  We consider two ways one might use algorithmic randomness to characterize a
probabilistic law. The first is a generative chance* law. Such laws involve a
nonstandard notion of chance. The second is a probabilistic* constraining law.
Such laws impose relative frequency and randomness constraints that every
physically possible world must satisfy. While each notion has virtues, we argue
that the latter has advantages over the former. It supports a unified governing
account of non-Humean laws and provides independently motivated solutions to
issues in the Humean best-system account. On both notions, we have a much
tighter connection between probabilistic laws and their corresponding sets of
possible worlds. Certain histories permitted by traditional probabilistic laws
are ruled out as physically impossible. As a result, such laws avoid one
variety of empirical underdetermination, but the approach reveals other
varieties of underdetermination that are typically overlooked.
