Preventing Byzantine failures in the context of cloud computing is costly. Traditional BFT protocols induce a fixed degree of replication for computations and are therefore wasteful. This paper explores probabilistic Byzantine tolerance, in which computation tasks are replicated on dynamic replication sets whose size is determined based on ensuring probabilistic thresholds of correctness. The probabilistic assessment of a trustworthy output by selecting reputable nodes allows a significant reduction in the number of nodes involved in each computation task. The paper further studies several reputation management policies, including the one used by BOINC as well as a couple of novel ones, in terms of their impact of the possible damage inflicted on the system by various Byzantine behavior strategies, and reports some encouraging insights.