- The elements of combination
- Sight of the board
- Combinational vision
- Varieties of error
- Candidate moves
- The calculation of variations
- Good practice and further reading
- Net reading
"It is a mistake to think that combination is solely a metter of talent, and that it cannot be acquired"-- RETI
[Concidentally this document was followed by a useful UseNet post by NM Dan Scoones.]
The way it works is this:
My mum and dad taught me how to play chess, and when I was about 9 I went to the school chess club. I sat down to play a small boy, took the Black pieces and was mated in four moves (Scholar's Mate). To the best of my recollection I have never fallen for it since, and while I can't ever remember perpetrating that particular sequence on anyone else, I have delivered mate on f7 a number of times.
Learning and applying tactics is just that: you learn to recognise a pattern, you see it coming if someone tries it on you, and you can apply it in similar positions in your own games. In fact, once you know the patterns, a lot of the calculation comes pretty easily.
"Those chess lovers who ask me how many moves I usually calculate in advance, when making a combination, are always astonished when I reply, quite truthfully, 'as a rule not a single one' "-- Richard RETI.
It used to be thought - perhaps because of statements like this, and a little early psychological research - that there wasn't much difference in the abilities of strong and weak players at analysis: rather, it was all about judgement and experience. There might not be a lot of difference between GMs and IMs, but there is increasing evidence that among we club players, there are large and important differences [see Simon Webb's panel tests]. So, the patterns and judgements are important, but you must also train yourself to analyse. Sir Peter Medawar once remarked, rather testily:
"the spread of secondary and latterly of tertiary education has created a large population of people, often with well-developed literary and scholarly tastes, who have been educated far beyond their capacity to undertake analytic thought".[A sentiment to be found in his splendid demolition of Teilhard de Chardin's The Phenomenon of Man, first printed in Mind, then collected in The Art of the Soluble]
No less a tribute may be paid to the editors at Batsford and Cadogan and Chess Digest: there is a population of chessplayers who know about mysterious Rook moves, Super-Quart Grips, the Inverse Phalanx, and the latest wrinkles in the Sicilian, but who cannot reliably spot three-move tactics or win a Rook Ending. This piece is dedicated to the first of these failings.
Here's a nice example, which I think is not out of most players' reach: have a go at solving it (White to move and win) before reading on.
The different combinational themes are often called motifs.
The theme or motif of this combination is the fork. There is almost no way you can find the combination in this position if you have not seen this pattern before.
First, we examine the position for pointers. The Black pieces are not very well coordinated, and the Black King and Queen seem almost in reach - for example, if we had protection for e6, we could think about e5-e6+ winning the Queen. In fact, f4-f5 provides that protection, so 1. f5 (Knight moves) 2. e6+ looks excellent, except that Knight moves 1...Ng6xe5, but it starts to look as though we might be on for something here.
More details: we can, by Bxg6+, bring the Black King a little closer, and check it by f4-f5. In fact, we can check it immediately by e5-e6. Maybe some combination of these ideas might allow us to lure Black pieces to e6 and g6, and fork them by f4-f5.
So, this fork becomes the idea of our combination.
Next, the combination must now be calculated and the correct move order sorted out.
We might try 1. Bxg6+ Kxg6 2. e6 when if Black takes it 2...Qxe6, we win with 3. f5+, but Black can safely sidestep with 2...Qe7.
Purdy coined the splendid term smite: you must
learn to examine smiting moves, checks and captures. These
are the most forcing and the key to starting most combinations.
With this in mind we can reconsider our combination:
the starting move 1. e6+ is perhaps surprising, but once we consider the move at all we can see that is it very forcing, and after 1...Kxe6 or 1...Bxe6 we can play 2. f5(+) winning a piece.
So, Black seems obliged to play 1. e6+ Qxe6. Now again, 2. f5 fails to 2...Qxe3. Humph.
The forcing sequence 2. Bxg6+ Kxg6 3. f5+ Bxf5 seems almost to fizzle out, but then (aha!) 4. Nf4+ forks King and Queen. Missed anything? No, all looks OK, so, Black has to lose a piece, probably by 1...Bxe6 when a couple of Pawns will be partial compensation.
