Triangulation in chess: how to lose a move and win

Sometimes you'd win if only it were your opponent's move. Triangulation is how you hand the move over: your king walks a small triangle and comes back to the same square, while the other king, with fewer squares to use, can't copy it.

The method, played out

White wants to win the pawn on c6, and Black's king is guarding it.

White to move. Step through the triangle.

The triangle: e5, f6, e6

1.Ke5 heads for d6, and Black's king answers on d7 to stop it. Then 2.Kf6, the first step of the triangle, and Black has to keep guarding: 2...Kd8. Now 3.Ke6 brings White's king where it wanted to be, and Black's king has had to move off d7.

Then in

4.Ke7 takes d7 and d8 away from Black's king, so it can't get back to guard c6. 4...Kc8 5.Kd6 Kb7 6.Kd7, and the c6 pawn falls.

The mistake

Heading the wrong way at the start lets Black's king settle: after 1.Kc4?, 1...Kd8 holds, and it's only a draw. The same goes for 2.Ke4? Ke8 in the middle of the triangle: the king has to go round, not back.

The idea to remember

When the kings mirror each other and you need the other side to move, walk a triangle. You come back to the same square a move later; the other king, short of room, can't do the same.

Train it

This is one of the endgame techniques OptiChess teaches as a walkthrough: the moves play themselves until a moment that matters, then you find the move, checked against the tablebase. The basic king duel behind it is the opposition. More endings are in the chess endgame trainer.

Try it. Real positions, set at your level, every answer checked against the board. No account needed to start.

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