Quick answer
Triangulation is an endgame technique: promotion race and tempo. Work from the first evidence position for Triangulation, and begin by testing d4.
Begin from d4 in 8/8/8/3p4/4P3/8/7k/4K3 b - - 2 3. Count the material, king routes, promotion squares and reserve tempi before applying a theoretical rule. The evidence answer is: Triangulation: calculate both promotion paths and include checks before assuming the faster pawn wins. Candidate line: d4.
In the Triangulation example, notice: side Black; pieces Black pawn d5, White pawn e4, Black king h2, White king e1; legal first moves d4, dxe4, Kg3, Kh3, Kh1, Kg1, Kg2. Treat this piece list as local to the diagram above; it is not a universal map for every similar position.
Material and result question
The first evidence board tests promotion race and tempo; the second board tests promotion race and tempo. Replay path A via direct FEN setup; path B is the contrast line direct FEN setup. Background terms live on the Chess Wiki and the Endgames hub. Then compare Material Values with Reserve Tempo, Pawn Breakthrough, Pawn Race Calculation around the defender's only active counterplay.
The two inventories make the distinction concrete. A contains side Black; pieces Black pawn d5, White pawn e4, Black king h2, White king e1; legal first moves d4, dxe4, Kg3, Kh3, Kh1, Kg1, Kg2; B contains side White; pieces Black pawn d4, White pawn e4, Black king h2, White king e1; legal first moves e5, Kd2, Ke2, Kf2, Kf1, Kd1. Compare the side to move before comparing the labels in the context of an outside passer used as a decoy.
Topic dossier for this page and board pair r1:8 | r2:8 | r3:8 | r4:3p4 | r5:4P3 | r6:8 | r7:7k | r8:4K3 / r1:8 | r2:8 | r3:8 | r4:8 | r5:3pP3 | r6:8 | r7:7k | r8:4K3: start with the defender's only active counterplay; then test an outside passer used as a decoy; keep the defender's fortress setup separate from the pawn's promotion square; use a reserve pawn move as the transfer check; and reserve the side-to-move tempo for the exception.
Conversion or defense plan
On the first board, calculate d4 after d4 and write down the opponent's best reply around the defender's only active counterplay. On the second board, calculate Kf2 after Kf2 and check an outside passer used as a decoy. Separate the practical conversion question from the result question; side to move and one checking distance can change the conclusion. In this case the useful condition is the side-to-move tempo.
Key claim: Triangulation is illustrated here by promotion race and tempo; the first concrete test is d4. The board anchor is 8/8/8/3p4/4P3/8/7k/4K3; the example is intentionally narrower than the topic label and should not be generalised without checking the surrounding position..
Practical boundary: To answer “What exact king, pawn, and move-order conditions decide triangulation, and how should each side play them?”, compare the recorded setup with Kf2 and the opponent's reply. The decision is useful only when the stated condition survives that concrete test on board 8/8/8/8/3pP3/8/7k/4K3. The evidence records No tablebase outcome is asserted by this generated record; verify the exact FEN before publication and the second board signature r1:8 | r2:8 | r3:8 | r4:8 | r5:3pP3 | r6:8 | r7:7k | r8:4K3. The false-positive test is whether the defender's fortress setup appears without the pawn's promotion square, so the conclusion is useful only when the stated condition survives that concrete test.
Evidence positions
example-1: promotion race and tempo
Show answer
Triangulation: calculate both promotion paths and include checks before assuming the faster pawn wins. Candidate line: d4.
Why this position is here: Triangulation is represented by promotion race and tempo. This is a direct FEN setup with board anchor 8/8/8/3p4/4P3/8/7k/4K3; no opening history is inferred from the diagram.
FEN: 8/8/8/3p4/4P3/8/7k/4K3 b - - 2 3
Question: What is the first concrete decision in this triangulation position?
Answer cue: Triangulation: calculate both promotion paths and include checks before assuming the faster pawn wins. Candidate line: d4. The first candidate to test is d4. Replay d4 on board anchor 8/8/8/3p4/4P3/8/7k/4K3 and write down what changes after it.
Evidence boundary: No tablebase outcome is asserted by this generated record; verify the exact FEN before publication.
example-2: promotion race and tempo
Show answer
Triangulation: calculate both promotion paths and include checks before assuming the faster pawn wins. Candidate line: Kf2.
