Michaela Bocheva¹, Brian Scholl¹; ¹Yale University

One of the foundational tasks of perception is to detect and characterize *structure* in our local environments—in the form of objects, events, and even abstract statistical regularities. And this can be explored indirectly by asking how people perceive randomness (that is, the lack of structure). Many studies over many decades have explored the ability to detect *whether* a sequence of items is random or not, in a categorical sense. Here, in contrast, we ask how people perceive different *degrees* of randomness, and we provide some counterintuitive answers. People viewed coin-flip outcomes, one by one, and used a slider to report how random the sequence appeared. Different sequences had varying degrees of actual randomness, as determined by bits per symbol, and the probability of an outcome repeat. This allowed us to ask: Are people equally sensitive to all degrees of structure? Or might they be especially sensitive only to whether a sequence has any structure (or no structure at all) — or to whether a sequence is more or less structured than some average value? In fact, none of these were true. Instead, certain degrees of structure were far more discriminable from each other, even while equating objective differences. For example, when characterized in terms of average information, people were highly sensitive to the difference between 0.6 and 0.7 bits—while showing no ability to discriminate between other similarly adjacent values. This pattern was surprising even to observers: we collected continuous confidence ratings for each of the randomness judgments, and these diverged from the actual patterns of sensitivity in qualitative ways. In particular, people were confident for extreme degrees of structure, but *not* for extreme degrees of randomness. We conclude that people are sensitive to structure as a continuous variable in nonuniform ways that prioritize some degrees of structure over others.