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A tendency to perceive illusory streaks or clumps in random sequences of data—the hot hand phenomenon—has been identified as a human universal tied to our evolutionary history of foraging for clumpy resources. We explored how this misperception of randomness and, more generally, ecologically relevant statistical thinking develops ontogenetically. Based on previous work with adults, we developed three tablet-based decision-making tasks that assessed how 3- to 10-year-old children in the U.S. and Germany decide whether sequential events will continue in a streak or not, their understanding of randomness, and their ability to reason about randomness in spatially dependent terms. Our analyses suggest that children, like adults, hold strong expectations of clumpy resources when they search through and reason about 1- and 2-dimensional statistical distributions. This evolved psychological default to clumped resources decreases somewhat with age. Future research should explore possible early interventions to improve statistical literacy and minimize the detrimental effects that (mis)perceptions of streaks and patterns can have on everyday life.