Probabilistic laws of nature, as they are usually understood, are extraordinarily permissive. For example, a probabilistic law of a coin toss experiment is compatible with any sequence of results, including the all heads sequence (HHHHH......) and the alternating heads-tails sequence (HTHTHT......). This feature can be problematic, as it gives rise to a variety of metaphysical and epistemological underdetermination. We consider two ways one might use algorithmic randomness to strengthen the content of a probabilistic law. They provide much tighter connections between probabilistic laws and their corresponding sets of possible worlds, and allow us to eliminate several philosophical problems about probabilistic laws. (Joint work with Jeffrey A. Barrett; paper version at https://arxiv.org/pdf/ 2303.01411.pdf)