Corresponding Squares

Corresponding squares (also called relative squares, sister squares and coordinate squares (Mednis 1987:11–12)) in chess occur in some chess endgames, usually ones that are mostly blocked. If squares x and y are corresponding squares, it means that if one player moves to x then the other player must move to y in order to hold his position. Usually there are several pairs of these squares, and the members of each pair are labeled with the same number, e.g. 1, 2, etc. In some cases they indicate which square the defending king must move to in order to keep the opposing king away. In other cases, a maneuver by one king puts the other player in a situation where he cannot move to the corresponding square, thus the first king is able to penetrate the position (Müller & Lamprecht 2007:188–203). The theory of corresponding squares is more general than opposition, and is more useful in cluttered positions.

Corresponding squares are squares of reciprocal (or mutual) zugzwang. They occur most often in king and pawn endgames, especially with triangulation, opposition, and mined squares. A square that White can move to corresponds to a square that Black can move to. If one player moves to such a square, the opponent moves to the corresponding square to put the opponent in zugzwang (Dvoretsky 2006:15–20).

One of the most famous and complicated positions solved with the method of corresponding squares is the following endgame study composed by World Champion Emanuel Lasker and Gustavus Charles Reichhelm in 1901. It is described in the 1932 treatise L'opposition et cases conjuguées sont réconciliées (Opposition and Sister Squares are Reconciled), by Vitaly Halberstadt and Marcel Duchamp.

Suggested Solution of Corresponding Squares :

1. Kb1 Kb7

2. Kc1 Kc7

3. Kd1 Kd8

4. Kc2 Kc8

5. Kd2 Kd7

6. Kc3 Kc7

7. Kd3 Kb6

8. Ke3 and White wins by penetrating on the kingside. Each of White's first seven moves are the only one that wins (Müller & Lamprecht 2007:193–94).