| The definition of a key square is as follows: |
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If the attacking king is on a key square, the attacker wins.
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| The definition does not mention the location of the defending king. This is because the defending king may be anywhere on the board—the attacker still wins. |
| Also the definition does not state who is to play. This is because the attacker will win no matter who is to play—the attacker or the defender. |
| This definition is very common in endgame literature, but there is an important extra requirement often taken for granted: |
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The defender must not have any counter play.
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Some books on the endgame neglect to add this requirement—probably because they consider it to be trivialAs for instance André Chéron writes in one of his books: "... vorausgesetzt natürlich, daß der Bauer sich in Sicherheit befindet", and "natürlich vorausgesetzt, daß dieser [the defending king] ihn [the pawn] nicht nehmen kann", both from "Lehr- und Handbuch der Endspiele, Zweiten Auflage, Band II", André Chéron, 1964, p.23. A more contemporary (20 years later) example is: "If the king of the superior side can enter one of these vital squares, the game is won, unless the opponent can immediately capture the pawn", "Chess Endings, for the practical player", Ludek Pachman, 1983, p.23. Either that, or the occurrences of key squares are drastically reduced, and not consistent with the key squares presented in the literature. . |
| The exact meaning of counter play depends on the kind of endgame the key squares relate to. In king and pawn vs. king endgames it translates to: |
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The defending king must not be able to capture the pawn right away.
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| That is, if the defending player is to move, he must not be able to just capture the pawn. |
| Normally the pawn should not be advanced unless the king can be certain to control a key square. Whenever the pawn is moved the key squares change, and if the pawn is advanced while the defending king prevents the attacking king from gaining control of one of the new key squares, the win is no longer certain. |
| The identification of key squares can be divided in two: is the pawn a rooks pawn or not? The key squares are very different in these two cases. A rooks pawn is considerably more difficult to queen than a non-rooks pawn. First we will examine the case where the pawn is not a rooks pawn. |
| Key squares of a non-rook pawn |
| A non-rooks pawn offers the most variation in key squares. The identification of key squares is divided into two further cases: if the pawn has passed the center line (at least made it to the 5th rank) there are six key squares, otherwise there are only three The number of key squares does not relate to the center line because it is the center line. It relates to the distance of squares from the center line to the queening square. If the board was not 8x8 but 10x10 the number of key squares would depend on whether the pawn had made it to the 7th of the 10 ranks, and not the 6th of the 10 ranks . |
| Pawn on the 7th rank |
| When the pawn is on the 7th rank there is actually one key square less (i.e. one less than the normal six key squares when the pawn has passed the center line), because the pawn is standing on one of the key squares—if the king could be on e7 along with the pawn, it would control the queening square as well. |
| A pawn on the 7th rank only needs the promoting square to be covered by the king. If the king is positioned in front of the pawn, a defending king is unable to prevent the attacking king from moving to the (opposite) side and queen the pawn. Notice how none of the key squares leaves any possible counter play for the defender. |
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| Pawn on the 6th rank |
| If the pawn is on the 6th rank it is the same idea. If the attacking king is not immediately in front of the pawn, the pawn will move forward, and we have a pawn on the 7th rank. The key squares of a pawn on the 7th rank are the same as for a pawn on the 6th rank Apart from the square the pawn would be occupying on the 7th rank. . Consequently if the king was on a key square before the pawn move, then it must also be on a key square after the move, and the queening is secured. |
