King and pawn versus king endgame

Chess endgame

The chess endgame with a king and a pawn versus a king is one of the most important and fundamental endgames, other than the basic checkmates. It is an important endgame for chess players to master, since most other endgames have the potential of reducing to this type of endgame via exchanges of pieces. Players need to be able to determine 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 ), so checkmate can be forced. In the first paragraph of one of his books on endgames, Peter Griffiths emphasized the importance of this endgame:

There is simply no substitute to a clear understanding of when and how these positions are won or drawn, not only so that one can play them accurately, but in order to recognize in advance what the correct result should be. If you can do that, you can exchange off quite confidently from a more complex position. In the positions in which the pawn wins, at most nineteen moves are required to promote the pawn (with optimal play) and at most nine more moves to checkmate, assuming that the pawn was promoted to a queen. Except for the section on defending and some actual games, it will be assumed that White has a king and pawn and Black has a lone king. In general, Black should place their king in the path of the pawn to try to prevent its promotion.

The most basic rule applies when the pawn can queen unassisted by its king. The rule of the square determines if this is possible. In this position, the pawn is on the fifth square from the queening square (counting the queening square itself). A square of 5×5 squares with the queening square in one corner and the pawn in an adjacent corner can be imagined. (An easy method is to construct the square with a diagonal from the pawn to the last rank.) If the black king can move into this square, he can catch the pawn, otherwise the pawn wins the race. In this position, if it is Black's move, he can move Kb4 and enter the square, catching the pawn. If it is White's move, the pawn advances, the square shrinks to 4×4, and the king cannot move into the square, so the pawn queens. (See Wikibooks – Chess/The Endgame for further discussion on the rule of the square.) Even if the defending king can move inside the square of the pawn, the attacking king may be able to block it, as in the diagram from Fishbein. 1 Ke4
Moving into the square. 2. Kb4 Kd5 3. Kb5! Kd6 4. Kb6! Kd7 5. Kb7! Kd6 6. a5 Kc5 7. a6 Kb5 8. a7
and the pawn promotes. 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 the Réti endgame study (by Richard Réti, 1921), the white king is outside the square of the black pawn, two tempi short of catching the pawn. However, White can draw by "going after two birds at once". 1. Kg7! h4 2. Kf6! Kb6
If 2 h3 then 3. Ke7 or 3. Ke6 and the pawns promote together. 3. Ke5! Kxc6
If 3 h3 then 4. Kd6 h2 5. c7, draw. 4. Kf4, resulting in a draw.

If the defending king is within the "square", then the pawn cannot queen without the help of its own king. The first concept that needs to be introduced is that of the key square, also known as a critical 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 (assuming that the black king cannot capture the pawn). 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. 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.

Pawns other than rook pawns have a much better chance of promoting. If the pawn is on the second, third, or fourth , 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 the diagram on the left. 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, see the diagram in the middle. 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 (see the diagram on the right). An easy way to remember the key squares is to note that if the pawn is not beyond the midpoint of the board, there are three key squares that are two ranks ahead. If the pawn is on the fifth or sixth rank there are six key squares on the two ranks in front of the pawn. If the pawn is on the seventh rank, the adjoining squares on the seventh and eighth ranks are key squares. 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 the diagram on the right, with the white king on either the square indicated or the square marked by a cross, the position is stalemate if Black is to move. This is sometimes known as the b (or g ) pawn trap. In this position, the best move is 1. Kh6! If
1. Kf6 Kh7
Now if 2. g6+ then 2 Kh8! draws, or
2. Kf7 Kh8
does not work for White because 3. g6?? is stalemate. White must play
3. Kg6 Kg8
getting back to the original position, followed by 4. Kh6. This position and sequence of moves came up in a game between Harry Golombek and Arturo Pomar. It is actually much older, having first appeared in Giambattista Lolli's 1763 book.

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 this diagram, 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).

Conditions (a) and (b) are met in this diagram, if Black is to move. The game could continue
1 Kd6 2. Kf5 Kd7 3. Kf6 Kd8 4. e4 Kd7 5. e5 Ke8 6. Ke6
White takes the opposition. White's king has reached the sixth rank before the pawn; 6. e6?? Kf8 draws. 6 Kd8 7. Kf7
and White wins. There are several other variations, depending on Black's moves.

Now consider defending positions when only one of the conditions of Rule 2 is met, which is not sufficient to win if the defender is able to prevent the attacker from getting a position that meets at least two of the conditions.

If the king is in front of the pawn and neither of the other two conditions is met, the defense is easy. In this diagram, with White to move, Black's king is in front of the pawn, but it is not on its sixth rank and it does not have the opposition. White draws by
1. Kb2
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 their king to take this direct opposition.) Then if the black king steps to the side, White simply maintains the opposition:
1 Kc4 2. Kc2
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 b4 3. Kb2 (next diagram)

Note that 3. Kb1 would lose to 3 Kb3 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 b2 or b3, unless Black advances the pawn again, in which case the king moves between b1 and b2. Black cannot disrupt this without stalemate, for instance 3 b3 4. Kb1 Kc3 5. Kc1 b2+ 6. Kb1 Kb3 stalemate.

In this diagram, the black king is on its sixth rank, but with Black to move it does not have the opposition. If the Black king moves, the white king simply goes to d2 (best) or d1. If the pawn advances to d2, the white king moves to d1, and 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.

In the game Svetozar Gligorić–Bobby Fischer, Yugoslavia 1959, White can get the king in front of the pawn, but he does not have the opposition and is not on the sixth rank. Black must make sure that White does not get the opposition or get the king to the sixth rank:
1 Kb8! Any move by Black to the seventh rank loses because White can take the opposition and reach a key square. (The move 1 Kd8 allows the white king to reach the key square a6.) After 1 Kb8, Black draws by taking the opposition if the white king advances, e. g. 2. Kc5 Kc7! draws or 2. Kb5 Kb7! draws.

This position from Gata Kamsky–Vladimir Kramnik, Nice 2009, was reached after the exchange of rooks in a rook and pawn versus rook endgame. Black draws easily:

125 Ke7
Ke8 also draws. 126. Kd5 Ke8 127. Kd6 Kd8
Taking the opposition. 128. e7+ Ke8 129. Ke6 stalemate.