The Shadow of the Past: Amortized Inference and Belief Revision using Chess as a Model System
Abstract
How do humans allocate scarce cognitive resources across a stream of related decisions? Russek, Acosta-Kane, van Opheusden, Mattar, and Griffiths (2025) predict reaction time on each chess move from the within-move Benefit of Computation, treating moves as if they were drawn independently. We ask whether those costs also depend on computation carried forward from the previous move. In chess, a player who has calculated a likely opponent reply can often reuse that work; a surprising reply should force revision. On 135,608 quality-filtered Lichess puzzles attempted by 74,609 unique users, the within-puzzle log-RT spike is +0.309 (Cohen's __ = 0.235; paired __ = 86, N = 135,608; BF10 > 10100). Hierarchical regression climbs from __2 = 0.011 (Russek-static) to 0.282; the amortization interaction is large when predictability is operationalized by the human-style Maia-2 (__ = _0.054, __ < 10_27) and not significant under Stockfish best-move predictability. A threeparameter Bayesian Sampling Model with Cache recovers cache strength __ = 0.085 [0.071, 0.099], with 100% of bootstrap draws positive. The H1 spike is roughly twice as large in solved puzzles as in failed ones (__ = 26.2, __ < 10_150); this pattern suggests active engagement rather than passive surprise. The findings replicate on a 2024 Lichess cohort and on FIDEWorld Rapid + Blitz 2024 over-the-board play.