Pawn endgame
King and Pawn vs King
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King and pawn versus king is small enough to learn exactly and rich enough to expose loose rules. Key squares describe where the stronger king can guarantee promotion in the relevant set-up. Their location changes as the pawn advances, rook’s pawns have separate geometry, and the side to move can decide whether the king reaches them.
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Key squares
For a non-rook’s pawn on its second, third or fourth rank, start with the three squares two ranks ahead: the square on the pawn’s file and its two neighbours. Once the pawn reaches its fifth rank, the nearest key squares are only one rank ahead. Thus a white pawn on e5 has d6, e6 and f6 as key squares. In the diagram White’s king is already on e6, and Syzygy gives a win with either side to move. That does not mean “two ranks in front” is a universal formula.
The opposition decides the rest
When the king has not reached a key square, opposition can force the defending king to yield an entry square. In direct opposition, with the kings facing and one square between them, the side to move must step aside; whether that is good depends on the pawns and available side squares. A pawn move may transfer the move, but spending it too early can remove the only reserve tempo.
The rule of the square
If the kings are far apart, you do not need to calculate — use the rule of the square. Picture the square whose side runs from the pawn to its promotion square: if the defending king is inside it (or can step inside on its move), it catches the pawn; if not, the pawn promotes untouched.
The rook-pawn exception
A pawn on the a- or h-file has no key square on the outside of the board. If the defending king reaches the promotion corner in the basic king-and-pawn ending, the stronger king often cannot dislodge it without stalemate. Do not transfer the three-key-square rule from a central pawn to a rook’s pawn; check whether the defending king can reach the corner and whether the attacking king can exclude it in time.