Combinations and sacrifices

Recently, May 2009, at the Chessbase site Edward Winter published a new column in his series “Chess Explorations”. These columns are based on Winter´s numerous “Chess Notes”, which can also be found on the internet and in several books from him. These “Chess Notes” make an interesting and entertaining reading for everyone with a broad interest in chess in all its aspects. Here by recommended!

The column in question was titled “What is a Chess Combination?”. It was mostly based on “Chess Note 1960” (!!). Yes, Winter has produced an incredible quantity of them - so far, according to the website, 6105! The “Chess Note 1960” was also published in Winter´s: “Kings, Commoners and Knaves” from 1998. The ChessBase column did leave something out compared to that, but also added a page from Cecil Purdy´s article “What is a Combination?” from 1955.

Cecil Purdy (1906-1979) was an Australian IM and the very first world champion in correspondence chess. He was also an esteemed chess writer with his own magazine and many fine books on his record. I suppose he was a kind of dean in that field in his part of the world, at least I have not heard of anyone who could equal him. His writings were also widely acknowledged internationally, also, but far from only, because of his often controversial, independent and non-authoritarian points of view, also on the subject “combinations”, but more on that later.

Now, the issue here is combinations and sacrifices. As you can understand from the above, Winter started this discussion up more than ten years ago, but that does not really matter to a dedicated researcher, no matter what the subject is. And especially this subject, “the combination”, is at the very core of chess. You cannot have chess without combinations, so the discussions and the tentative understandings of what it is, I guess we will always have as long as there is chess. “Combinations - The heart of chess”! Yes - sic! -, and that was also, according to Winter (who else?), the title of a book by Irving Chernev.

The long-lasting discussion goes on the definition of a “combination”, which I will hereafter refer to as a “C”. Usually I do not join such discussion with much engagement, as I find other issues far more important. But in this case the concept and the phenomena it covers are absolutely essential to chess, and especially when it comes to playing the game. For chess didactical reasons it is therefore of the utmost importance to have a clear, all-embracing definition. If we have to teach our students/pupils a subject, at first we need ourselves to have a clear, conscious understanding of it. And chess students, from the very beginner to the strongest masters, need to learn to see and handle C´s, and they are never really finished with that business. Yes, this is true! Even the super GMs do some “tactical” exercises now and then. I know that from many sources.

Actually I do not find any of the many definitions of C, which Winter quotes, completely satisfactory. The closest agreement I can come to, is with the old sage, Emanuel Lasker in his sublime “Manual of Chess”.

In the “Third book”, on “The Combination,” he writes about the many variations a chess player has to calculate during a game, and then it comes: “In the rare instances that the player can detect a variation or net of them which leads to a desirable issue by force, the totality of these variations and their logical structure are named a “combination”…” That is a fine formulation, as it also describes the process whereby the C occurs to the player. I am also for the formulation “… variation or net of them”, as I think a C is not always just a string of moves with no nodes. But I do not think that C´s are “…rare instances”. They are everywhere during a game of chess, most of them of course not actually seen on the board, but hidden in the calculations of the players. Many of them lead to “a desirable issue” for the opponent, and the player who sees them has to take measures against them. Overall the question about the motive of C´s needs to be tightened up. Of course no player would actually play a C if he did not think it led to “a desirable issue”, but it often happens that his calculations are wrong and the C does not lead to the goal. In Lasker´s definition there is no place for “unsound” C´s.

For some reason some of the greatest authorities on the game have insisted on having a sacrifice (hereby referred to as a “S”) in the course of the C. Most notably we have Mikhail Botvinnik, former WCh and by many hailed as the "patriarch" of Soviet chess. He defines a C as “A forced variation with sacrifice”. Romanovsky (one of the older Russian-Soviet masters, quite influential by his writings in the early Soviet Union), according to Purdy, had set up a definition, very much in line with and expanding on Lasker´s, which did not include sacrifices He was criticised by Botvinnik, “…because it would include things which come under the category of manoeuvres rather than combinations” (cited from Purdy). I had never read that before and it really baffled me, because I have always experienced and regarded Botvinnik as excellently clear in his thinking and formulations. In my view a “manoeuvre” is something only ONE of the players can carry out – a C is a forced string or sequence of moves by BOTH players. “Manoeuvres” and C´s have nothing in common, whatsoever. They can only have some connections, as a C can be a means to carry out a manoeuvre.

