Engine-Equal, Human-Unequal: A Reproducible Outcome Skew in Engine-Assessed Equal Chess Positions

Abstract:Among chess opening positions that a strong engine judges essentially equal (Stockfish 18 evaluation within 10 centipawns of zero, depth-stable) and that humans actually reach on Lichess (October 2025; 1,661 positions, 16.1M occurrences), human results are not balanced. Positions carry outcome skews, each the gap between its games' actual results and what the players' ratings predict, whose directions are stable properties of the naturally-reached position: some positions favour White, others Black. These skews reproduce across three re-partitions -- disjoint player-account sets (primary), time, and disjoint rating bands -- and on an out-of-sample month eight months later. On the primary split, each position's skew is measured once in each account group, and the replication slope asks how well one measurement predicts the other after removing rating and opening-family effects: one means undiminished carry-over; zero, no linear relation. We find 0.69 (family-clustered 95% CI [0.65, 0.74]), rising to 0.94 on the most-popular, best-measured positions. The slope's value depends on the position mix. Existence is the invariant claim: it survives every tighter evaluation band, search depth, calibration, and popularity cutoff we test, and replicates within blitz and rapid separately. The typical skew is small (median $|\delta| \approx 0.018$, about two percentage points of White score), yet it reproduces, position by position, across disjoint accounts. At these positions the disfavoured side also thinks longer. Even where the evaluation is most confident, it is not a sufficient statistic for human outcomes. The result is observational, and the causal question is left to a pre-registered randomised companion study.

27 pages, 3 figures, 3 tables. Code and data: this https URL

Artificial Intelligence (cs.AI); Physics and Society (physics.soc-ph); Applications (stat.AP)

arXiv:2607.25655 [cs.AI]

(or arXiv:2607.25655v1 [cs.AI] for this version)

https://doi.org/10.48550/arXiv.2607.25655 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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