Sharper, Not Safer: The Direction of Human Deviations from Engine Play

Abstract

Version v5 (September 2026). Corrected estimator for all mixed models: the player random intercept described in the text was missing from the fitting helper in earlier versions. All 23 models were refit under a correction specification locked before the refit; 24 printed values changed at printed precision, no conclusion changed. The fault is disclosed as the fourth item in Section 6. Correction specification, refit report, and old-to-new numbers table: docs/ in the GitHub repository. When a human player departs from a chess engine's preferred move, is the departure noise, or does it have a direction? I analyze 1,970 rated online games by titled players: 50,021 middlegame position-moves; 120,723 engine evaluations in total, comprising 63,429 root and context evaluations for the magnitude analysis and 57,294 successor evaluations for the direction analysis, all at fixed depth with five principal variations. All evaluations are converted to win probability before differencing. Deviation magnitude behaves as a noise account predicts. It falls with rating, rises with position volatility, and rises under time pressure. The direction of deviation does not. I define a move's riskiness as the steepness of the opponent's punishment curve: the win-probability gap between the opponent's best and fifth-best replies. At equal expected loss, human moves sit on steeper curves than the engine's choice (intercept +1.22 win-probability points, p = 1.6 × 10 ³⁵;⁻ 59.85% of deviations toward the sharper side, sign-test p = 1.8 × 10 ¹⁷ ). The effect survives a ⁻ ⁰ liquidation control and two pre-specified robustness variants, and it strengthens under time pressure. A risk-averse agent should retreat to recoverable positions; players sharpen instead. A pilot-stage association between deviation direction and a previously measured style dimension collapsed on the full sample, and I report it as unsupported. My reading is that human play optimizes an objective the engine does not share, one that prices the opponent's fallibility, though on average the sharpening is not repaid in results. All hypotheses, parameters, and variants were fixed in advance. Two pipeline faults caught during execution are disclosed in full.