Against this Purdy rebelled, as you can see and read in Winter´s article. Purdy brought this position to the reader´s attention:

White wins by playing 1.Bb5+, Ke7 2. Nf5+,Ke6 3.Nxg7+ and white wins black´s queen. Here there is no S, but it is a completely forced sequence of moves. Is this not a C? As Purdy put it: “I hardly think that Botvinnik would call this a manoeuvre…”.

The crucial point is that games of chess abound with such forced sequences of moves, and that they -the C´s - are something special in the vast jungle of chess variations. And most importantly: To play any kind of decent, meaningful chess, you need to be able to manage them to some extent, even if it is just a little. And to manage them, you first of all need to be able to distinguish them from the rest of the variations. Because C´s can be your strongest weapon in the fight, but also the most dangerous pitfalls, if you are not aware of them, and that applies no matter if there is a S included or not.

So, in my view Purdy’s line is indeed a C. Another thing is that, as a reader of “Chess Notes” pointed out, white could play even better in the line given with 3.Bc4!,Qxc4 5.Qxd6+ mate! And then the C would after all include a S. That was bad luck for Purdy, but I believe we got his point.

Purdy gave his definition of a C as: “Play of which the initial moves would lead to gain in every possible variation, through weakness at more than one point”. And another, later and shorter one: “A sudden coup which brings about a substantial gain, no matter what reply the enemy makes”, of which one he states that it “…is not an attempt at complete definition, but at one which will be understood by beginners…”. Well, I never really understood why beginners in a certain field should be provided with especially simplified and reduced explanations and definitions, at least not if we are not dealing with children. But, anyhow, I prefer the first and oldest definition, even though I have my objections. To add that something about “weaknesses” is redundant. It will not be possible to gain anything by any means, if your opponent’s position does not have weaknesses – we have known that since Steinitz. And, again, he leaves out unsound C´s. And then there is still something lacking, something about the units actually taking part in the C. More on that later.

But about S´s I will stretch it further: You never have a S in a C! Of course you quite often give material in these forced lines to gain your desired goals, but is this really a S? It could be that you could call it so, technically as a means in one of the steps in the sequence. But as we are dealing with a forced line which leads (or should lead) to something more than you had before you initialized it, I do not think you can say that you “sacrifice” anything. A true, genuine S is when you in a position give material for some far-sighted goal, the course to which you can not calculate precisely in detail.

This distinction is also very important for didactical reasons. A beginner’s first real, pure joy from chess comes very often, if not always, from C´s, where material is given away in its sequence – and I suppose most of us never really grow out of that joy. But to manage such C´s is by no way the most difficult step in a player’s development, even though such steps you simply have to climb, otherwise you will not get higher. Far more difficult is it to learn to carry out a genuine S with a farsighted goal, and many players, even quite strong ones, never really manage it, and so back off from them.

And now, to illustrate the above outline – and add some more - some positions from very recent games, all collected from the three latest issues of New In Chess.

This is from Leko-Morozevich, Amber 2009.

White is to move and plays 40.Ng5+! and black resigned. 40.-,hxg5 41.Qh5+,Kg8 3.Re8+ is mate.This is a genuine C, and white even gives up materiel in the sequence, so every one will agree on that.
For a super GM as Leko to carry out this C is just a matter of technique, and he probably saw it in a flash, even though the game was played blindfold. But I still think he enjoyed the moment.

In the former white´s desired goal was check mate. Here it is more modest, which in fact is the case with most C´s. It is Anand-Leko, Amber 2009, again played blindfold.

White wins with 1.Bxf7+!,Rxf7 2.Qh8+,Kxh8 3.Nxf7+ with an ensuing decisive material advantage, which wins the endgame, at least for a strong player. A C with this mechanism was also seen in a WCh-match game Petrosian-Spassky, 1966, and you can be sure the present WCh knew of this. That is also part of his chess education.

These were easy cases, but then what about this:

Morozevich-Topalov, Amber 2009, again played blindfold.


Black has just played the unfortunate 39.-a6?, which is followed up by a surprisingly forced sequence: 40.e5!,Rh6 41.e6,Ne5 ( 41.-,fxe6 42.Re7+ ) 42.e7,Kf6 43.Nd5+,Ke6 44.Rd8 and black resigned. Here we have several nodes in the string, the most attractive line being 40.-,Rd1 41.Rd8! and there are still more nodes, but it is a forced win in all lines.

