Chess Signatures of Play

Abstract

A game of chess is a stream: a time-ordered sequence of moves, each carrying an engine evaluation, a measure of accuracy, a measure of position complexity, and a clock reading. We model a game as a multivariate path and apply the signature transform of rough-path theory to obtain a reparametrization-invariant, graded feature set that records the order and interaction of in-game events without a parametric likelihood. We show that a player's law of play is identifiable from the expected signature up to tree-like equivalence, construct a signature-kernel two-sample test on path space, and recast cheating detection as an anytime-valid sequential test: a signature conformance score becomes an e-process whose error is controlled for every sample size at once by Ville's inequality, with fluctuations calibrated on the moderate-deviation scale. The discriminating information lives in the signature's Levy areas, which measure whether accuracy rises precisely when positions become hard--the fingerprint of engine assistance that aggregate match-rate statistics discard. In a controlled study the test holds exact type-I control and detection power rises from negligible for subtle assistance to 0.98 for blatant assistance, with a median detection time matching the growth-rate prediction. Calibrated to Magnus Carlsen's documented elite accuracy, the monitor does not flag world-champion-level play; and we exhibit cheating strategies that leave every aggregate statistic, including the best-move-frequency z-score of the Regan system, unchanged yet are caught cleanly by the signature--making precise how an order-aware, anytime-valid test strengthens the prevailing approach to chess anti-cheating.