So, the elements of a combination are motif, idea, and calculation. You don't really change gear from one to the other when trying to come up with a combination in practice, but you do need to work on each separately if you are to improve.
How did your attempt match up to my account of the solution? Missed the idea? Missed a defence? Muddled the move order? Hopefully what I describe below can improve your performance in each aspect. Even if that one seemed totally beyond you I'll at least show you how such a standard can be approached.
"A thorough understanding of the typical mating combinations makes the most complicated sacrificial combinations leading up to them not only not difficult, but almost a matter of course."-- TARRASCH
You must know all these motifs:
- K - knight forks
- L - last rank
- M - mating pattern
- N - network nobbled (Nterference)
- O - overloading
- P - pins
- Q - queening
- R - retreat
- S - sacrifice at castle gates
- T - two for the price of one [double attack]
- U - undermining (removing the guard)
- U2 - unmasking (discovery)
- V - vulnerable f7
- W - weakening King's-side
- X - X-ray (skewer)
Once you are aware of these motifs you can apply them in your own games. See also Combinational vision below.
"The technician, whose vocabulary has been doubled by Dr. Euwe, will find that White could have saved his soul by a desperado combination. Had this failure anything to do with the fact that Dr. Euwe's terminology was not yet existent at that time!?"-- Reinfeld, to Thomas-Euwe, Carlsbad 1929.
You can get this far solving positions one move deep, two moves deep, three moves, four moves, five moves and six moves deep. They are all knight forks, if you want a hint, although other motifs may make an appearance.
This 'decoy' of the Queen onto a forking square is very common in combinations with a Knight Fork motif.
1. Nd5 Qe6 2. Qxe4 Qxe4 3. Nf6+ 1-0 Black has better moves than 2...Qxe4, but if Black cannot recapture on e4, White wins a piece.
1. Qb5 Qxb5 2. c8=Q+ Kf7 3. Qxe6+ Kxe6 4. Nc7+ Kd7 5. Nxb5 1-0
1. Re8+ Kd7 2. Re3 Qg7 3. Rxd4+ Qxd4 4. Rd3 Qxd3 5. Ne5+ 1-0
Remember, this was a correspondence game, so time wasn't the issue - despair was.
[3.Nf2 Qxh2+ 4.Kf1 Nxe5 5.Qc5 Nxf3 6.gxf3 -+;
3.h3 Qe1+ 4.Rf1 Qxf1+ 5.Kxf1 Rxd1+ 6.Rxd1 Ne3+ -+]
The other resource, besides these tactical problems, is simple chess studies: at their best they can make you pay close attention to the geometry of the board, like this one:
In an actual game, you just play this straight away as the best winning attempt because there are so many ways for Black to go wrong. But for practice, can you follow it to the finish? These open-field combinations can be hard to keep track of, because of the apparently great number of choices at each turn.
[1.... Kf4 2. Qf3+ Kg5 3. Qg4+ Kh6 4. Qg6#]
[1... Kf5 2. Qh3+ Ke4
or [2... Kg5 3. Qg4+]
3. Qf3+ Kd4 4. Nc6+]
2. Qe1+ Kf4 3. Qf2+ Kg5 4. Qg3+ Kf5 5. Qg4+ Kxe5 6. Qg3+ Kf5 7. Qxb8 1-0
Experience: Once you have seen something, you might be able to implement an analogous idea in your own games. This is more than knowing the motifs; I mean you should continue to broaden your experience of combinations by examining new examples. An example from my own modest practice: I have known about knight forks for ages (ever since I kept finding them arriving on c7, checking and forking Ke8/Ra1). But once I had seen the famous finish of a Petrosian-Spassky game (see the entry for Petrosian in the Style section of Canon), I could see the same thing going on in my own game.
This rather reminds me of the old psychological tests based on embedded figures; finding combinations seems a bit like that.
Imagination: I used to think that the creative imagination was something mysterious and intangible, which could neither be described nor trained. While there may always be something elusive about artistic creation, some thinking by people like Liam Hudson and Daniel Dennett gave me some cause to hope. Creativity is not a simple product of unfathomable inspiration, but a result of firstly, generating lots of (mostly junky) ideas, and then weeding them out to discover the ones that work. If this is true of the expressive arts, then it surely also applies to chess, where the ideas have such concrete prompts on the board, and the selection of the ideas that work can be put to the simple test of analysis.
