Triangulation: losing a move to win

About this endgame

Some positions are won only with the other side to move. Your king stands on d4 with pawns on c4 and d5; the black king on b6 guards the pawn on d6 and watches c5. With Black to move the defence would collapse, so you have to hand over the turn first. Twenty-four moves to do it and win.

What you will learn

• 01 How a triangle of king moves passes the turn to the opponent.
• 02 Why the defending king cannot answer with a triangle of its own.
• 03 Which first moves win, and which two throw the win away.

The technique

Imagine the same position with Black to move. The king on b6 has to leave, and wherever it goes your king gets through: round by e4, f5 and g6 towards e6 and e7, and the d6 pawn falls. You cannot hand over the move with a pawn, because c5 at once lets Black hold. So the king does it.

Walk the king round a triangle: d4 to d3, d3 to c3, then back to d4. That is three moves. The black king has only two squares that keep the position, b6 and c5, so after two moves of its own it is back where it started and it is Black to move in the position you wanted. If the black king goes to c5 to attack the c4 pawn, your next move guards c4: Kc3 after Kd3, or Kd3 after Ke3 or Ke4.

Kd3, Ke3 and Ke4 all win, each as the start of a triangle. Kc3 as a first move only draws, and so does pushing c5 straight away. Once the black king leaves b6 for the seventh rank, stop circling and go round by the king side: the black king cannot guard d6 and keep yours out at the same time.

How to practise it

Play White. Count the squares before you move: three for your king, two for Black. After the triangle, take the long walk round to the d6 pawn. Winning the pawn inside twenty-four moves ends the drill.

Questions people ask

What is triangulation in chess?

A king manoeuvre over three squares that returns to the same position with the opponent to move. It works when the defending king has only two squares that hold the position, so it cannot copy the triangle.

When should I look for triangulation?

In king and pawn endings where you would win if it were the opponent to move and no spare pawn move exists. A position of mutual zugzwang plus room for your king to circle is the signal.