A Quantitative Framework for Measuring Randomness in Simulated Card Shuffles

We present a computational framework for quantifying randomness in riffle-shuffled decks using spatial and information-theoretic metrics. Simulated Gilbert–Shannon–Reeds shuffles of a 52-card deck are analysed via Moran’s I to detect spatial clustering of suits and ranks, alongside Shannon entropy measures capturing positional and sequential unpredictability. Across 10,000 trials, seven riffle shuffles yield near-zero mean spatial autocorrelation and high overall entropy, consistent with classical results. However, substantial trial-to-trial variance is observed. Component analysis further reveals asymmetric randomisation: suit relationships decorrelate significantly faster than rank relationships, with rank entropy consistently lagging. This suggests structural biases in riffle dynamics that preserve remnants of initial rank ordering. The approach offers an empirical complement to existing theoretical work, demonstrating how spatial statistics and entropy can jointly characterise the multidimensional nature of randomisation.