Is this a C? I think it is, but I admit it is a difficult case to categorize. To do that we have to take into account the playing strength, and thereby the players´ capacity to calculate lines. I have no doubt that Morozevich calculated this all out (blindfold!), and also lesser gods than him could do that. But less strong players would likely fall back from calculating all the lines after especially 40.-,Rd1. Anyhow, I believe most players, from a certain, rather low level, would see and play 41.Rd8, just to set up the pin, and then win the game, employing the forced line of the C. And it does happen that you intuitively stumble into a C. It is a C anyway. And most important: It is possible for a human brain to calculate this all out, and a player who wants to improve simply has to learn to do that.

Some more questions emerge on this case:


Carlsen-Grischuk, Wijk-an-Zee 2009.


Here Magnus played the completely forcing 33.Ba6!, There are many lines after this, but black can do nothing about the passed pawns white creates. The game went 33.-,Bf6 34. Bxb7, Rxb7 35.c6,Rxb6 36.Rc1! This is necessary as 36.c7??,Rc6! stops the pawns, so Carlsen indeed had to calculate something before playing Ba6. 36.-,Bxb2 37.d7 and black resigned.

But, as I wrote, there are many lines after 33.Ba6! – did Carlsen see them all through? I am not sure. It is about this “desired goal” of the C, which again is about the ability to evaluate the positions at the end of the forced sequence of moves. This ability to evaluate positions is quite likely what really counts when it comes to playing strength. From that it follows that strong players at times can stop earlier in their calculations of the sequences, because at an earlier point they can evaluate the position. They – so to say – do not have to see the movie to the bitter end. In this case it could be that Carlsen stopped his calculations when he saw the two mighty pawns reach the sixth rank, which mostly is decisive. But lesser gods would probably want, by calculation, to be absolutely sure that one of the pawns would actually queen.

Now this is about the distinction between S and C, between which I admit it can be difficult to draw the borderline:

Aronian-Leko, Amber 2009


Once again blindfold, and in spite of that I do not think Aronian found it difficult to find the next sequence of moves: 21.Rxg6+,fxg6 22.Qxg6+,Kf8 23.Qxh6+,Ke7 24.Nf5+,Kf7 25.Nd6+,Ke7 26.Rd1,Rf8 27.Rd5,Rf6 28.Qh7+,Kf8 29.Rg5 and black resigned.

Is this a S or a C? I believe it is the latter, mainly because I think Aronian simply regards the execution of this series of moves as pure technique. I believe he calculated the lines with the queen checks and when the knight could enter the battle after Nf5+ he stopped, evaluating the position as simply won, as if he had entered an ending two pawns up. No reason to go further, when he was sure to reach his desired goal.

The next position was heavily in focus at the Internet Chess Club, when it was transmitted live:

Kamsky-Topalov, Match Sofia 2009
Kamsky has a splendid position, but it still took him 30 more moves to gain the victory after he played the cautious 43.Bb4. As he points out in his comments in NIC, he could have won a lot faster by playing 43.Bxf8!,Rxd2 44.Qc1!,Rxf8 45.Rxf6,Qd7 46.Ngf1,Rd6 47.Nf5!. He admits that he did not see the last, strong move in the sequence. This line is of course a genuine C, there are not even that many nodes in the string, but with its many hanging pieces it is not that easy to see through.

At the ICC some members seems to enjoy having their computer engines working on the positions in the games they are watching. At times it can be quite irritating with all these “comp eval´s” in positions that are not at all suitable for it. But when it comes to C´s, the “comps” of nowadays are merciless, they see it all, that’s it. And in the position above they – as quickly as light – saw the C that Kamsky missed. At the ICC some members, and presumably fans of Kamsky, went almost berserk, waiting for his move (fortunately, you only join this club in cyberspace!), which of course made them all fall down, as it was not what the “comps” had suggested. Some of them even took the liberty to criticise poor Kamsky, who was after all, after four hours´ play and in an immensely tense match situation, still sitting there playing, trying his best. Well, these people should try for themselves if they could find a C like this: But I doubt they will ever be able, the way they make use of their silicon oracles. This is a sad aspect of modern chess.

The next position contains a possible C, which the player replaces with a genuine S. It is from a crucial last round game between the two penultimate leaders of the B-group in Wijk-An-Zee, annotated in NIC very open-mindedly by the happy, young winner.


Caruana-Short, Wijk-an-Zee 2009
The game so far has been wild and fluctuating, which, in connection with the tense competitive situation, quite likely has taking its toll on the players. However, they keep on fighting it out.

