In research on causal inference and in related paradigms (conditioning, cue learning, attribution), it has been traditionally taken for granted that the statistical contingency between cause and effect drives the cognitive inference process. However, while a contingency model implies a cognitive algorithm based on joint frequencies (i.e., the cell frequencies of a 2 x 2 contingency table), recent research on pseudocontingencies (PCs) suggests a different mental algorithm that is driven by base rates (i.e., the marginal frequencies of a 2 x 2 table). When the base rates of two variables are skewed in the same way, a positive contingency is inferred. In contrast, a negative contingency is inferred when base rates are skewed in opposite directions. The chapter describes PCs as a resilient cognitive illusion, as a proxy for inferring contingencies in the absence of solid information, and as a smart heuristic that affords valid inferences most of the time.