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  Key Squares

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

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

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

  1 Ka6! Ka8 2 b6 Kb8 3 b7+–

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

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

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

  J. Moravec, 1952

  1 Kf2!

  On 1 Kg1? Kd7, Black’s king successfully defends the pawn, whereas now, it is too late: 1…Kd7 2 Kg3 Ke6 3 Kh4+–.

  1…h4! 2 Kg1!!

  The natural 2 Kf3? is refuted by 2…h3! If the pawn is taken, Black’s king heads for h8. And if 3 g4, White cannot gain control of the key squares on the sixth rank: 3…Kd7 4 Kg3 Ke6 5 K×h3 Kf6 6 Kh4 Kg6.

  2…h3 3 g3!

  The key squares for a pawn on g3 are on the fifth rank – closer to White’s king.

  3…Kd7 4 Kh2 Ke6 5 K×h3 Kf5 6 Kh4 Kg6 7 Kg4+–.

  Tragicomedies

  Coull – Stanciu

  Saloniki ol 1988

  The lady playing White, Scotland’s Board One, saw that she must lose the d5-pawn, and therefore resigned. What can I say, except: No comment needed!

  Spielmann – Duras

  Karlsbad 1907

  1 Rf4?? Kg5! White resigned.

  Corresponding Squares

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

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

  Opposition

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

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

  Return to Diagram 1-1, where we see the simplest case of the opposition (close, vertical). With White to move, there is no win: 1 Kc5 Kc7; or 1 Ke5 Ke7. Black to move loses, because he must allow the enemy king onto one of the key squares: 1…Kc7 2 Ke6; or 1…Ke7 2 Kc6.

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

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

  1…Kc7!

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

  2 Ka6

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

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

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

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

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

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

  H. Neustadtl, 1890

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

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

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

  H. Mattison, 1918*

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

  1 g6! fg 2 f5!

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

  2…gf 3 Kg1

  Black controls the distant opposition, but he cannot convert it into the close opposition. The problem is that after 2…Kg5 3 Kf1, outflanking with 3…Kh4 has no point; and on 3…Kf4 (g4), it is White who takes the close opposition by 4 Kf2 (g2), and Black’s king cannot use the f5-square as it is blocked by its own pawn. If the king and the pawn could both occupy this square simultaneously, then on the next move the outflanking would be decisive; unfortunately, the rules of chess do not allow such a thing.

  J. Drtina, 1907

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

  In such situations there is usually a “major” line, in which is it vitally important to capture the opposition. And when the enemy king retreats from it, you must outflank it. In this instance, that would be the f-file.

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

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

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

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

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

  F. Sackmann, 1913

  The first thing White must do is seize the opposition.

  1 Kf5! Kb6

  Black’s king must be the first one on the sixth rank. If it had been on a7 in the starting position, then 1…Kb7! would lead to a draw, since White could no longer seize the opposition: 2 Ke6 Ka6!=; or 2 Kf6 Kb6!=.

  2
Kf6!

  The rest is the standard technique of converting the distant opposition into the close opposition. Here, the “major line” is the seventh rank.

  2…Kb7 3 Kf7! (3 Ke5? Ka7!=) 3…Kb6 (3…Kb8 4 Ke6!) 4 Ke8! (outflanking!) 4…Ka7 5 Ke7! Ka8 6 Kd6! Kb7 7 Kd7! Kb6 8 Kc8+– (the final, decisive outflanking).

  Instead of the easily winning 7 Kd7!, White might also play 7 K×c5?! Kc7 8 Kb4 Kb6 9 c5+! (9 K×a4? c5 10 Kb3 Ka5 11 Kc3 Ka4 12 Kb2 Ka5 13 Kb3 Kb6 14 Kc3 Ka5=) 9…Ka6 10 K×a4.

  George Walker analyzed a similar position as far back as 1841. We shall return to it in our next section – mined squares.

