In virtually every activity we engage in — from analyzing economic trends, to predicting which of two football teams is more likely to win a game — our minds are tasked with separating signal from noise. Such computations benefit from the fact that our minds are highly attuned to the statistical structure of the world. But how quickly do we detect statistical structure — and to what extent is our sensitivity to structure rooted in perceptual processes? To address this, we asked observers to judge whether briefly presented visual stimuli were generated randomly or non-randomly. In as little as a tenth of a second, people exhibited the same stable biases of statistical perception that they exhibit in classic cognitive tasks (i.e., without time constraints). These results suggest that certain biases of subjective probability may arise not from how we think about randomness, but from how we perceive statistical information in the first place.