Pawn Endgames

start position

White to play and win.

This puzzle by Lasker first appeared in the Chigago Tribune in 1901.

In order to truly understand how to win, we must first find the key squares that white's king must reach in order to win the game.

b5

The a-pawn falls if white's king gets here.

g5, h5

The f-pawn falls, white wins.

Using the standard, distant, and virtual oppositions, we can give the squares numbers.

4a	5	4
BK	3	2
	1		BP			6
BP			WP		BP
WP		1	WP		WP		6
	2a	3	2
	4a	5	4
WK	2a	3	2
						a7=2a

Key squares are in blue.  Numbers represent posts for creating oppositions.  Colored bars represent the places where kings must be to prevent the other from getting through.  Location on the bars means nothing.

In order to win, he must break through.  If his king moves to a 1 square and black's king moves to the other next turn, white can't break through and it is a draw.  However, if black's king is on b6 (black's 1 square) and the white king moves to c4 (the other 1 square), the black king is forced to move and the white king can get to a key square (1. ... Ka6 2. Kd3 +- breaking through on h5, 1. ... anything else 2. Kb5+-)  This applies to all the other numbered squares (moving to a blank square loses for black, draws for white).

Now for the solution!

1. Kb1!

Black's king is on 2a.

1. ... Kb7 2.Kc1! Kc7 3.Kd1! Kc8 4. Kd2! Kd7 5. Kb5 +-

White breaks through on the queenside.