  Tragicomedies

  Yates – Tartakower

  Bad Homburg 1927

  Black has a won position. 1…ab is possible; 1…Qc3!? 2 R×b5+ (2 Ka2 Qc2+; 2 ba Q×a3) 2…Kc6 3 ba Q×a3 is also strong. Tartakower, however, decided to transpose into a pawn ending, which he thought was won.

  1…Q×b4?? 2 ab ab 3 Kb2 Kc4 4 Ka3! b2 (4…Kc3 is stalemate) 5 Ka2!

  Black had missed this move when he traded off his queen. He had hoped to win the b4-pawn and seize the opposition, but miscalculated. After 5…Kc3 6 Kb1 K×b4 7 K×b2, the draw is obvious.

  Yusupov – Ljubojevic

  Linares 1992

  White’s rook is tied to the defense of the pawn at g3. Black would have won easily if he had transferred his rook by 1…Ra3! (to prevent the white king from approaching the pawns: 2 Ke4 f5+! and 3…Kf6 wins), followed by …Kf6-g7 and …f7-f6 (or …f7-f5).

  Instead, Black played 1…Rf5?? 2 Ke4! R×g5 3 hg

  White has the opposition, but Ljubojevic had counted on 3…f6 4 gf K×f6 5 Kf4 g5+

  Yusupov replied 6 Kf3!, and it became clear that the opposition on the f-file would give Black nothing, since 6…Kf5 is met by 7 g4+! hg+ 8 Kg3=. And as soon as Black’s king goes to the e-file, White’s king immediately takes the opposition.

  6…Kf7 7 Kf2! Ke6 8 Ke2! Kd6 9 Kd2 Kc5 10 Ke3! Draw.

  Exercises

  Mate Black with just one [mating] move by the rook.

  Mined Squares

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

  Here are two quite typical examples of mined squares.

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

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

  1 Kf6! Kb5

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

  2 Ke7! Kc5 3 Ke6!+–

  Black to move plays 1…Kb5! White, however, is better off than his opponent in that the loss of a pawn does not mean the loss of the game: he replies 2 Ke4 (but not 2 Kf6? Kc4! 3 Ke6 Kc5–+) 2…Kc4 3 Ke3 K×d5 4 Kd3, with a draw.

  And now, let’s return to a position we reached while analyzing F. Sackmann’s study (Diagram 1-11).

  The only winning try is to get the king to the d6-square. To keep the opponent from counterattacking successfully on the queenside, it is important to begin the march with the black king as far away as possible. This consideration shows us the first pair of corresponding squares: a6 and b4.

  1…Kb7 2 Kb3! Ka6 3 Kb4! Kb7

  Now it is time to consider further action. Note the reciprocal zugzwang with the kings at d4 and b5; that means the d4-square is mined, and must be circumvented.

  4 Kc4 Ka6 5 Kd3!! Ka5 6 Ke4 Kb5 7 Kd4 (and Black is in zugzwang) 7…Ka4 8 Ke5 K×a3 9 Kd6+–.

  Alekhine – Yates

  Hamburg 1910

  A mistake would be 1 Kd4? Ke6; thus, the d4- and e6-squares are mined. And 1 Kb4? Ke6 2 K×b5 K×e5 3 K×a4 Ke4 4 b4 K×e3 leads to a queen-and-rook-pawn vs. queen endgame, which is, according to theory, drawn.

  1 Kd3 Kd7 (1…Ke6? 2 Kd4+–) 2 e4! f4 3 Ke2 Ke6 4 Kf2!!, and Black resigned. With a white pawn at e4 and a black one at f4, we already know the squares f3 and e5 are mined. White’s king avoided entering the f3-square first, while his opposite number had no similar waiting move, since the e5-pawn was in the way.

  Incidentally, White’s moves could also have been transposed: 1 e4 f4 2 Kd3 Ke6 3 Ke2! (3 Kd4?! Ke7).

