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This article explores the “hot hand illusion” from the perspective of ecological rationality. Monte Carlo simulations were used to test the sensitivity of typical tests for randomness to plausible constraints (e.g., Wald-Wolfowitz) on sequences of binary events (e.g., basketball shots). Most of the constraints were detected when sample sizes were large. However, when the range of improvement was limited to reflect natural performance bounds, these tests did not detect a success-dependent learning process. In addition, a series of experiments assessed people's ability to discriminate between random and constrained sequences of binary events. The result showed that in all cases human performance was better than chance, even for the constraints that were missed by the standard tests. The case is made that, as with perception, it is important to ground research on human cognition in the demands of adaptively responding to ecological constraints. In this context, it is suggested that a “bias” or “default” that assumes that nature is “structured” or “constrained” is a very rational approach for an adaptive system whose survival depends on assembling smart mechanisms to solve complex problems. [ABSTRACT FROM PUBLISHER]