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The Chess Endgame Study
A Comprehensive Introduction
By A. J. Roycroft Dover Publications, Inc.
Copyright © 1981 A. J. Roycroft
All rights reserved.
ISBN: 978-0-486-81628-9
CHAPTER 1
Casual Solver
Crossword puzzles have grades of difficulty and erudition. If 'Laundry not back, by George!' appeals as a clue for Washington, then the studies at the end of this chapter should also appeal, C. M. Bent being the composer of the crossword clue also. Sadly, though one accepts it as inevitable, the English morning papers carry the full range of crosswords, but almost never a study. And one evening paper sports studies, occasionally. What a welcome innovation if the early national dailies offered studies, even difficult ones (with clues!), for the fresh matutinal minds! 'Haven't you solved the Times study yet?' 'No, but I've cooked the one in the Telegraph', is a conversation yet to be overheard. A swing in popularity no greater than the familiar one of the electorate (who are the same people, at any rate in part, as the chess public), a swing away from crosswords and in favour of studies, would lead to an increase in playing strength over the whole country. Unfortunately a vicious circle exists, and such an event is likely only to follow an increase in playing strength. Nevertheless there is small doubt that if an international contest 'over the crossword puzzle' were feasible, the United Kingdom would beat the Soviet Union! Of course the absurdity of the idea of an international crossword puzzle match highlights the universal nature of the language we call chess.
The casual solver, then, is the newspaper solver. The diagram and stipulation ('White to Play and Win' or 'White to Play and Draw') are on one page and the solution is on another. A player of some strength may expect to solve from the diagram, but the majority player examines the picture cursorily for its main features and puts the position up only when he can also put his feet up, at home, where he has his familiar board and his familiar chessmen.
The preference of the majority player is for relatively few pieces. This turns out to be the very requirement satisfied best by endgame studies. 1 to 3 are extreme examples, in their elementariness and early dates, but they make the point. This visual simplicity makes studies the ideal material for both newspaper columns and that controversial chess medium, television. The solution should have a single main line of four or five moves. White 'must-nots' and Black 'oughtnots' should be at least as short and clear cut. The esoteric must be avoided like the bubonic. Many a columnist, being an expert, finds it hard to be elementary. I would think twice before putting 143 in a newspaper column for solving, for instance. Mate, stalemate and win of the queen are the three basic courses to be permuted on the diet sheet. Pawn promotion is also permissible as a reverse of the win-of-the-queen coin. Perhaps the furthest that other themes may be explored is the avoidance of stalemate, which will frequently be by underpromotion.
The newspaper solver hardly thinks about chess apart from the column he peruses. He is hazy about basic endings like bishop and knight against the lone king. If asked for a normal result when a minor piece is opposed by two, the latter also with a pawn, his answer will lack confidence.
He would like a simple set of rules, something that hangs together and is easily memorised. It is a pity that the labour of gathering together an apt selection of studies and the complete set of rules to apply is so great. Even when this has been done, there is no guarantee that the next study the solver happens to meet will be soluble from the rules he has learnt. Almost inevitably it will not.
This suggests a profitable approach. A trio of examples will illustrate what rules apply, and, just as vital, the method of solving. There is only one. That method is employed by all successful solvers, even if unconsciously. It consists of certain repeated logical steps.
No mystery surrounds these 'rules'. In our sense a rule is a shorthand way of saying that with white force so-and-so against black force such-and-such the result in all normal cases is a win (or draw). Applying such a rule in practice involves the recognition, visually or otherwise, of the presence in the position of the respective forces to which the rule relates. This may happen not only in the diagram, visually, but in the analysis of variations or with colours reversed. If the reader is not familiar with a fair number of these rules he should pay particular attention to this chapter and to its examples. He should also try to devote a little time, preferably not alone but with a devil's advocate opponent, to study of the early chapters of any elementary textbook on the endgame. Much that is in this book, certainly much analysis, can be understood only after considerable practice with these really basic elements has made them almost instinctive. Mastering these short-cut judgments, which is all these rules are, saves an enormous amount of time and energy in woodshifting. To blurt out the truth, studies are insoluble otherwise, unlike problems, where the limitation of solution length lends a totally different flavour — it is either mate at that move number, or it is not. In a problem, analysis beyond the length specified in the stipulation has no conceivable point whatever. There is no such mechanical cut-off mechanism in the study. Instead there has to be this judgment, this acquired sense of when to apply the rules of normal behaviour of the chessmen. On balance, this should encourage the beginner. He is not expected to probe deeply as yet. The hope is that depth will come later, and gradually. Many newspaper solvers are capable of more, if properly coaxed and coached.
4 is a mating study, which is not to say that every line ends in mate. It is fairly typical of the short solution style.
