Triangulation: Endgame tempo in chess
Triangulation
Definition
Triangulation is an end-game maneuver—most often executed by a king, but occasionally by a queen or rook—in which a piece travels along three (or more) squares that form a geometric triangle, returning to its starting square while losing a move (tempo). The goal is to hand the opponent the move and thus place them in zugzwang, a position where any legal move worsens their situation.
Why Triangulation Works
- With perfect play, many simplified endgames are theoretically drawn—unless one side can change the move order.
- By “wasting” a tempo, the stronger side forces the weaker side to move at an inconvenient moment, often separating the enemy king from a critical square, or forcing a pawn to advance into capture.
- Because kings normally have only one legal move in tight endings, the tempo change caused by triangulation can be decisive.
Typical Endgames Featuring Triangulation
- King + Pawn vs. King—the classic “outside the square” opposition struggle.
- Opposite-colored bishop endings—a bishop can sometimes triangulate on long diagonals.
- Queen endings—when both sides are in perpetual-check territory, a queen may triangulate to lure the enemy king onto an awkward square.
Illustrative Mini-Example
Imagine the bare-king position below. White’s objective is to give Black the move while maintaining the opposition.
• After 3…Kd7 4. Kf6 White grabs the opposition and would win if a pawn were present.
• The white king’s path c4–d5–e5 forms a little triangle, costing a tempo.
Classic Game Reference
Capablanca – Tartakower, New York 1924
In the rook-plus-pawn ending (move 42 onward), Capablanca used king triangulation
Kf2–e2–e3–f3 to shoulder Tartakower’s king away from the f-file, converting the extra pawn.
Historical & Strategic Significance
Before the computer era, triangulation was considered almost “mystical”—proof of the subtlety of endgames. World champions from Lasker to Carlsen have exploited it:
- Smyslov vs. Pfleger, Dortmund 1973—Smyslov’s bishop wandered on c3–d4–e3–c3 to lose a move and oblige Black’s knight to retreat, paving the way for a passed pawn.
- Carlsen vs. Karjakin, World Ch. 2016, tiebreak Game 2—Carlsen triangulated with his king in a rook endgame, forcing Karjakin’s rook onto passive defense.
Practical Tips
- Count moves: If both kings can reach the same critical square in the same number of moves, look for a triangulation resource.
- Know your “triangular circuits.” Common ones are squares of the same color (e.g., c4–d5–e4 in a light-square triangle).
- Do not forget that pieces other than the king can triangulate—rooks on an open file, or queens on diagonals and ranks.
Interesting Facts & Anecdotes
• The term comes from classical geometry; early Russian texts called it “walking the triangle.”
• In Soviet chess schools, trainers often made pupils solve “triangulation races” blindfolded to
improve visualization.
• Engine tablebases show that some seemingly “simple” triangulations require as many as six
precise moves—human grandmasters usually spot only the three-move patterns!