Shuffling a standard 52-card deck may seem trivial, but from the perspective of mathematics and physics, it is a fascinating example of a dynamical system with an enormous number of possible states. This analysis demonstrates that the shuffling process is theoretically reversible, and the probability of a spontaneous decrease in entropy is not zero, although it is extremely small. In this paper, we discuss deck permutations, system entropy, and the probability of returning to an ordered state, using principles from nonlinear dynamics 1–4.
Marek Berezowski (Wed,) studied this question.