Proceedings of the Annual Meeting of the Cognitive Science Society

How do humans allocate scarce cognitive resources across a stream of related decisions? Russek et al. (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 live-game tactical sequences (extracted from the Lichess puzzle database and re-timed against the original 2019 Lichess game database) played by 74,609 unique players, the within-sequence log-RT spike is +0.309 (Cohen’s 𝑑 = 0.235; paired 𝑡 = 86, N = 135,608; BF10 > 10100). Hierarchical regression climbs from 𝑅2 = 0.011 (Russek-static) to 0.282; the amortization interaction is large when predictability is operationalized by the human-style Maia-2 (𝛽 = −0.054, 𝑝 < 10−27) and not significant under Stockfish best-move predictability. A three-parameter Bayesian Sampling Model with Cache recovers cache strength 𝑠 = 0.085 [0.071, 0.099], with 100% of bootstrap draws positive. The H1 spike is roughly twice as large in solved sequences as in failed ones (𝑡 = 26.2, 𝑝 < 10−150); this pattern suggests successful tactical recognition followed by decisive recalculation rather than passive surprise. The findings replicate on a 2024 Lichess cohort and on FIDEWorld Rapid + Blitz 2024 over-the-board play.