Ockham's razor is the principle that, all other things being equal, scientists ought to prefer simpler
theories. In recent years, philosophers have argued that simpler theories make better predictions, possess
theoretical virtues like explanatory power, and have other pragmatic virtues like computational
tractability. However, such arguments fail to explain how and why a preference for simplicity can help one
find true theories in scientific inquiry, unless one already assumes that the truth is simple. One new
solution to that problem is the Ockham efficiency theorem, which states that scientists who heed Ockham's
razor retract their opinions less often and sooner than do their non-Ockham competitors. The theorem
neglects, however, to consider competitors following random ("mixed") strategies and in many applications
random strategies are known to achieve better worst-case loss than deterministic strategies. In this paper,
we describe two ways to extend the result to a very general class of random, empirical strategies. The first
extension concerns expected retractions, retraction times, and errors and the second extension concerns
retractions in chance, times of retractions in chance, and chances of errors.