Put simply, this suggests that someone like Tal can come up with great ideas because they come up with loads of ideas, good, bad and indifferent, and then can select the great one. The problem with most of us is not that we are failing to come up with enough good ideas, but we are failing to come up with enough ideas, full stop. Our ability to spot combinations is limited by our tunnel vision, considering only a few moves of a stereotyped nature, and not having the habit of looking at every thing once, no matter how foolish at first sight. Developing imagination, then, is not a matter of learning how to do something terribly magical, but to some extent involves putting aside what you think you know (retreating pieces is bad, putting your Queen en prise is bad) and considering moves that only very good players - or very bad players! - look at.
- A tactic appears for you: you miss it.
- A tactic appears for your opponent: you miss it.
- A tactic appears for you: you see it but analyse it wrongly.
- A tactic appears for you: you see it and analyse it correctly, but wrongly assess the outcome.
- A tactic appears for you: you see it and analyse it correctly, but stop analysis too soon.
Ah, if only it was all like that...
[21. Qe6 Qd8 22. c6 or even 21. Rxd7 Kxd7 22.Rd1]
Patzer sees a check... It didn't affect the outcome in the end but White had to start all over again to build up another combination.
There are lots of opening traps like that: White bites off more than he can chew.
20. Nh3 Qg4 21. Ng5 1-0
Simple over-optimism: I didn't consider 20...g5.
[34. Kh2! ...when it's all a bit tricky!]
34... Qe8 35. Re6 Qxa4 36. Re7+ Kg6 37. Rxc7 Qd1+ 0-1
The tactic was obvious enough, what I failed to assess was how good White's pieces would be in the ending.
[28... Qc7! wins, I think]
29. Bxe4 Qxe4 30. Nxc4
And of course I realised here I'd blown it:30... Bxa4? 31. Nd6!
This is very common: stopping analysis at the end of a sequence favourable to you. But after that, it's your opponent's move!
As we start to comment more deeply on these examples, we see two sources of error: mistakes or bad habits in analysis, on the one hand, but also misjudgements on the other - errors in the general assessment of the board or the opponent. It is just the first of these I am concerned with here; else we are raising another big issue about attitude.
Getting your mind rightCombinations do not usually come out of nowhere - they are based on a superiority in position, and you can tell when a combination is likely to be around:
I don't know any exercises to improve your mental attitude, but awareness - particularly self-awareness - is important in eliminating all sources of error, not just tactical ones. I have written and collected material elsewhere about getting your mental attitude right: there are examples (good and bad) in the Psychology section of the Canon, there is some good advice on a Poster for Juniors, and in a compilation of Advice for the middlegame. However, in this document on tactics I'll mention the issue of attitude in this aside, and return to the matter at hand.
- Exposed or "stalemated" Kings are always vulnerable
- Undefended or 'hanging' pieces aften lead to trouble.
- Pieces which are defended only as often as they are attacked can also lead to trouble, because their defenders are at least partly immobilised..
"No combination without a considerable plus, no considerable plus without a combination [...]-- LASKER.
In the beginning of the game ignore the search for combinations, abstain from violent moves, aim for small advantages, accumulate them, and only after having attained these ends search for the combination - and then with all the power and will of intellect, because the combination must exist, however deeply hidden."
I like this quote, but it has to be said that while there are 'just' and logical combinations where you (say) carry out a combination based on a campaign against the long-term weakness of a Pawn, there are also 'accidental' combinations which seem to be based on nothing but the chance arrangement of pieces, and there are also traps - so diligence in searching for tactics is required at almost every move.
- you must routinely check all positions for tactical opportunities
- you must think for your opponent as well as yourself
"All candidate moves should be identified at once and listed in one's head. This job cannot be done piecemeal, by first examining one move and then look at another."-- ALEXANDER KOTOV
The idea is, to make sure you don't overlook some vital idea at the start of analysis.
Varley - Hewson, WECU Jamboree [B18], 1993Black has a restricted position and is behind in 'development' (=getting his pieces out) but his pawn structure is very solid. Can Black get away with this, or can White show the flaw in Black's move order by the sacrifice Bxe6? What do you think?