Now there is, according to Caruana, a C that should win for black: 47.-,cxd2!48.Rxc6,dxe1N+! 49.Kf1,Nxf3 50.Rxd6,fxe4. This, according to Caruana, “…leads to an amusing endgame. Black is winning, but it is possible to lose control”. Here you see that if the desired goal of this C is reached, it depends on the evaluation of the nontrivial endgame it leads to. The sequence is not that difficult to calculate (underpromotion, but with check, and almost no nodes), so it all hangs on this endgame. Caruana believes it is winning for black. Well, I am not so sure, and it could be Short had the same opinion. But the continuation of the game indicates that it after all was by far the best to play this C. Short seems simply to have evaluated the consequences of the following S wrongly.

Instead he played 47.-,Nh4+!? Caruana: “A Shock! At first I was sure I was going to be mated immediately, but after I calmed down I realized that I was safe for the time being.” That seems to indicate that he at first thought that Short had come up with a C, that he had overlooked., and such incidents can indeed be shocking! Well, it could also be that Short thought he carried out a C, but overlooked something, turning it into an unsound S.

Then came 48.gxh4,Rg6+ 49.Kh3,Qd7 50.Qh5,cxd2 51.exf4,Rh6 and now Caruanas 52.Qg5+? should be a mistake, “…letting black off the hook” . He gives 52.Rg1+ as better, leading to an advantage for white in, again, a nontrivial endgame. In the continuation Short missed some chances to give perpetual check and finally lost.

And now we come to some remarkable recent S´s.


Akopian-Vachier-Lagrave, Ol Dresden 2008
White played the S 19.Bxg6!, Nxg6 If 19.-,fxg6 20.Rxf6,Qxf6 21.Rf1 wins the queen for the two rooks. Timman in NIC: And now “Black has little to hope for”. That is an evaluation from some kind of an expert. I believe him, the queen and the two knights are a formidable force, which black will not be able to contain, but it is still an evaluation. In the game came
20.Nf5,Qe5 21.Qxb6,Bxe4 22.Qxd6+,Qxd6 23.Nxd6,Bxc2 24.Rxf6 and white had regained his material and black´s position had fallen apart. Very nice, but not that, comparatively, difficult - that is for a strong GM. It could be on the border to being a C, as I claim the above Aronian-Leko is. But still, this is after all a far more complicated position, where even the best calculators cannot see to the end of all the branches of the tree of variations. The move 19.Bxg6 has to be based on some kind of intuition, so it is a S.

And finally, once again Caruana, this time as the ignitor of the fireworks:



Caruana-Berg, OL Dresden 2008
With all his heavy pieces on the king side and most of black´s off side it is no surprise that white can turn to drastic measures: 20.Nxf7!,Kxf7 21.Rxe6!, Nc5. It is not that difficult to see that black after 21.-,Kxe6 will be mated by force. In a way you could call this an “imbedded” C, which was most likely calculated by Caruana. 22.Rxd6!,Rxd6 23.Qf4+ I doubt if Caruana went much further than this in his pre-calculations. It is obvious that black is under hard pressure with his exposed king. 23.-,Ke7 24.Re1+,Kd7 25.Bb5+,Bc6 26.Qf5+,Ne6 27.Bxd6,Qxd6 28.Rxe6 and black resigned. That went fast, but black does have some alternatives which could have prolonged the fight, eg. 21.-Qc6!?. But in praxis it would have taken a super-human effort to stand up against this onslaught. Maybe Rybka could have managed, but I doubt it. You may try it out for yourself, if that is of some interest to you.

I hope the above has provided some clarity on the issues, in at least provoked some thoughts. But we are still in a need for a proper definition of a C.

For that we may turn to an authority, not mentioned or cited by Winter, even though he is mentioned in one of the comments from his readers. That is Yuri Averbakh, in his heyday one of the strongest Soviet GM ´s, later an esteemed and leading writer and researcher on, in particular, endgames. Averbakh deals with the subject in a most accurate and profound way in his “Schachtaktik für Fortgeschrittene”, Sportsverlag 1978, translated from Russian and also published in several English versions, “Chess tactics for Advanced Players”, the first of these also by Sportsverlag, 1984. Whether the latter is a directly translated, maybe even from Russian, or adapted version, I am not sure.

In a short chapter, “Was ist eine Kombination?” (“What is a Combination?”), Averbakh deals with most of the above mentioned attempts at definitions, apart from Purdy´s, whom he does not mention (It could he did not know of him at the time of writing). He does criticise Botvinnik, and brings up some more examples to undermine his definition.

