King and pawn versus king

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This article uses algebraic notation to describe chess moves.

The chess endgame with a king and a pawn versus a king is the most important and fundamental endgame, other than the basic checkmates. It is important to master this endgame, since most other endgames have the potential of reducing to this type of endgame via exchanges of pieces. It is important to be able to tell quickly whether a given position is a win or a draw, and to know the technique for playing it. The crux of this endgame is whether or not the pawn can be promoted or queened, so checkmate can be forced.

In the positions in which the pawn wins, at most nineteen moves are required to promote the pawn (with perfect play) and at most nine more moves to checkmate, assuming that the pawn was promoted to a queen (Levy and Newborn 1991:144).

In all of this discussion, it will be assumed that White has a king and pawn and Black has a lone king. In general, Black should place his king in the path of the pawn to try to prevent its promotion.

Contents 1 Rule of the square 2 Key squares 2.1 Rook pawn 2.2 Other pawns 3 Opposition 4 Rules 4.1 Case 1, conditions (b) and (c) are met 4.2 Case 2, conditions (a) and (c) are met 4.3 Case 3, conditions (a) and (b) are met 5 Defending 5.1 Application 6 See also 7 References 8 Further reading 9 External links

[edit] Rule of the square

The first thing to realize is that the pawn may be able to queen unassisted by his king, simply by advancing to the queening square before the opposing king can capture or block the pawn. The rule of the square is useful in determining whether the pawn can queen unassisted, or whether the king can stop the pawn. In this position, the pawn is on the fifth square from the queening square (counting the queening square itself). A square of five by five squares with the queening square in one corner and the pawn in the other corner can be imagined. (Often, the easiest method of constructing the square is to draw a diagonal mentally from the pawn to the queening square; this is the diagonal of the square). If the black king can move into this square, he can stop the pawn, otherwise the pawn wins the race. In this position, if it is Black's move, he can move to b4 and enter the square, therefore he can stop the pawn. If it is White's move, the pawn advances, the square shrinks to four by four, and the king cannot move into the square, so the pawn queens (Müller and Lamprecht 2000:15). See Wikibooks - Chess/The Endgame for further discussion on the rule of the square.

Note that in some cases, the king can catch a pawn when he is outside the square by creating threats that must be parried, and gain a tempo. In this study (diagram 2) by Richard Réti, the white king is outside two tempi short of catching the black pawn. However, White can draw by "going after two birds at once". (Also see endgame study.)

• 1. Kg7 h4
• 2. Kf6 Kb6

If Black moves 2. ... h3 then 3. Ke7 and White supports his own pawn, and they queen together, resulting in a draw.

• 3. Ke5 Kxc6

If 3. ... h3 4. Kd6 h2 5. c7, draw.

• 4. Kf4, and the white king can stop the black pawn (Dvoretsky 2003:35).

[edit] Key squares

If the defending king is within the square, then the pawn can't queen without the help of its own king. The first concept that needs to introduced is that of the key square. A key square is a square such that if White's king occupies it, White can force the pawn to promotion, regardless of where the black king is and regardless of which side is to move, and against any defense. The key squares are relative to the position of the pawn. Whether or not the white king can reach a key square depends on the position of the pieces. Of course, even if the white king occupies a key square, accurate play is still required in order to promote the pawn (Müller and Lamprecht 2000:20-22).

Note that the key square is in front of the pawn. Endgame expert Yuri Averbakh said, just as a father leads his child across the road rather than pushing the child in front, the king should also lead the pawn to the queening square.

[edit] Rook pawn

A rook pawn (on the a-file or h-file) has much less chance of promoting than other pawns. The reason is that if the opposing king can get to any square in front of the pawn, it can't be driven away from the file, and the pawn can't queen. Black can always draw if he can reach the c8 square for an a-pawn (pawn on the a file) or the equivalent f8 for an h-pawn, except for the position in Diagram 4, with White to move. Therefore, an advanced rook pawn generally has two key squares: b7 and b8 for an a-pawn, and g7 and g8 for an h-pawn. The key squares are indicated by the black dots in the position in Diagram 3:

If White's king can reach either of the two key squares, he can keep Black's king away and the pawn will promote. If the Black king can reach any of the squares marked with a dot or an "X", it stops the pawn (Silman 2007:105-6).

