Triangulation

Triangulation works when three things line up. One: the critical position is a mutual zugzwang; whoever moves, loses ground. Two: your king has three useful squares to rotate around. Three: the enemy king is confined to two (an enemy pawn or your king's shadow takes the third away). Then the arithmetic is merciless: you take three steps around your triangle, the defender can only alternate between two squares, and the zugzwang position returns, with the defender to move.

It feels like breaking the rules: you lose a tempo on purpose, in a game where everyone fights to gain them. But in a mutual zugzwang, the tempo is a hot potato, and triangulation is how you pass it.

In the position above, White's king probes both wings (toward c5 on one side, toward g5 on the other), and Black's king must answer every probe from exactly the right square to keep the entry points covered. But Black's own pawn on e6 steals a square from its king and blocks the e-file shuffle: Black is one answer short.

So White's king ambles around its triangle, Black's king runs out of correct replies a move too soon, and the white king walks in to win the e6-pawn, after which the rest is the king-and-pawn atom. Play it out against the tablebase; feeling the defender run out of squares teaches more than any diagram caption can.

The trigger pattern: you'd win if it were their move, and direct king approaches all bounce. That exact frustration (“every square I want is covered, but he's barely holding”) is the signal. Count squares: if your king has a spare square and theirs doesn't, triangulate.

Queens can triangulate too (the queen-vs-rook ending is won by exactly this: recreating the zugzwang with the defender to move), and the general form is the theory of corresponding squares. But the king triangle in pawn endings is where the idea lives in practice: small, common, and worth a full point every time it appears.