| Again if the king is on the square immediately in front of the pawn, the defending king will not be able to prevent the attacking king from moving to the (opposite) side (remaining on a key square) and queen the pawn. |
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| Let us examine a position where the attacking king is not on a key square, with a pawn on the 6th rank. |
| Because the white king is not on a key square, the win is not secured—it depends on the circumstances. |
| If white is to move, he cannot queen the pawn: [[1.e7† Ke8 2.Ke6≡]]. Also he cannot take the opposition from black: [[1.Ke5 Ke7]]. Nor [[1.Kd5]] where white tries to use the fact that black cannot play [[FIG:1...Kd7]] to keep the opposition, because the pawn is covering d7. This is because black can return the favor by playing [[1...Ke8]], and now white cannot respond with [[FIG:2.Ke6]], because the pawn is in the way. White cannot win! |
| If black is to move, then white wins even if his king does not control a key square. This is because the black king is in zugzwang. The only move that does not immediately surrender a key square to white is: [[NEW:1...Ke8]], but then [[2.e7 Kf7□ 3.Kd7]], the king is on a key square and the win is secured. White did not have control of a key square, but he could gain control of one due to zugzwang. |
| Reciprocal zugzwang: When both players would prefer the opponent to play (i.e. when both players are in zugzwang). |
| In the starting position of this diagram we have reciprocal zugzwang. Reciprocal zugzwang is also called mutual zugzwang |
| If you find it difficult to remember the reciprocal zugzwang in this position, there is an easy rule to remember: |
| If the pawn reaches the 7th rank without check it queens. If it reaches the 7th rank with check it will not (i.e. it will end in stalemate) |
| There is an exception to this rule: If the attacking king controls the queening square, the pawn will always queen. |
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| Exception: The knight pawn |
| There is an exception regarding the key squares of a knight pawn, when the pawn is on the 6th rank. |
| No matter which of the "key squares" c7 or c8, the white king would occupy, black to play would be stalemate. But if white is to play they still have "key square value", because white in both instances cover the pawns path towards queening: [[1.b7† Ka7□ 2.b8Q]]. The remaining four key squares are without reservations, i.e. they are real key squares. |
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| Let us retract a few moves and see how white could have prevented this from happening. |
| The right plan is to move the white king to the other side of the pawn before it is advanced: [[1.Kc7 Ka8□ 2.Kb6! Kb8□ 3.Ka6 Ka8]] (to prevent [[FIG:4.Ka7]]), but now the pawn can be advanced without stalemate: [[4.b6{@(deco(type:remove), deco(type:zone, squares='a8xb7'))}]], and we have reached the reciprocal zugzwang previously seen [[4...Kb8□ 5.b7{@(deco(type:remove), deco(type:zone, squares='a7, a-c8, c7'))}]], reaching the 7th rank without check, [[5...Kc7□]], and now white can play [[6.Ka7]] and wins. Notice how all the black moves are forced, except one. |
| Black to move loses after: [[NEW:1...Kb8 2.Kb6 Ka8 3.Kc7]], and now there is no stalemate in the corner: [[3...Ka7□ 4.b6†{@(deco(type:remove), deco(type:zone, squares='a8xb7'))} Ka8 5.b7†{@(deco(type:remove), deco(type:zone, squares='a7, a-c8, c7'))} Ka7 6.b8Q†{@(deco(type:remove))} Ka6 7.Qb6‡]]. Or after: [[NEW:1...Ka8 2.b6{@(deco(type:remove), deco(type:zone, squares='a8xb7'))} (2.Kc7 Ka7 3.b6†{@(deco(type:remove), deco(type:zone, squares='a8xb7'))} Ka8 4.b7†{@(deco(type:remove), deco(type:zone, squares='a7, a-c8, c7'))} {etc.}) Kb8□ 3.b7{@(deco(type:remove), deco(type:zone, squares='a7, a-c8, c7'))}]], reaching the 7th rank without check, hence winning. This last variation also shows how white wins if the king was originally on a8. |
| Because of this exception to the rule, we can make the observation: Queening a knight pawn is more difficult than queening a bishop or center pawn—but it can be done! |
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| Pawn on the 5th rank |
