According to absolutist moral theories, agents may not violate their duties for the sake of arbitrarily valuable consequences. Yet intuitively, it is permissible to take a sufficiently small risk of violation for the sake of the consequences. The Risk Problem is that it is notoriously difficult to give a principled account of how good consequences can justify the small risk, but no larger quantity of good consequences could justify the larger risk. I show that extant solutions to the Risk Problem have fatal flaws, then offer a theory that avoids these issues. The basic idea is that agents maximize rounded expected deontic weight (the degree to which, in some outcome, they uphold their duties) and use expected value to break ties. We find that absolutists have a generous helping of standard decision-theoretic resources at their disposal. Then, we use these resources to start doing absolutist decision theory, discovering surprising results about how absolutists should relate to preference axioms. They must, for instance, give up the Sure Thing Principle and the dominance principles it secures. Fortunately, as we come to see, these principles are unattractive—and arguments for them unconvincing—to the absolutist.