Step One: Examine the material (first without pawns, then with pawns). White has a knight against a pawn, the pairs of rooks on either side cancelling each other out. This is not enough to win in normal situations, for with exchange of one or both pairs of rooks a book draw is obtained. We rely on a book rule which, for further clarity and simplicity, is formulated here as two rules.
Rule 1: Without pawns, the advantage of a minor piece ahead (whatever the other material on the board, provided it is level) draws only. (An advanced player reading this chapter will know that with a larger number of pieces on the board the winning possibilities of a minor piece ahead are greater. The whole is not only more than the sum of the parts, but the bigger the sum the bigger the difference! The newcomer should ignore this, at least on a first reading.)
Rule 2: The advantage of a rook ahead wins.
Step Two: Examine the stipulation.
White has to win. Since, from Rule 1, a draw is normal, we must look for something exceptional. This is the case with all studies, but it is surprising how easily it is forgotten. Also, the exceptional can take many guises. In this position the exceptional can only be mate or win of a rook.
Step Three: Examine the position.
Apart from two things, Black is in a very poor situation, his king being vulnerable (hemmed in on the edge and nearly mated). The two things in his favour are threats (see the next step).
Step Four: What does Black threaten ?
The two threats are to promote the pawn now on f2; and to capture the white rook on b4.
Step Five: Is the position clear enough to list white defences to the threats?
Yes, this is not too difficult. 1. Rb1 fills the bill. If the answer to this question were negative, we should have to search for clues. This will be part of the following example. So, the white rook is played to b1, and we go to Step Six.
Step Six: What does White threaten?
Answer: mate next move, by 2. Ra6. Threats are like the New Testament poor, always with us but only too easily ignored. In studies there is always (except in cases of Zugzwang or blockade) a threat, and our efforts must be directed towards identifying it. A threat is always a move or moves. A general or strategic threat is never enough to solve a study which, unlike a game, is always in a state of crisis.
Step Seven: Choose Black's reply.
It may be that there seems to be no defence of any sort, as a move of the c4 rook to c6 or c7+ is met by capture, after which Rule 2 applies (that is, White wins on material and we need analyse no further) even if there were no mate to follow. In fact, only by moving a rook to b4 can Black create any obstacles in White's way. On b4 a black rook has the relatively subtle effect of removing the white rook on b1's guard of the knight. Thus 2. Ra6+ would now be a blunder since it permits the reply 2. ... K x b5. As there is no obvious reason for choosing one black rook rather than the other, let us take them both and, to be quite impartial, in alphabetical order namely the a-file rook first: 1. ... Rab4. See 4a.
Step Eight: What does Black threaten?
Step Four asked the same question. The solver can now see that the process is a cycle around identifying threats and selecting moves accordingly. It is precisely what computer people call 'an instruction loop'. In other words we have an iterative process. There are, then, only seven distinct steps in solving a study, and it is not too hard to imagine the first three being performed in one visual operation.
Black threatens both 2. ... R×b1 and 2. ... Rf4. The latter move is a threat because of ... Rf7+ to follow. Note, however, that if the white rook on bl moves away, 2. ... R×b5 is not an effective reply because 3. Ral+, Ra4; 4. Ra6+ wins, or 3. ... Kb4; 4. Rb1 +, Kc3; 5. R6 × b5 wins, in each case by Rule 2.
It is at this point that we need a spark. If studies were always plain sailing they would not be a challenge. If White achieves nothing by moving his rook on bl, can he do better by moving something else? In view of the latent black check on c7 only 2. Sd6 really suggests itself.
Step Nine: Repeat steps four to seven as necessary.
This is a separate step purely for convenience of presenting a series of steps. It involves the iterative process and in the course of it making sure both that our analysis is sound and that all variations are accounted for. Seeing the move 2. Sd6 takes us over the hill. We observe that the white rooks are safe from capture due to the inbetween move (often called by its German name 'Zwischenzug') of 3. S×c4+, and the alternative 2. ... Rc7+ is met by 3. Sb7+, R×b7+; 4. R×b7, R×b7+; 5. K×b7 and wins, this line being one move longer than our recommended maximum for the chapter; White has to be careful to avoid here 4. K×b7?, R×b6+; 5. R × b6, f1Q and it is Black who wins. Now, there is no mate in this line, and though neat enough it is hardly very memorable. Let us now go back and play the other black rook on the first move, 1. ... Rcb4, see 4b. We can now see that this looks better for Black, since 2. Sd6 does not attack a rook and hence 2. ... R x b6 would be safe, though not 2. ... R×b1; nor 2. ... f1Q; because of 3. Sb7 mate. This time the spark, shock or jolt is provided by 2. Sd4, with two mating threats, 3. Ra6 and 3. Sc6. But Black has the reply 2. ... R×b6. This covers the mates and gives Black a Rule 2 win, unless the position is an exception. Is it? Yes, it is. 3. Rb5 +!!, R×b5; 4. Sc6, mate! That is the flavour of a mating study. Note, after 1. ... Rcb4; that 2. Sc3? is met by 2. ... f1Q; guarding both b5 and a6 squares.