An enterprising sacrifice! White hopes to catch Black's King in the centre.
Unflappable Exeter player Brian Hewson calmly sidesteps the main line of a sacrifice (11...fxe6) threatening a pin on the e-file.
12. O-O Bxf4 13. Bxf4 fxe6 14. Qxe6+ Kh8 ... and Black consolidated and won. [0-1]
It is often the case that players will analyse one line very deeply but fail to spot an early alternative - as mentioned above, Grandmaster Kotov advised many years ago to identify each candidate move at the outset before analysing any one move deeply. Had White done this he could not fail to notice the possibility of Black castling, and should then spot the classic pattern of Q and K lined up on the e-file which suggests a pin from a Black R on e8, and could not fail to realise that it refuted the sac.
There are certain sorts of moves which are easy to spot (or train yourself to spot: like checks, captures, and so on. There are also certain classes of move which are difficult to make yourself consider - here are a few surprising/paradoxical moves. You should (a) make sure you know these models, (b) collect and review other examples, (c) see if there are either types of moves which you or somebody else found difficult to anticipate.
The error made by Karpov above is actually a common one - missing an undeveloping retreat.
Other errors of this sort - hard types of move to spot - include long moves, sideways moves by Queens, captures by Pawns away from the centre, and so on. Another example:
How about that one: a Queen moving backwards into a position where it can be captured!
'Silent' sacrificesYou can get so used to looking for 'smiting' moves that apparently non-forcing, 'quiet' sacrifices can be surprising:
[19. e5 f5 20. Qxe8 Nxe8 21. Ne2 Bxe5 22. Rxf5 Bf6= ]
This is what I mean: a silent sacrifice of the Rook, which actually leaves Black helpless. Chess may not be an art, but moves like this have a strong aesthetic effect, at least for me - I like the apparent subtlety of the sacrifice without a check or capture, and I like the drama of giving Black an apparently free move for the defence - which he cannot make use of. 19... Kg8
[19... h6 20. e5 [20. Rxh6++- ] 20... Kg8+- ]
20. e5 h6 21. Ne2 1-0
"examine moves that smite!"
But have a look at this:
Surprising and elegant, this 'creeping move' impressed many, including Kotov who has cited it more than once. The move prepares to answer ...Qe6 with Bxc5 and leads to a swift win. To Kotov, this was a far more brilliant move than the Queen sacrifice that ended the game.
26... Kg7 27. Nd5 Qe6 28. Bxc5 Bxc5 29. Qxc5 Nb5 30. Qe3 Qc6+ 31. Kb1 Nd4 32. Rc1 Qb5 33. Nc7 Qe2 34. Ne6+ Kh7 35. Qh6+ 1-0
It's hardest of all to spot a 'creeping' move in the middle of a combinational exchange. Here is a simple example:
7... Nd6 [better 7... d6]
8. Bg5 f6 9. Re1 fxg5 10. exd6+ Ne7 11. Ne5 cxd6 12. Qh5+ g6 13. Nxg6 Qa5 14. Nxh8+ Kd8
Have a look at the next diagram and see what you think.
[Obviously not 15. Qf7 Qxe1#]
It is tempting to try a forcing move, but none work.
"A quiet move in the midst of an attack is the sign of the master" - Du Mont
15... Qf5 (else Qf7) 16. Nb5 Ng6 17. Qxg5+ 1-0
- Candidate moves must be established straight away and they must be clearly enumerated.
- Once we have established all the candidate moves, we then proceed to work out the variations arising from them one by one.
- In analysing complicated variations, one must examine each branch of the tree once and once only.
- This task cannot be split into parts, by examining one move fully and then looking for the next one.
bare trunk bare trunk with coppice bush side-branchThrough practice, I would have thought anyone could master the art of analysing "bare trunks" and "trunk-with-branch" - what is required here is the ability to visualise the board several moves ahead.
Also, I think also the "coppice" type of position is not out of most players' reach. What is required here is organisation - to list the moves required at the outset, and to work through them methodically.
