King and Pawn Versus King Endgame - Rule of The Square

Rule of The Square

	a	b	c	d	e	f	g	h
8									8
7									7
6									6
5									5
4									4
3									3
2									2
1									1
	a	b	c	d	e	f	g	h

Rule of the square

The first thing to realize is that the pawn may be able to queen unassisted by his king, simply by advancing to the queening square before the opposing king can capture or block the pawn. The rule of the square is useful in determining whether the pawn can queen unassisted, or whether the king can stop the pawn. In this position, the pawn is on the fifth square from the queening square (counting the queening square itself). A square of five by five squares with the queening square in one corner and the pawn in an adjacent corner can be imagined. (Often, the easiest method of constructing the square is to draw a diagonal mentally from the pawn to the last rank; this is the diagonal of the square). If the black king can move into this square, he can stop the pawn, otherwise the pawn wins the race. In this position, if it is Black's move, he can move to b4 and enter the square, therefore he can stop the pawn. If it is White's move, the pawn advances, the square shrinks to four by four, and the king cannot move into the square, so the pawn queens (Müller & Lamprecht 2007:15). See Wikibooks - Chess/The Endgame for further discussion on the rule of the square.

From Fishbein

	a	b	c	d	e	f	g	h
8									8
7									7
6									6
5									5
4									4
3									3
2									2
1									1
	a	b	c	d	e	f	g	h

Black to move. Black can move inside the square of the pawn, but the white king can block it.

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 (Fishbein 1993:2).

Study by Richard Réti, 1921

	a	b	c	d	e	f	g	h
8									8
7									7
6									6
5									5
4									4
3									3
2									2
1									1
	a	b	c	d	e	f	g	h

White to move draws

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 Black moves 2. ... h3 then 3. Ke7 and White supports his own pawn, and they queen together, resulting in a draw.

3. Ke5 Kxc6

If 3. ... h3 4. Kd6 h2 5. c7, draw.

4. Kf4, and the white king can stop the black pawn (Dvoretsky 2006:26).