| If we move the pawn back to the 5th rank the key squares follow the pawn one square down the board. If the attacking king is on a key square on the 7th rank, the pawn can simply move forward, and we have a situation as described previously with a pawn on the 6th rank. If the king is on a key square on the 6th rank the situation is more complicated. |
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| Let us examine an example where the attacking king is on a key square on the 6th rank. |
| White to play wins after: [[1.e6 Ke8 2.e7 Kf7□ 3.Kd7]] as we have previously seen. If black tries [[1...Kc8]] the white king will move [[2.Ke7]], and it controls a key square of the pawn on the 6th rank, and the win is secured. |
| If black is to play white has the opposition and the white king cannot be denied access to a key square on the 7th rank: [[NEW:1...Ke8 2.Ke6 Kd8 3.Kf7]], and now the white king controls one of the future key squares. |
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| Pawn on the 4th rank |
| If the pawn has not yet made it past the center line it only has three key squares. |
| If white, as in this position, does not control a key square, the win is not secured. |
| If white is to play, black can keep the opposition unless white moves the pawn: [[1.e5 Ke7]], but then white cannot get the opposition either, because black uses the fact that the pawn is in the way. If white does not continue advancing the pawn: [[2.e6 Ke8]] This is the move that black cannot play if the pawn has passed the center line, and why these key squares are not valid, and consequently the number of key squares are reduced from six to three. , black threatens to take the opposition, for instance: [[2.Ke4 Ke6]]. Either way white is not able to secure a key square, because black can either take the opposition himself or prevent white from getting the opposition. |
| If black is to play, white can secure the win. After [[NEW:1...Ke7 2.Ke5]] black cannot continue to cover all three key squares, and when white places his king on any of the key squares and plays e5 the win is secured, because the white king will also be occupying a key square of a pawn on the 5th rank (i.e. the pawn on e5). |
| Importance of the opposition: The opposition plays a crucial role in the struggle for the key squares, and hence for the ability to promote. When the pawn has not passed the center of the board, the attaking king will need the opposition to secure the win |
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| Let’s examine another example with a pawn on the 4th rank. |
| White has the opposition, but black can use the pawn to take the opposition, using the fact that the white king cannot move to b4: [[1...Kb8!]] and white cannot retake the opposition with [[FIG:2.Kb4]] because of the pawn. Any other move and black takes the opposition. |
| Btw. black loses after [[1...Kd8? 2.Kb5 Kc7 3.Ka6 Kb8]], and the black king must go back and forth between a8 and b8, because it cannot permit white to play [[FIG:Ka7]], gaining control of the promotion square. The pawn will reach the 7th rank without check: [[4.b5 Ka8 5.b6 Kb8 6.b7 Kc7 7.Ka7]]. |
| The fact that the pawn is able to reach the 7th rank without check is decisive. If blacks king was on a8 when the pawn moved to b7, it would have been a draw: 6.b7† Kb8□ 7.Kb6≡ . |
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| Let’s examine another example of this strategy: "Either I have the opposition, or I’ll make sure you don’t get it". This time black has the pawn. |
| If black moves the king to the 4th rank, heading for the key squares, white will take the opposition. This makes it easy for white to reach the c-file: [[1.Kd1 Kd5 2.Kc1]]. Blacks distant opposition is gone and the game is drawn. In the actual game black continued a little further: [[2...Ke4 3.Kc2]], taking the diagonal opposition and covering the key squares. The rest is technique: [[3...Kd5 4.Kd3 c4† 5.Kc3 Kc5 6.Kc2 Kd4 7.Kd2 c3† 8.Kc2 Kc4 9.Kc1 Kd3 10. Kd1 c2† 11.Kc1 Kc3≡]]. White continued to either take the opposition or prevent black from getting the opposition. Notice how the pawn reached the 2nd rank with check while black did not control the promotion square. As we have noticed previously, this draws the game. |
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| Pawn on the 3rd rank |
| On the 3rd rank the pawn also has three key squares. |
| In this position the kings are far apart. It will take white four moves to reach any of the three key squares.
