King and pawn endgames are the purest form of chess endings, where technique and understanding often outweigh material considerations. A passed pawn is one with no opposing pawns on its file or adjacent files, and it is the central strategic asset in such endings. Connected passed pawns on adjacent files are mutually defending and often unstoppable, while a protected passed pawn gains additional security from another pawn behind it. The rule of the square determines whether a king can catch a passed pawn: by drawing an imaginary square from the pawn with sides equal to the number of squares to promotion, one can see at a glance whether the defending king can intervene in time. When the king is "out of the square," the pawn promotes.
The concept of opposition is fundamental. Two kings facing each other with one square between them hold the opposition, and the player who holds it gains crucial tempo. In direct opposition, the kings are on the same file, rank, or diagonal with one square between. Distant opposition refers to an odd number of squares between them on the same line, and diagonal opposition specifically describes kings on the same diagonal with one square between. The general principle of opposition control is that whoever takes the opposition first often wins the game. Key squares are specific squares whose occupation by the king ensures the pawn's promotion, and the corresponding squares technique maps out the precise king-pawn relationships needed to control tempo.
Advanced techniques include triangulation, a maneuver where the king moves along three squares to return to its starting position while the opponent is forced to move, thus handing the move back. Shouldering involves using one's king to block the opponent's king. The rule of the king in front of the pawn states that with the king in front and proper opposition, most pawns win; the exception is the rook pawn, where the defender's king can often reach the corner and draw. The Réti maneuver is a famous geometric trick where the king moves along a diagonal, simultaneously chasing the opponent's pawn and supporting its own, and geometry beats mere counting. With the king on the 6th rank and the pawn on the 5th, the position usually wins except in a- and h-pawn cases.