In this study, we examined perceptions of binary sequences under uncertainty in an attempt to depict a holistic and unifying framework. The first experiment applied a projection method that motivated participants to observe binary series and provide descriptions of their possible underlying mechanisms or processes. This procedure revealed four distinct perceptual categories: two previously studied categories of chance mechanisms and human performance, associated with the gambler's and hot-hand fallacies, and two newly identified categories-periods and processes and traits and preferences. The next three experiments tested the associations between the four categories and the alternation rates of the observed sequences under three categorical decisions structures: screening, discrimination, and classification. The results reveal the relativity of binary sequence perception. They show that the categories of chance mechanisms and periods and processes reflected rather stable perception across all tested conditions, whereas the other two categories were more susceptible to the context in which they were embedded. The findings support previous research on the gambler's fallacy and show that the hot-hand fallacy is confined to comparisons of human performance and chance mechanisms. A proposed developmental hierarchy suggests that all four categories embody basic cognitive structures that assist in detecting, decoding, and interpreting both inanimate and social aspects of the environment.