Black can reach c5 and d5 in three moves but it will take four moves to reach b5. It would be hopeless for white to reach c5 or d5 before black. |
| Also b5 looks impossible because black can cover b5 in time by reaching c6 in three moves: [[1.Kc2 Ke7 2.Kb3 Kd6 3.Kb4 Kc6]]. But the fact that black must play [[3...Kc6]] to prevent [[FIG:4.Kb5]] makes it possible for white to take the opposition with [[4.Kc4]], and the rest is technique. White advances the king as far as possible: [[4...Kd6 5.Kb5 Kc7 6.Kc5 Kd7 7.Kb6]], before he moves the pawn: [[7...Kd6 8.c4 Kd7 9.c5 Kc8 10.Kc6 Kd8 11.Kb7 Kd7 12.c6†]], and covering both the promotion square and the pawn, the king secures the win. |
| If white had moved around the pawn on the right side, black would have drawn: [[1.Kd2 Ke7 2.Kd3 Kd7]] (distant opposition) [[3.c4 Kc8 4.c5 Kc7]], and black can continue to either have the opposition or use the pawn to prevent white from getting the opposition. This prevents the white king from reaching a key square. |
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| Pawn on the 2nd rank |
| A pawn on the 2nd rank is special, and the key squares are no exception. Basically the same rule applies, as for any pawn that has not passed the center line, it has three key squares. But a pawn on the 2nd rank can choose to act as if it was on the 3rd rank by moving two squares. Because of this we have six key square candidates: |
| The key squares on the 4th rank do not require any further analysis, they rely on the same argument as the key squares of a pawn on the 3rd and 4th rank. But are the squares on the 5th rank really valid? |
| If the attacker (white in the diagram) is to play, the pawn can move to the 3rd rank (i.e. d3) and the alleged key squares on the 5th rank would be the key squares of the pawn after the move. |
| If the white king was on d5, the black king would not be able to cause any problems, because the definition of a key square states that the defending king must not be able to capture the pawn right away. This leaves no room for the black king to be on the c-, d- or e-files below the 7th rank, and the move d3 is perfectly safe to play. And this is the case whether or not it is black or white to play. |
| If the attacking king is not on the same file as the pawn (i.e. it is on c5/e5), it leaves room for the defending king to occupy a key square on either the 4th or the 5th rank. |
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| If the defending king is on the 4th rank–if for instance the white king was on c5 and the black king was on e4. |
| Then [[1.d3† Kxd3=]], loses the pawn. But after [[1.d4]], black has no better than: [[1...Kf5]] The black king cannot continue to threaten the pawn without leaving the square of the pawn (when it advances), hence losing. , as the pawn covers e5, but then: [[2.Kd6]], and the king is on a key square of the d4-pawn. Hence white can force a continuation that wins if he is to play, but what if black is to play? Then [[NEW:1...Kd3]] wins the pawn, and the key square is not valid! |
| If we used an older definition of key squares (i.e. less specific on counter play), that required the defender to have no counter play of any kind, we could accept all three squares on the 5th rank as valid. But according to our contemporary definition only the one in the middle is actually valid. |
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| Let us examine an example where the kings are far apart. |
| Counting moves easily proves that white can reach a key square on the 4th rank, and even though black can take the opposition when it happens: [[1.Kd2 Kd8 2.Ke3 Ke7 3.Ke4 Ke6]], white will be safe. Due to the extra pawn move, white can gain the opposition and push his king forward: [[4.e3 Kf6 5.Kd5]], and white controls a key square of the pawn on the 3rd rank. |
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| "Right away" |
| In the definition of key squares it is stated that the defending player should not be able to capture the pawn right away. This is the most common requirement in modern endgame literature Whether it is stated or not (i.e. considered to trivial to mention). , and it is the definition that has most practical value, giving the key squares that makes most sense. |
| If this requirement was not added (i.e. the requirement of no counter play was removed), we would have to dismiss all the key squares from which the king is not covering the pawn. Consequently a non-rooks pawn would only have key squares when it was at least on the 5th rank, and not before. These key squares would be perfectly okay Some of these key squares might actually not be correct, as their validity in the previous diagrams have been proven based on a less strict definition of a key square. The statement only proves to show that the number of key squares are significantly reduced, which is the point of the discussion. , but adding the simple requirement above, yields far more key squares of practical value–as we have seen in previous examples. |
| Earlier in endgame history For instance [Cheron-2] p.23-24, or [Fine41] p.9. The later having the definition: "The rule is that if the White King is two or more squares in front of his Pawn he always win; if he is one square in front of his Pawn he wins only if he has the opposition". Notice how the last part is not correct—the "he wins only if" part does not apply if the pawn is on the 5th rank or further up the board. the requirement was simply that the defender could not capture the pawn, now or later. This turned a lot of squares into key squares. For instance a pawn on the 2nd rank would have no less than 15 key squares. |
| Again perfectly okay, but it left a more complicated task to the player: when exactly does the defender not have any counter play? In previous examples we have seen the attacker move his king as far as possible ahead of his pawn to gain space for the pawn, and this "as far a possible" was just another way of saying: as long as the defender does not get any counter play (i.e. will not be able to capture the pawn). |
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| b8 is not only a critical square, it is also a key square. |
If the pawn has passed the center line there are two key squares
There is one exception to the two key squares, when the pawn has passed the center of the board. If the defending king can move next to the pawn: [[1...Kb5]], the pawn cannot reach safety, and it is lost.