The pawn can also promote in the position in Diagram 4 (if White is to move), after

1. h7

However, in practice most of the time the black king can stop a rook pawn because it is usually close enough that the white king can't prevent it from getting in front of the pawn (or capturing it).

[edit] Other pawns

Pawns other than rook pawns have a much better chance of promoting. If the pawn is on the second, third, or fourth rank, there are three key squares - the square two squares in front of the pawn and the squares to the left and right of that square. The key squares are indicated by the black dots, for example see Diagram 5:

If the pawn is on the fifth or sixth rank, there are six key squares: the square in front of the pawn and the squares to the left and right, as well as the square two squares in front of the pawn, and the squares to the left and right of it, diagram 6 for example:

When the pawn is on the seventh rank, the key squares are the squares on the seventh and eighth rank that touch the pawn's square (Diagram 7):

Once White's king occupies a key square he can keep the opposing king from blocking the advance of the pawn, as will be shown below.

There is an exception to the key squares rule with a knight pawn, the black king in the corner, and Black to move. In Diagram 8, with the white king on either the square indicated or the square marked by "x", the position is stalemate if Black is to move.

It is important to emphasize that White wins if he gets his king to any key square, and the path to a key square is not always direct. For instance, in Diagram 9, the key squares for White are b5, c5, and d5. However, Black can prevent the white king from reaching a key square directly, e.g.:

1. Kd2 Ke7

2. Kd3 Kd7

3. Kc4 Kc6 (taking the opposition, see below).

However the white king can reach a key square (b5) by going on the other side of the pawn:

1. Kc2! Ke7

2. Kb3 Kd6

3. Kb4 Kc6

4. Kc4 (opposition) Kd6

5. Kb5

or

4... Kb6

5. Kd5

and the white king has occupied a key square and has a winning position.

[edit] Opposition

Main article: opposition

The second concept needed is opposition — when two kings face each other with only one square in between, the side with the move may have to move the king away and allow the opposing king to advance. The other king has the opposition.

However, Averbakh pointed out that the opposition is a means to an end; the end is penetration to a key square. If you can penetrate without the opposition, then do so. In diagram 10, White should seize a key square by playing:

• 1. Kc5

and moving to a key square on the next move (e.g. 1... Kd7 2. Kb6). Taking the opposition by 1. Ke4 draws (as do any other moves).

[edit] Rules

Here are some rules that apply:

Rule 1: With one exception, if the black king can get to the square in front of the pawn or the square in front of that (which are key squares), he draws. The exception is the position in Diagram 11, and only if White is to move because of

1. d7 Ke7

2. Kc7,

followed by

3. d8Q.

Otherwise, if the black king stays on one of those two squares, he keeps the white king from occupying a key square.

Rule 2: White wins if at least any two of the following conditions are met:

• (a) his king is in front of the pawn
• (b) he has the opposition
• (c) his king is on the sixth rank. (Müller and Lamprecht 2000:21)

There are three cases to be considered.

[edit] Case 1, conditions (b) and (c) are met

Conditions (b) and (c) are met in Diagram 12, if it is Black's move.

1... Kd8

2.d7 Kc7

3. Ke7 (a key square)

followed by

4. d8Q,

and White wins. This position illustrates an important rule of thumb: If the White king is on its sixth rank, the pawn must be advanced to the seventh rank without giving check. (If White's king is on the sixth rank and the pawn checks the Black king when it advances to the seventh rank, the black king can move in front of the pawn, resulting in a draw. White has to either give up the pawn or move the king behind the pawn into stalemate.)

[edit] Case 2, conditions (a) and (c) are met

Conditions (a) and (c) are met in Diagram 13, with either side to move.

If it is Black's move in Diagram 13, the game could go

1... Kd8

2. Ke6 Ke8

3. d6 Kd8

4.d7

and White wins because the pawn advanced to the seventh rank without giving check, as in the position in Diagram 12.

If it is Whites move in Diagram 13,

1. Kc7 (a key square)

and Black cannot prevent the pawn from queening.

[edit] Case 3, conditions (a) and (b) are met

Conditions (a) and (b) are met in Diagram 14, with Black to move

The game could continue

1... Ke6

2. Kc5 Kd7

3. Kd5 (a key square)

taking the opposition

3. ... Ke8

4. Ke6 Kd8

White takes the opposition. White's king has reached the sixth rank before the pawn, now the pawn can advance.