Precisely the same steps may be applied to J even though this is a study to draw.
Step One: Examine the material.
White has a rook against a bishop. This is a normal draw by Rule 1 as the advantage of the exchange is less than a minor piece.
Step Two: Examine the stipulation.
White is to draw, but as it is a normal draw anyway there must be a catch somewhere.
Step Three: Examine the position.
The catch is clear. Black has a pawn about to queen. With queen and bishop against rook Black would have an enormous material advantage and would win by Rule 2.
Step Four: Black's threats?
Nothing deep here. Black will promote on g1.
Step Five: Is our way clear for White's reply?
No, it is not. 1. Kh3 does nothing about the threat, and 1. Rg3, B × g3 makes things even worse. So, knowing that there is a solution, we hunt for clues. One clue is that, for drawing purposes, White has too much material. He needs only to capture the g2 pawn at any price to settle the result. There do not seem to be any other clues. That the stipulation is a draw suggests a stalemate possibility, but only an experienced solver would suspect stalemate here. A piece of advice — sacrifice! Even if there seems no point, try it and see. 1. Rf4+, B×f4; 2. Kf3, g1Q is a dead end for White, so try 1. Rd3+.
Steps Six and Seven: White's threat and Black's reply.
No trouble about either of these steps. Unless the offer is accepted, White plays 2. Rdl. Therefore 1. ... K×d3.
Step Eight: Black's threat?
As before, to queen his pawn.
Step Nine: White's reply?
Continue with the same logic. 2. Kh3 is no good, as it was no good previously, but 2. Kf3 attacks the black pawn, blocks the white pawn, and invites 2. ... g1Q (or R), which a moment or two's blinking shows to be the stalemate we can now kid ourselves we suspected would be there all along! White's rook sacrifice did three things: got rid of a superfluous piece; enticed the black king onto a desired square (completing the stalemate net forcibly); and vacated a square for the white king. Reasons enough. Why, fascinating question, was it not obvious? Anything else? Yes, what about other black promotions, to knight or bishop? No stalemate then. No, but 2. ... g1S+; 3. Kg2 and White takes one of the black pieces, leaving a draw by Rule 1.2. ... g1B leaves Black with two bishops on the same colour, and no black pawns. This may as well be Rule 3, a draw. Even nine bishops (the legal maximum) cannot mate if they all run on the same diagonals.
6 is a win of the queen. Note that unlike the two preceding examples, the particular idea or 'theme' here may be expressed as either a win or a draw, depending on the position after the queen is captured. In this case it is a win.
Steps One, Two and Three: On material there is a draw only. The position is very open and it is remarkable that a win is given. Could there not be a misprint? No, if only because the alternative stipulation of a draw is absurd, since it is already at least a draw. Of course, if the diagram is mis-printed (it happens!) then this is bad luck. It can be most exasperating, not least to the composer or columnist who is flooded with letters from would-be solvers whose family week-ends have been ruined.
Step Four: Black's threats. Simply a move like 1. ... Qd6, or 1. ... Qa3. Black's position does not look bad (he even threatens to mate if White removes his guard on g7), but his queen is a little hampered, and his king exposed to checks.
Step Five: We can hardly try a sacrifice here, to get us out of our quandary, but there are three checks to be tried: 1. Qh4+, 1. Sh5+ and 1. Sd5+. The first leads nowhere after 1. ... Ke5, and while the second looks promising, if Black is careful he escapes after 1. Sh5+, Ke5 (1. ... Ke7?; 2. Qb4+, Ke8; 3. Sg7+); 2. Qf4+, Kd5 (2. ... Ke6; 3. Qe4+ looks very strong) 3. Sf6+, Ke6 and White is out of steam. Actually, 1. Sd5+, Ke5 does not look much more promising, and one can well imagine a solver spending more time on 1. Sh5+ than on 1. Sd5+. Yet the latter is the first move of the solution.
Steps Six, Seven and Eight: The leap comes on White's second move. The clue is that the two black men, the king and queen, are in a knight-fork relationship, and the only way to threaten this fork is to play 2. Sb6. It is incredible, but we shall now prove that White wins Black's queen in two or three more moves. The queen has fourteen legal squares to go to, yet none is a sanctuary.
(Continues...)
Excerpted from The Chess Endgame Study by A. J. Roycroft. Copyright © 1981 A. J. Roycroft. Excerpted by permission of Dover Publications, Inc..
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