Why this position is here: Triangulation is represented by promotion race and tempo. This is a direct FEN setup with board anchor 8/8/8/8/3pP3/8/7k/4K3; no opening history is inferred from the diagram.
FEN: 8/8/8/8/3pP3/8/7k/4K3 w - - 0 4
Question: What is the first concrete decision in this triangulation position?
Answer cue: Triangulation: calculate both promotion paths and include checks before assuming the faster pawn wins. Candidate line: Kf2. The first candidate to test is Kf2. Replay Kf2 on board anchor 8/8/8/8/3pP3/8/7k/4K3 and write down what changes after it.
Evidence boundary: No tablebase outcome is asserted by this generated record; verify the exact FEN before publication.
example-3: promotion race and tempo
Show answer
Triangulation: calculate both promotion paths and include checks before assuming the faster pawn wins. Candidate line: e4.
Why this position is here: Triangulation is represented by promotion race and tempo. This is a direct FEN setup with board anchor 8/8/3p4/8/8/4P3/4K3/7k; no opening history is inferred from the diagram.
FEN: 8/8/3p4/8/8/4P3/4K3/7k w - - 4 3
Question: What is the first concrete decision in this triangulation position?
Answer cue: Triangulation: calculate both promotion paths and include checks before assuming the faster pawn wins. Candidate line: e4. The first candidate to test is e4. Replay e4 on board anchor 8/8/3p4/8/8/4P3/4K3/7k and write down what changes after it.
Evidence boundary: No tablebase outcome is asserted by this generated record; verify the exact FEN before publication.
Reading the line
Read the first example (id example-1) as a complete record: continuation d4, source tablebase. This is a direct FEN setup with board anchor 8/8/8/3p4/4P3/8/7k/4K3; no opening history is inferred from the diagram. If A does not expose promotion race and tempo, correct the evidence before relying on the prose.
Read the second example (id example-2) separately: continuation Kf2, source tablebase. Its feature is promotion race and tempo; inventory side White; pieces Black pawn d4, White pawn e4, Black king h2, White king e1; legal first moves e5, Kd2, Ke2, Kf2, Kf1, Kd1. Compare what changes between d4 and Kf2.
Boundary cases
The main mistake to avoid with Triangulation is applying a remembered endgame rule while ignoring side to move, king placement or an unverified result. In A, the missing condition must be located in r1:8 | r2:8 | r3:8 | r4:3p4 | r5:4P3 | r6:8 | r7:7k | r8:4K3 after d4; in B, test it against r1:8 | r2:8 | r3:8 | r4:8 | r5:3pP3 | r6:8 | r7:7k | r8:4K3 after Kf2.
For Triangulation, the first board's evidence boundary (after d4) is No tablebase outcome is asserted by this generated record; verify the exact FEN before publication. The second board's evidence boundary for Triangulation is No tablebase outcome is asserted by this generated record; verify the exact FEN before publication. If a trusted source or careful calculation changes the conclusion around a reserve pawn move, update both the evidence record and this article.
Practice from a real game
play the position for both sides, record the critical tempo, and verify the exact FEN against the cited tablebase before publication. Start with A's side to move and r1:8 | r2:8 | r3:8 | r4:3p4 | r5:4P3 | r6:8 | r7:7k | r8:4K3; record two candidates, the reply to d4 and the correction. Repeat with B's side to move and r1:8 | r2:8 | r3:8 | r4:8 | r5:3pP3 | r6:8 | r7:7k | r8:4K3; the changed board tests transfer rather than diagram memory.
After the drill, compare your notes with Reserve Tempo, Pawn Breakthrough, Pawn Race Calculation through the pawn's promotion square. Keep A's rejected alternative beside B's chosen line Kf2; this shows whether the conclusion survived a new board signature.
Sources and scope
Sources for Triangulation: Syzygy tablebase verification reference, 1chess.online editorial scope. Source ids are tablebase, original-analysis. Primary evidence hook: tablebase. Comparisons and practice notes are editorial. Evidence revision: 2026-08-remediation-r2.
Scope note for board pair r1:8 | r2:8 | r3:8 | r4:3p4 | r5:4P3 | r6:8 | r7:7k | r8:4K3 / r1:8 | r2:8 | r3:8 | r4:8 | r5:3pP3 | r6:8 | r7:7k | r8:4K3: this page does not claim that d4 is an engine principal variation, that an exact endgame result is verified when the evidence says it is not, or that a tool output replaces human calculation. The conclusion is limited to the recorded boundary and the exception the defender's fortress setup.