The statistics of small samples are often quite different from those of large samples, and this needs to be taken into account in assessing the rationality of human behavior. Specifically, in evaluating human responses to environmental statistics, it is the effective environment that matters; that is, the environment actually experienced by the agent needs to be considered, not simply long‐run frequencies. Significant deviations from long‐run statistics may arise through experiential limitations of the agent that stem from resource constraints and/or information‐processing (...) bounds. The article draws together recent work from a number of areas in judgment and decision making ranging from randomness perception (Hahn & Warren, ), information sampling (Hertwig & Pleskac, ; Kareev et al., ), and consequences of choice for exploration or exploitation (e.g., Denrell, ) to demonstrate how proper consideration of these deviations leads to reevaluation of behaviors that are otherwise deemed irrational. (shrink)