Determinism and chance from a Humean perspective

On the face of it ‘deterministic chance’ is an oxymoron: either a process is chancy or deterministic, but not both. Nevertheless, the world is rife with processes that seem to be exactly that: chancy and deterministic at once. Simple gambling devices like coins and dice are cases in point.2 On the one hand they are governed by deterministic laws – the laws of classical mechanics – and hence given the initial condition of, say, a coin it is determined whether it will land heads or tails when tossed.3 On the other hand, we commonly assign probabilities to the different outcomes of a coin toss, and doing so has proven successful in guiding our actions. The same dilemma also emerges in less mundane contexts. Classical statistical mechanics assigns probabilities to the occurrence of certain events – for instance to the spreading of a gas that is originally confined to the left half of a container – but at the same time assumes that the relevant systems are deterministic. How can this apparent conflict be resolved?