Triangulation (chess)

Triangulation is a tactic used in chess to put one's opponent in zugzwang (a position when it is a disadvantage to move). Triangulation is also called losing a tempo or losing a move.

Triangulation occurs most commonly in endgames with only kings and pawns when one king can maneuver on three adjacent squares in the shape of a triangle and maintain the basic position while the opposing king only has two such squares. Thus, if one king triangulates by using three moves to return to the original square and the opposing king cannot do the same, he has lost a crucial tempo and reached the same position with the other player to move. Triangulation can occur in other endgames and even in some middlegames (Flear 2004:15).

Consider this position, with White to move. Here, Black has the opposition, and is keeping the white king out. However, if White had the opposition (i.e. it were Black's move in this position), the black king would have to move away from d7 and allow the white king to advance. Black's king must stay close to where it is – he must prevent the c-pawn from advancing and he must not let himself be driven to the edge of the board. The squares d5 and d7 are corresponding squares. When White's king is on d5, Black's king must be on d7, with White to move in order for Black to prevent the advance of the White king. White has a triangle of squares available: d5, e5, and d4. White can win by the following maneuver:

and now the triangulation is complete and we have the same position but with Black to move. White has gained the opposition and Black is now in zugzwang. There may follow:

and White will win (Dvoretsky 2006:21). (There are other ways for White to win after his third move.)

In this 1978 game between Lev Alburt and future World Champion Garry Kasparov, Black wins by triangulating:

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