Triangulation
Triangulation is a way for a king to hand the move to the opponent: it makes a three-move loop over neighboring squares and returns to its starting square, while the enemy king, with less room, cannot copy the loop.
Kings cannot pass, but they can waste time on purpose. If your king walks to a neighboring square, then to a third square touching both, and finally back to where it started, three moves have gone by and the board looks exactly as before. The trick pays off when the opponent cannot spend the same three moves without leaving a post. Then the starting position returns with the other side to move, which is the whole point when that position is a zugzwang.
Three conditions make it work. The loop squares must be safe and must not release any square your king is guarding. The defending king must be tied to a short list of squares, usually by your pawns or by its duty to watch an entry point. And the target position must really be lost for the side to move, so check that first.
The diagram shows a classic use. White wants this exact position with Black to move and gets it with a walk that ends on e4 again. Related tools are the reserve tempo, where a spare pawn move does the same job more cheaply, and corresponding squares, which explain why the defender cannot keep pace.
Typical errors are starting the loop when the defender also has room to mirror it, and choosing a loop that lets the enemy king slip through on the way.
A neighboring idea is Trebuchet. The trebuchet is a mutual zugzwang in which two kings stand on either side of a pair of locked pawns, each beside the enemy pawn, so whoever must move loses a pawn and the game.
Compare it with Mutual zugzwang. A mutual zugzwang is a position in which whichever player has to move is worse off, so each side would gladly pass, and the result depends entirely on whose turn it is.
Endgame ideas like "Triangulation" are won or lost on small details, which a coach can check in your own games. The first lesson with George Li is where that review starts.
Related terms
Zugzwang is the bind of having to move when standing still would be best: the player on move has only moves that weaken the position, and since passing is not allowed, the duty to move itself costs something.
A mutual zugzwang is a position in which whichever player has to move is worse off, so each side would gladly pass, and the result depends entirely on whose turn it is.
Corresponding squares form a map for blocked pawn endings: each square the attacking king might use is paired with the square the defending king must occupy in reply, and missing a pair lets the attacker break through.
A reserve tempo is a spare, harmless move, usually a pawn move, that one side can make without damaging its position, passing the obligation to move across to the opponent.
Opposition is a standoff between the two kings on one file or rank with a single empty square between them; whoever does not have to move holds it, because the other king must give up ground.
Guides that go further
What to decide first, the questions to ask, what a first lesson should show and the red flags to avoid.
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A game review, a read on your level and a written study plan from George Li.
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