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.
Rule of the square
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.
Key squares
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.