  Tragicomedies

  Kobese – Tu Hoang Thai

  Yerevan ol 1996

  The position is drawn. White sets a last trap, which unexpectedly succeeds.

  1 Bd1+!? Kh4??

  1… Kg6! was necessary, 2…h5 and 3…g4=.

  2 Bg4 h5 3 Kf5! hg 4 hg and Black resigned.

  It is worth noting that 1 Bf5!? must be met not with 1…Kh4?? 2 Bg4+–, but with 1…g4! 2 B×g4+ (2 hg+ Kg5 3…h5=) 2… Kg6, with a draw (doubters are referred to the beginning of Chapter 4).

  Exercises

  The next pair of exercises are rather difficult. In each, you must judge whether Black ought to go into the pawn endgame.

  Triangulation

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

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

  1 Ke5!

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

  1…Kc6 (1…Ke7 2 c6) 2 Kd4 Kd7 3 Kd5

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

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

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

  Fahrni – Alapin

  1912

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

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

  Along with d5 and c5, White has two equally important squares: c4 and d4; while Black has, adjoining the corresponding squares c7 and c8, only one square: d8 (or b8). With Black’s king on d8, White makes a waiting move with his king, from c4 to d4 (or the reverse). Black’s king will be forced onto c7 or c8, when White occupies the corresponding square and wins.

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

  H. Neustadtl, 1898

  Find two winning plans

  The author’s solution to this study involves the opposition, which White seizes with his very first move.

  1 Kd4 Kc6 2 Kc4 (2 g5? fg!= does not work) 2…Kd6 3 Kb5!

  The opposition can only win if it leads to an outflanking. Here the outflanking looks risky, but it turns out to be playable because of the line 3…Ke5 4 Kc6 Kf4 (4…h5 5 gh K×f5 6 Kd5) 5 Kd6 K×g4 6 Ke6+–.

  3…Kd5! 4 Kb6!

  White takes the opposition again, thanks to his reserve tempo, h4-h5. But first, the enemy king must be decoyed to a bad position – as far as possible from the g4-pawn.

  4…Kd6 5 Kb7 Kd7 6 h5! Kd6 7 Kc8 (another outflanking) 7…Ke5 8 Kd7 Kf4 9 Ke6+–.

  In 1968, during a session of training in the calculation of variations (I find pawn endings quite useful
for this), I discovered a second solution to this study, based on completely different logic.

  The d5-square is key here (with White’s king at d5, and Black’s at d7, White wins by h4-h5). By the way, with the pawn already on h5, occupying the d5-square is no longer decisive: the key squares are now on the sixth rank – c6, d6 and e6. Which leads us to an important conclusion: when the pawn structure changes, the system of key squares associated with the position generally changes too, just as with the system of corresponding squares.

  With White’s king at f4, Black must deal with the threat of g4-g5. It can be parried by putting the black king at e7 (but not f7, since then White will occupy the key square d5) – which immediately gives us two pairs of corresponding squares: f4-e7 and e4-d6. Next to these, White has two equivalent squares: f3 and e3. Black, meanwhile, has only one – d7. Thus, the winning mechanism becomes clear – triangulation!

  1 Kf4

  1 Kf3 – but not 1 Ke3? Ke5! 2 Kf3 h5 3 Kg3 Ke4.

  1…Ke7 2 Kf3 Kd7 3 Ke3! Kd6

  3…Ke7 4 Kf4! Kf7 5 Ke4 Ke7 6 Kd5 Kd7 7 h5+–.

  4 Ke4! Kc6 5 Kf4 Kd6 6 g5+–.

  Tragicomedies

  Yudasin – Osnos

  Leningrad 1987

  With his last move (1 Ke2-f2), Yudasin offered a draw, adding that this position was a well-known draw, which one might find in any book. His opponent, an international master and an experienced trainer (he trained Viktor Korchnoi for many years) believed him, and accepted his offer!