Why you would want to lose a move
Usually having the move is good, but in many endings the position you want is one where it is the opponent's turn. If it is your move instead, you cannot pass. Triangulation solves that: your king walks round a small triangle of squares, such as d5, e5 and d4, and returns to its starting square after three moves.
If the opponent's king can simply copy you, nothing changes. Triangulation works when the defending king is short of room, so that it cannot keep in step and ends up with the move in the critical position.
Corresponding squares
The idea behind it is corresponding squares. For each square of the attacking king there is a square, or a few, that the defending king must be on to hold. In the example, when the white king is on d5 with White to move, the black king must be on d7. Triangulation is a way of finding a route on which the defender cannot always reach the matching square in time.
Thinking in corresponding squares also helps you defend. If you know which square answers each enemy king move, you can keep the balance with simple waiting moves and refuse to be drawn into a zugzwang.
Where triangulation appears
It is most common in king and pawn endings, where the kings are close together and the pawns take squares away from both of them. It also appears with heavier pieces: in queen against rook, for example, the stronger side often makes a few quiet king or queen moves to reach a known winning position with the defender to move.
Before you start, check that your king really has three usable squares in a triangle and that the opponent's king does not. If both kings can triangulate, the manoeuvre just repeats the position.
Common mistakes
- Pushing a pawn to pass the move when a king triangle would do it without spending a pawn move you might need later.
- Starting a triangle when the opponent's king has room to make one too, so the position simply repeats.
- Forgetting to check that every square of the triangle is safe and not attacked by enemy pawns.
Questions about triangulation
What is triangulation in chess?
A king manoeuvre over three squares in a triangle that returns the king to its starting square, so the same position arises with the opponent to move.
Why is it called triangulation?
Because the king's route, for example d5 to e5 to d4 and back to d5, traces a triangle on the board.
Is triangulation the same as the opposition?
No, but they are linked. Triangulation is often the way to gain the opposition when you cannot take it directly.