Pawn endgame
Triangulation and Reserve Tempi
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In many pawn endings, moving first is a burden: the king must surrender an entry square or a pawn must advance before it is ready. Triangulation and reserve tempi are ways to change whose turn it is without changing the essential position. The aim is not to waste time; it is to hand the opponent a specific zugzwang.
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Start with the position you want
In the diagram, the result changes with the move. With White to move, king and e-pawn versus king is a Syzygy draw. Put Black to move in the same arrangement and Black loses: the king must yield ground, allowing White to secure the key squares. Before looking for a clever manoeuvre, define this target precisely: which opposing move would give your king entry?
What triangulation actually does
A king triangulates by visiting three squares and returning to the important square after three moves while the opposing king, constrained to a two-square route, returns after two. The extra move reverses the turn. A triangle is useful only if every square is safe and the opponent cannot use the time to change the pawn structure. The diagram above does not give White a working triangle; that limitation is part of the diagnosis, not a failure to remember a pattern.
A pawn move held in reserve
A harmless pawn advance on the other wing can perform the same job in one move. Count those moves before committing: a pawn may have one single-step tempo, perhaps two if it can advance twice safely, while a double move spends two squares at once. A move is not truly “in reserve” if it creates an enemy passer, abandons a protected square or lets the opposing king enter elsewhere.
A practical calculation order
- Name the zugzwang. Write the position in your head with the opponent to move and identify the concession you expect.
- Count move resources. List safe king triangles and pawn advances for both sides; the opponent may have a reserve tempo too.
- Check irreversible changes. Every pawn move alters squares permanently. Recalculate breaks and passed-pawn races after it.
- Calculate to the conversion. Reaching the desired move order matters only if the resulting king entry or pawn capture actually wins.