People often face the challenge of evaluating competing explanations. One approach is to assess the explanations’ relative probabilities – e.g., applying Bayesian inference to compute their posterior probabilities. Another approach is to consider an explanation’s qualities or ‘virtues’, such as its relative simplicity (i.e., the number of unexplained causes it invokes). The current work investigates how these two approaches are related. Study 1 found that simplicity is used to infer the inputs to Bayesian inference (explanations’ priors and likelihoods). Studies 1 and 2 found that simplicity is also used as a direct cue to the outputs of Bayesian inference (the posterior probability of an explanation), such that simplicity affects estimates of posterior probability even after controlling for elicited (Study 1) or provided (Study 2) priors and likelihoods, with simplicity having a larger effect in Study 1, where posteriors are more uncertain and difficult to compute. Comparing Studies 1 and 2 also suggested that simplicity plays additional roles unrelated to approximating probabilities, as reflected in simplicity’s effect on how ‘satisfying’ (vs. probable) an explanation is, which remained largely unaffected by the difficulty of computing posteriors. Together, these results suggest that the virtue of simplicity is used in multiple ways to approximate probabilities (i.e., serving as a cue to priors, likelihoods, and posteriors) when these probabilities are otherwise uncertain or difficult to compute, but that the influence of simplicity also goes beyond these roles.