5. d4 Ke8

6. d5 Kd8

7. Kd6

and White wins as above. There are several other variations, depending on Black's moves.

In any of these three cases, the white king is able to force his way onto a key square and thus reach a winning position. Accurate play from that position is still needed to win the game.

In positions in which at least two of the conditions are not met, it may or may not be possible to get to a position meeting at least two of the conditions, depending on the position of the pieces and who is to move. Recall that rule 1 above gives a condition which draws for Black.

[edit] Defending

Now let's look at defending this position when only one of the conditions of Rule 2 is met.

(a) the king is in front of the pawn

If the king is in front of the pawn and neither of the other two conditions is met, the defense is easy.

In Diagram 15, with White to move, Black's king is in front of the pawn, but it isn't on its sixth rank and it doesn't have the opposition. White draws by

1. Kd2

taking the opposition and preventing the black king from getting the opposition or advancing to its sixth rank. (Indeed, this is the only move that draws. Sometimes this position is reached after Black has captured a pawn. To draw, White must be in a position to move his king to take this direct opposition.) Then if the black king steps to the side, White simply maintains the opposition:

1. ... Ke4

2. Ke2.

If the pawn now advances, White gets to a drawn position by moving in front of the pawn. (Recall that if the opposing king is on the square in front of the pawn or the square in front of that, the position is a draw, with one exception.)

2. ... d4

3. Kd2, see Diagram 16.

Note that 3. Kd1 would lose to 3. ... Kd3 because Black now has satisfied all three conditions of rule 2.

Black to move cannot make any progress from this position, the white king simply stays on d2 or d3.

(b) the king has the opposition

In Diagram 17, with White to move Black's king has the opposition, but neither of the other conditions. White to move simply moves

1. Kd2

and black cannot promote the pawn, for example:

1. .. d3

2. Kd1 (Note, the defending king must drop back vertically) Ke3

3. Ke1 d2+

4. Kd1

and now either the king must move away from the pawn and allow it to be captured or move 4. ...Kd3 resulting in a draw by stalemate.

(c) the king is on the sixth rank

In Diagram 18 the black king is on its sixth rank, but with Black to move it doesn't have the opposition. If the Black king moves, the white king simply goes to d2 (best) or d1. If the pawn advances, a draw results as above.

A player should be familiar with both the attacking and defending roles, since a wrong move by the defender may allow the attacker to get to a winning position and a wrong move by the attacker may give up one of the conditions of rule 2, resulting in a draw.

[edit] Application

In diagram 19, if White is to move, then the only move to draw is 1. Kb1! Then White can take the opposition which ever way the Black king advances:

1...Kb4 2. Kb2 or

1....Kc4 2. Kc2.

Any other move allows Black to reach the key square, sometimes via the opposition:

1. Kd1 or 1. Kd2 then K-b4-a3 reaching the key square without needing the opposition.

1. Kb2 Kb4 or 1. Kc2 Kc4, in both cases giving Black the opposition.

[edit] See also

• Endgame
• Zugzwang
• Opposition (chess)
• Triangulation (chess)
• Corresponding squares

[edit] References

•   Dvoretsky, Mark (2003). Dvoretsky's Endgame Manual. Russell Enterprises. ISBN 1-888690-19-4. 

•   David Levy and Monty Newborn (1991). How Computers Play Chess. Computer Science Press. ISBN 0-7167-8121-2. 

•   Karsten Müller and Frank Lamprecht (2000). Secrets of Pawn Endings. Everyman Chess. ISBN 1-85744-255-5. 

• Silman, Jeremy (2007), Silman's Complete Endgame Course: From Beginner to Master, Siles Press, ISBN 1-890085-10-3

[edit] Further reading

•   Yuri Averbakh (1966, 1993). Chess Endings: Essential Knowledge. Everyman Chess. ISBN 1-85744-022-6. 

•   Reuben Fine and Pal Benko (1941, 2003). Basic Chess Endings. McKay. ISBN 0-8129-3493-8. 

•  Glenn Flear (2004). Starting Out: Pawn Endings. Everyman Chess. ISBN 1-85744-362-4. 

•   Karsten Müller and Frank Lamprecht (2001). Fundamental Chess Endings. Gambit Publications. ISBN 1-901983-53-6. 

[edit] External links

• King and pawn versus king

• About chess