Rule of the square

The rule of the square quickly shows whether the defending king can catch a pawn running alone toward promotion, when it reaches the last rank and becomes another piece. First imagine the square of the pawn, whose side length reflects the number of pawn moves remaining.

King inside or entering

On the square's boundary

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From c4 the pawn needs four moves to promote.

Four moves to promotion

From c4 the pawn needs four moves to promote. The square has corners c4, c8, g8, and g4, with the black king exactly on g4 at its boundary. The white king is far from the race.

1. From c4 the pawn needs four moves to promote.

If the defending king is already inside the square, it can normally catch the pawn. If it is the king's turn and the king can enter the square immediately, it also arrives in time. If the pawn's side moves first, the pawn advances and the square shrinks before the king approaches. The side to move can therefore decide the race.

The square shrinks

One move changes the boundary

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Start

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The pawn is on c2 and White is to move.

The pawn can still move two squares

The pawn is on c2 and White is to move. The calculation must account for c2-c4 being available as a single move.

1. The pawn is on c2 and White is to move.

The rule assumes a simple contest: an unsupported pawn, a clear path, and no checks or obstacles that alter the timing. An attacking king may block the defender's route, and other pieces can change the result. Treat the rule as a fast first test, not a complete evaluation of every endgame.

Altered conditions

Geometry is not enough

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From c5, three pawn moves remain, placing f5 on the square's boundary.

The entry square is controlled

From c5, three pawn moves remain, placing f5 on the square's boundary. The black king is on g5, but f5 is controlled by the white king on e5, so that geometric entry is not a legal square for the defender.

1. From c5, three pawn moves remain, placing f5 on the square's boundary.