fail-low: chess engine pruning upper bound
fail-low
Definition
In computer chess search (alpha–beta pruning), a fail-low occurs when a node’s returned evaluation is less than or equal to the lower bound of the search window (alpha). Put simply, the search result comes back “too low” compared to what the engine expected. Because the exact value lies outside the current window, the engine only knows an upper bound on the true score and often must re-search with a lower (wider) window to find the exact evaluation.
Typical context: aspiration windows. The engine begins a deeper iteration expecting an evaluation near its previous depth’s score, sets a narrow window around that guess, and if the new search returns below alpha, it “fails low,” widens the window downward, and searches again.
How it is used in chess
Fail-lows are a core concept for anyone reading or running a chess engine:
- Engine GUIs and UCI output: a fail-low is reported as an “upperbound.” In UCI, you might see something like: score cp 18 upperbound, meaning the true score is at most +0.18 pawns.
- Principal Variation (PV) flicker: when a search fails low, the engine may temporarily show a worse line or an incomplete PV, then settle after a re-search.
- Time management: frequent fail-lows cost time because they trigger re-searches; modern engines tune aspiration widths to reduce how often this happens.
Although the term is technical, commentators sometimes say “the engine failed low at depth 30” during broadcasts to explain sudden PV changes or a temporary drop in the evaluation bar, i.e., Engine eval in CP.
Fail-low vs. fail-high
- Fail-low: returned score ≤ alpha; the true value is ≤ returned score (an upper bound). UCI shows this as “upperbound.”
- Fail-high: returned score ≥ beta; the true value is ≥ returned score (a lower bound). UCI shows this as “lowerbound.”
Engines use these bounds, plus transposition tables and move ordering, to refine the search efficiently and converge on the Best move.
Why fail-lows happen
- Aspiration window set too tight around an optimistic guess, so the real position is worse than expected.
- New tactical resource for the opponent appears at the deeper depth, pushing the evaluation below alpha.
- Move ordering issues: the best defensive moves aren’t tried early, so the early partial result looks worse before re-searching properly.
- Search heuristics like null-move pruning or late move reductions can temporarily underestimate the position, especially near zugzwang or fortress motifs.
Aspiration window example (numbers)
Suppose at depth 18 the engine’s last score is +0.50. It begins depth 19 with an aspiration window alpha = +0.30 and beta = +0.70. If the search returns +0.10, that is below alpha and is a fail-low. The engine then re-searches with a wider window, for example alpha = −0.30, beta = +1.10, to obtain an exact score and stable PV.
UCI/GUI readout example
Engines commonly print lines of the form:
- info depth 22 score cp 23 upperbound nodes 34,000,000 nps 12,000,000 pv ...
Here, “upperbound” signals a fail-low at depth 22. The exact score is not confirmed; the true value is ≤ +0.23. The engine will typically widen the window and search again to remove the bound and produce an exact score (no bound flag).
On-the-board illustration
Fail-lows often arise when a deeper tactic refutes a previously optimistic line. For example, after 1. e4 e5 2. Nf3 Nc6 3. Bc4 Nf6 4. d3 d5!, deeper analysis might reveal that White’s earlier expectation of a slight edge is too rosy. The engine’s new depth finds ...d5! equalizing or even favoring Black, the score drops below the aspiration alpha, and the search fails low before re-searching to confirm the new PV.
Try exploring a short illustrative sequence (the viewer will derive the final position):
In practice, such moments correspond to visible “eval bar dips” as the Engine re-searches and stabilizes its Engine eval in CP.
Strategic and historical significance
- Search theory: Fail-lows are integral to alpha–beta, Principal Variation Search (PVS/NegaScout), and MTD(f), which all leverage minimal windows and re-search when fail-lows/fail-highs occur.
- Performance tuning: The rate of fail-lows strongly affects strength at fixed time controls (e.g., Blitz and Bullet chess). Proper aspiration widths, robust move ordering, and good transposition table usage reduce wasted re-search time.
- Zugzwang pitfalls: Classic endgame zugzwangs can mislead pruning heuristics. Engines mitigate this with “verified null-move” ideas to avoid spurious fail-lows or fail-highs around such positions.
- Broadcast commentary: In TCEC and other events, analysts frequently note “fail-low at depth 40” to explain sudden PV changes before the engine corrects itself.
Practical tips for analysts
- If you see “upperbound” in the GUI, wait for the next iteration; the engine is likely re-searching to get an exact score.
- Increase analysis time or disable aspiration windows if you need fewer bound results (at the cost of more nodes).
- Use multi-PV judiciously; it can stabilize output but also competes for time, potentially changing fail-low frequency.
- Cross-check with another engine or with longer analysis to confirm whether a fail-low signals a genuine tactical shift or just temporary pruning noise.
Interesting facts and anecdotes
- The vocabulary “fail-low/fail-high” became common with the rise of NegaScout/PVS in the 1980s. Today nearly all top engines rely on minimal windows, where bound results (and re-searches) are routine rather than exceptional.
- During famous man–machine matches like Kasparov vs. Deep Blue (1997), discussions of engine search behavior—though not phrased exactly as “fail-low” on broadcast—highlighted how narrow windows and deep tactics could cause surprising evaluation swings.
- In modern GUIs, bound flags explain many fleeting PV changes that viewers once mistaken for “engine indecision.” It is usually just the search window doing its job.
Related and useful links in this glossary
Quick recap
A fail-low means the search returned a value at or below alpha—lower than expected—so the engine only has an upper bound and will often widen the window and search again. Recognizing “upperbound” in engine output helps you interpret temporary PV changes and evaluation dips correctly.