What is most challenging is the type of position which is genuinely complex, like the "bush", when it is difficult for most of us to analyse everything relevant. Are they any hints or tips for making best use of the time we have, while our analytical skills are still developing? Yes indeed: we have advice from de Groot, from Nunn/Griffiths, and from Nimzovitch.
The chess master and psychologist De Groot, in commenting on transcriptions of players' verbal reflections, used to talk about 'progressive deepening'. If this strategy is to be adoted in must not resemble the feckless meandering described so amusingly by Kotov in his book Think Like a GM, switching dissatisfied from one move to another until you run out of time. However it has often seemed to me that rather than work six moves deep down line "A", then six moves each down line "B", it might be better to look (say) two moves deep in each of lines A-G, then go back to "A" and go four moves deep this time, and so on. It may be that you find the key to the position earlier than you would have done by a strictly sequential approach, and in any event, ideas which may be obvious from one line of analysis may come in handy when analysing other lines, where the same idea is not so obvious. There is an example illustrating the idea of 'progressive deepening' from Simon Webb's panel tests. Given a list of candidate moves, which lines do you start with? Purdy again: start with the most forcing moves. But if none look any better than the others?
Nunn and Griffiths advise: "Just plunge in"; take a look at this one, where "Black has a decisive attack" but there is no forced mate.
The first move to look at must be 15. Ba4 Nd2+ 16. Kc3 Qe3+ 17. Kb4 a5#
..."and straightaway you have learned a lot about the
That is, you can regain at least one piece whenever you wish, still keeping the K exposed. After this you can work your way methodically through the other lines, with the conclusions from your quick first assessment already in mind.
Sometime you can divert the task of analysis: play a good positional move relatively quickly.
nimzovitch - tartakower (karlsbad) [E81], 1929
[15. Bxf6 Bxf6 (Nimzo analysed briefly:) 16. Qh6 Bg7 17. Qxh5 h6 18. g5 f5 "now it is necessary to analyse several variations which are roughly equally good:" e.g. 19. gxf6 [or 19. gxh6] 19... Rxf6 20. Bh3]
"all of this is extremely complicated and therefore I played after no more than five minutes' thought"...
15... Bxf6 16. Rxh5 Bg7 17. Nh1 There followed:
17... f6 18. Qh2 h6 19. Ng3 Kh7 20. Be2 Rg8 21. Kf2 Rh8 22. Rh4 Qe8 23. Rg1 Bf8 24. Kg2 Nb7 25. Nh5
"with a strong solid game and chances of attack" - NIMZO [...1-0]
However, sometimes there is no such resource, and you must simply work your way through the variations as best you can.
"Let us repeat once more the methods by which we can increase our combinative skill:-- Euwe, Strategy and Tactics in Chess.
"(1) by careful examination of the different types and by a clear understanding of their motives and their premises
"(2) By memorising a number of outstanding as well as of common examples and solutions
"(3) Frequent repetition (in thought, if possible) of important combinations, so as to develop the imagination."
Since Euwe wrote, some other methods have become more available.
- Gaining practice and experience through tests:
- You have probably seen either the British Chess
Magazine column Find the Winning Continuation, or
the same idea in Chess magazine, called there
Winning Combinative Play. There are also books of tactical
positions for solving, one I quite liked for the basics was Chernev
and Reinfeld, Winning Chess.
If you are determined to get better, try the Russian chess training programme contained in three books by Livshits: Test your chess IQ, Vol.1 (for players up to BCF 160/ELO 1850), Test your chess IQ, Vol.2 (for BCF 160-200/ELO 2000) and Test your chess IQ, Vol.3 - Grandmaster Challenge (for BCF grades 200+/ELO 2000).
They all suffer from the drawback, in my view, of containing only combinations that work - there are no false but tempting opportunities offered to you, which is so often the case during a game, except in Livshits' books in a section called "Traps"(!). In fact, I believe that mass practice of tactical tests like this can lead to a false sense of optimism when presented with a promising tactical opportunity. Unless these tests have many hidden points in the variations you are required to spot, or include 'false' opportunities, they must be supplemented by other activities. Some support for this is found in Gene Thompson's article for Chess Scene.
More testing (literally) is the Chess Monthly magazine feature, How Good is your Chess? which takes you through a real game and gives you points (There is a book of these under the same name by Danny King; BCM have a similar feature called Test Your Chess.) Here's an easy example of such a test from the B.C.F., with answers.
