If you are studying these marbles, once you have an ergodic Markov chain, then it will satisfy the asymptotic equipartition theorem; this is a mathematical result in information theory. You can compare the entropy rate of the forward and time-reversed process and it will satisfy the fluctuation theorem. At this point, you are talking about mathematical theorems, like the Law of Large Numbers, so there really isn’t anything open to interpretation unless one wants to philosophize about it like Rosencrantz and Guildenstern.