Averbakh focuses on the very etymological core of the latin word “combination”, which means something like “tying together” (of some units). In the english version the phrase "connections" is used, so I will apply that from now on - even though I feel it lacks some dynamics. Maybe "relations" is better? Well, it does happen, that a word, completely broken away from its original etymology, is used as a term for a concept. But, anyhow, I can follow him: In a C there must be some units, pieces, which in some ways are in "connections". You cannot have a C with just one or two pieces. In fact Averbakh expresses that there must be at least three pieces connected in a C.

This attempt at dealing with the phenomenology of a C is very clever and something completely lacking in all the other mentioned definitions. On the definitions from Lasker and Romanovsky (and I suppose it will go for Purdy´s as well) Averbakh remarks: "You will note that both of these definitions have been completely disassociated from the connections of pieces and pawns, but they have retained two essential features connected with the combination: The forced moves and the winning of an advantage by the side carrying out the combination:" After dealing with Botvinnik´s definition, Averbakh states: “From all this follows that, of the two definitions of combination we have, one is too broad and the other too narrow”. That’s it! – expressing all my own doubts and sceptiscisms!

And then comes Averbakh´s definition: “A combination is a rearrangement of the connection of pieces of both sides, which forces a co-ordinated connection of contacts, which is advantageous to one side”. Sic!

This is the way it is translated in the english version of the book. Actually I am not completely satisfied with this translation. which in my eyes contains a little to many non chessic terms (eg. "contacts"). But I admit that with this one it is difficult to find the right phrases. So, here is the German wording, if you want try for yourself: “Eine Kombination ist die Umgestaltung einer Verknüpfung von figuren beider seiten, die forciert zu einer koordinierten Verknüpfung von Bindungen führt, die für eine Seite vorteilhaft ist.“ I would be happy if someone could provide me with an improved version.

But basically this definition is fine, as we now have it all: The starting point of the process (some "connections of pieces”), the actual process (the “rearrangement...”), the end state of the process (the “coordinated connections...”) and the goal of the process. That a C is this “forced sequence of moves” you can easily deduce from the definition. And, if you look for it, you can also have the unsound C under this umbrella.

What Averbakh explicitly was after, was a definition which could be applicable in the “categorization” of C´s. After giving his bid, he goes on: “This determining of the concept we need for the classification of the combinations. We will see that, despite the huge number of combinations, it falls very easy to classify them according to the final connections og contacts, of which there is actually only a few.”

And then he goes on in his book, categorizing C´s. For “winning C´s” he is boiling it all down to some 7-8 types. Well, you may question that, but the crucial point is that Averbach manages to create some order and his “categorization” provides you with a powerful, didactical tool. If you study his examples, you will be sure to experience a lot of the utmost importance to a chess player, but maybe not all of it.

The only criticism I can come up with regarding Averbakh´s definition, is that it is not exactly accessible to a common chess player, eg. a beginner working on his own. Yes, it is an excellent tool for the expert, who works on providing some examples for coaching, teaching or writing, as Averbakh himself shows in his book, but I think we still need something more broadly intelligible.
Now I am almost through, and I know this little piece of text does not at all close the book. I am thinking about how to improve, or rather expand, the definition, and maybe I will come up with something in a while. Or maybe there is someone out there for a bid?

Finally, to all these definitions, also Averbakh´s, you could add something like: “The sequence of moves, constituting the combination, must be within the capacity of the human mind to calculate.” That is if you really want to come down to basics.

After all it could be that the game of chess is NOTHING but combinations. Some imagined Supreme Being, maybe some future super computer, could become (or is?) able to calculate the game all through. I suppose it will tell us that a game of chess by correct play by both parties should end in a draw. Such play could be phrased as “super drawing combinations”. But if you in any given position differ from these correct paths, there will be a “super combination” that inevitably will lead to your defeat.

Many a human chess player regards strategic, positional play as something more difficult and dignified than carrying out combinations. In the light of the paragraph above, what are in fact all these fine, elaborate terms used on this kind of play? They are merely heuristics we humans have to make use of because of our limited calculating powers. And so are basically also our humble attempts at defining C´s. It is the same as attempts to define the world: You can not really do it, but you can come with some good advicess on how to deal with it - and we need a lot of that!

I read in a review of Averbakh´s book that he was into some kind of "molecular" research on chess. It could be that he is rather on the cosmological level.

First and last in chess is the combination!