Well there's a little more physics to it, namely that biases towards certain distributions are small -- i.e. that systems always have paths to a large number of

Well there's a little more physics to it, namely that biases towards certain distributions are small -- i.e. that systems always have paths to a large number of states. The laws of physics has to be such that they exhibit asymptotic equipartition. In your example, assuming that particles positions are iid over the entire container generates the second law, but only because the dynamics of the system allow such approximation -- imagine instead that particles liked to almost irreversibly "stick together", then the system would converge to most particles on a single side.