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 simplest and most important uses of corresponding squares is in this king and pawn versus king endgame. Assume that the black king is in front of the pawn and the white king is behind or to the side of the pawn. The black king is trying to block the white pawn and the white king is supporting its pawn. If the white king gets to any of the key squares (marked with "x"), he wins. Suppose the black king moves to the square labeled "1" near him (square c8). Then if the white king moves to the corresponding square (also labeled "1", square c6), he wins. Conversely, if the white king moves to the "1" square then the black king must move to the corresponding square to draw. Thus if both kings are on the "1" squares, the position is a reciprocal zugzwang. Note that the second player moving to one of the corresponding squares has the advantage. Being on a square when the opponent is not on the corresponding square is a disadvantage.

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