There has been little research on infants’ development of causal inference in the second year after birth. We report an experiment in which 9- to 18-month-old infants viewed visual sequences consisting of three looming shapes, one after another. Half of the sequences (causes) were predictive of an attention-getting reward (effect), and the other half were non-predictive. The statistical complexity of predictive sequences was varied between conditions. We analyzed latencies of infants’ eye movements toward the reward location. Older infants yielded more anticipatory eye movements in predictive than non-predictive sequences. Effects of both infant age and complexity of causal sequences were observed. To qualitatively account for these findings, we formulated a Bayesian model based on generic priors favoring simple causal events coupled with noisy shape identification.