- Other Books for study
- Most of the above is 'practice makes perfect' style with little
explanation. The theory of candidate moves and trees
of analysis I found in Kotov, Think like a
Grandmaster (a summary is also to be found in Kotov, Plan
like a Grandmaster). This book also describes how Kotov used
to analyse complicated master games, writing down his conclusions
for comparison. Both books give test positions with a full tree of
Another important book for theory is Nunn and Griffiths, Secrets of Grandmaster Play. It is a deliberately educative book, showing, firstly, what a complete analysis of a game looks like, but also giving lots of practical tips and observations, and trying to show how much players really see at the board.
- Gaining practice and experience through exercises:
- One of the best exercises is to play tactical games, against a player of about your own strength or better. If the point is to develop tactics, there can be no better way of doing this for most people than practicing against a computer - that will show you how thorough you really are!
- Playing-out of positions
- There are also some good ideas in Dvoretsky, Secrets of chess tactics. In particular, he describes the technique of "playing-out" of positions for which an analysis has been published. For example, he played on from positions found in the Nunn/Griffiths book with his pupils (Yusupov and Dolmatov) as if the position had arisen in a game against the clock. This is a realistic test and you can check your conclusions against what Nunn has analysed. Of course, you can use a computer to play positions out.
- Examining your own games:
- Always a good idea - and it is quite possible to do so concentrating mostly on the number and type of tactical errors you make. Mistakes are perhaps inevitable, but to be worked on - for example, try to eliminate one-move mistakes, then two-movers, and so on. Also, make sure you are spotting opportunities for your opponent as well as yourself. I'm sure becoming more efficient or more consistent in this regard would result in a rise in grade for most of us, without any great new insights being gained.
- Blumenfeld's rule for avoiding blunders:
- After you have decided but before moving, write the move down,
and before playing it, check it again for any tactical features you
may have missed. After this fresh look, then you move. This is
"It often happens that a player carries out a deep and complicated calculation, but fails to spot something elementary right at the first move. In order to avoid such gross blunders, the Soviet master B. Blumenfeld made this recommendation:-
When you have finished your calculations, write down the move you have decided upon on the score sheet. Then examine the position for a short time 'through the eyes of a patzer'. Ask whether you have left a mate in one on, or left a piece or a pawn to be taken. Only when you have convinced yourself that there is no immediate catastrophe for you should you make the planned move."
You've all seen people do this. I've also seen people do it badly. The idea is to snap youself out of the trance of analysis and take a fresh look.
I have seen players write down a losing move while nodding and smirking, look over the board again still nodding, and then play the move. Useless - just going through the motions. I guess they were just revising their latest thoughts on the position. You must jump! snap! start! your thinking again, to see if you have overlooked anything at the start of your thinking. You are not checking conclusions - you are checking assumptions. [If they had genuinely re-started their thinking there would have been a change in body language - not a smooth progression from choosing to writing to blundering, nodding all the while, but "now then, sit up straight, start worrying, what have I missed?"]
Online exercises from John Coffey and
Worked example from Gabriel Schwartzmann
Kotov's classic Think Like a GM, the first chapter of which has been very influential.
A nice piece of self-reflection from an amateur, Gene Thompson, first published in Chess Scene.
"The pleasure of a chess comination lies in the feeling that a human mind is behind the game, dominating the inanimate pieces with which the game is carried on, and giving them the breath of life."-- RETI
Alexander, The Penguin Book of Chess Positions
Avni, Danger in Chess
British Chess Magazine, Find the Winning Continuation
Chernev and Reinfeld, Winning Chess
Chess magazine, Winning Combinative Play
Chess magazine, How Good is your Chess? (Book of same name by Danny King)
Dvoretsky, Secrets of chess tactics
Kotov, Think like a Grandmaster )_candidate moves, tree of analysis, analysis of master games
Kotov, Plan like a Grandmaster )
Livshits, Test your chess IQ, Vol.1
Livshits, Test your chess IQ, Vol.2
Livshits, Test your chess IQ, Vol.3 - Grandmaster Challenge
Nunn and Griffiths, Secrets of Grandmaster Play