better than 21 e6+ e7) 21…e7 (or 21…d8 22 d3+ c7 23 f4+ c8 24 e8+) 22 b4! c7 23 c5! and Black can resign.

‘4b2) 20…g7. Now White has no useful checks, but he can attack the queen, which is as good as a check. Yes, that’s quite a move! 21 e3. This threatens a check with the rook at d7. If 21…c7, then 22 g4+ f7 23 d7+. There is just 21…b4 left, but then 22 d7+ g6 23 f7+ f5 24 g4+ e4 25 xf6 and he can’t stop all the mate threats. I should think so too. King in the centre exposed to all my pieces!

‘4b3) 20…g6. Can this save him and so refute the sacrifice on f6? How can that be, how can the king defend himself from the attack of my three pieces? Just look for the right move!’

And without much trouble White will find the win here too. 21 e4+!. Moves which don’t look too threatening at first sight can turn out to be decisive. 21…f7 22 a5. White must threaten the rook check at d7 with gain of time. Two last ditch defences are possible, but neither works: 22…c5 23 d7+ e7 24 b4 g5+ 25 f4 and if 22…h6+, 23 b1 ad8 (23…hd8 24 xh7+ g7 25 h5+ and 26 xb6) 24 c4+! g7 25