. If it is further down the board (i.e. on the 2nd-4th rank) there are no key squares!If we use the older definition of a key square and exclude all counter play, and not just the immediate capture of the pawn, the key squares apply to a pawn on any rank. Endgame literature usually presents the two key squares without any reservations. |
| Not only does a king on the key squares cover the promoting square, but it also prevents the defending king from occupying the corner (i.e. it covers a8 and b8 against the defending king). |
| The two key squares are also critical squares for the defending king, We have already established b8 as a critical square, and b7 secures the defenders access to b8, while it does not leave room for the pawn to queen. |
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| Why are a7 and a8 not key squares? Because the defender has a special way of drawing that only applies to a rooks pawn. |
| Black to play not only draws by taking the opposition: [[1...Kc5]], preventing white from ever reaching a key square: [[2.Ka6□ Kc6]], but white has an additional problem, he is imprisoned in front of the pawn, and blocking his own pawn from queening. The only way he can escape is to advance the pawn: [[3.a5]], or black will continue to have the opposition, but then: [[3...Kc7]], but this only makes matters worse, when it comes to the key squares. By gaining control of c7 black will be able to move perpetually between c7 and c8, and white will never control a key square. When the king is on c8 white could play [[FIG:Kb6]] to prevent [[FIG:Kc7]], but then the defending king moves to b8, and the draw is even more obvious. |
| White to play wins after [[NEW:1.Kb6]], and black cannot intervene. White does not even have to control a key square, as the pawn will run to safety: [[1...Kc4 2.a5]] [[2.Kb7]], controlling a future key square of the a-pawn will give black counter play: [[2...Kb4]], and the pawn is lost: [[3.a5 Kxa5]]. As always the key squares are only valid if the defending king cannot capture the pawn right away. After [[3.a5]] white controls a key square, but it is not valid, because the defending king can capture the pawn right away! etc. |
| If the defending king occupies either c7 or c8 he will cover both key squares, but are c7 and c8 critical squares? If the pawn does not need the support of its king they are not. If the pawn is on a7, and the attacker is to move, the defending king will be outside the pawns square and the pawn queens. If the defender is to move, c7 is always a critical square, but c8 is not a critical square unless the attacking king is not on a6/b6 preventing black from playing [[FIG:Kb7]]. |
| These exceptions are noticeable but not very interesting, as they only occur if the defending king was never able to enter the square of the pawn in the first place. |
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| Let us examine another race for the key squares. |
| Both kings are three moves away from controlling the positionThe white king must reach g7, and black must reach f8., and it comes down to who has to play. |
| In the game it was black to play: [[1...Kd8 2.Kh5 Ke8 3.Kg6 Kf8]], and now white will not control a key square: [[4.Kh7 Kf7 5.h4 Kf8]] (½-½). |
| White to move wins: [[NEW:1.Kg5 Kd8 2.Kf6 Ke8 3.Kg7]], and white controls a key square of the pawn when it advances to h5, and black cannot capture the pawn. In this variation white moved in "a shouldering way", which should be second nature to any player in pawn endings, but here it was not required—going up the h-file and then [[FIG:Kg7]] would be sufficient. |
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[Silman07] 107Silman uses the opposite rook file, and has a pawn on h5 (as an example).
| We have previously established that b7 and b8 are critical squares for the defending king, and c7 and c8 are almost critical squares, with some (trivial) exceptions. Are there any more critical squares? |
| All the squares on the a-file are also critical squares for the defending king (as long as they are in front of the pawn, obviously). This is quite easy to see, as the attacking king will not be able to both defend the pawn and prevent the defending king from reaching the corner. |
| The defender has many critical squares, but the attacker has only two key squares. All in all, the attacker faces a difficult task of queening the pawn. |
| We already have two critical squares with some exceptions, and we could add more, but they would have even more exceptions. And strictly speaking, if a critical square has exceptions it is not truly a critical square. |
| Taking the liberty to include c7 and c8, we have the critical squares in this diagram. |
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