In many tasks, human behavior is far noisier than is optimal. Yet when asked to behave randomly, people are typically too predictable. We argue that these apparently contrasting observations have the same origin: the operation of a general-purpose local sampling algorithm for probabilistic inference. This account makes distinctive predictions regarding random sequence generation, not predicted by previous accounts-which suggests that randomness is produced by inhibition of habitual behavior, striving for unpredictability. We verify these predictions in two experiments: people show the same deviations from randomness when randomly generating from non-uniform or recently-learned distributions. In addition, our data show a novel signature behavior, that people's sequences have too few changes of trajectory, which argues against the specific local sampling algorithms that have been proposed in past work with other tasks. Using computational modeling, we show that local sampling where direction is maintained across trials best explains our data, which suggests it may be used in other tasks too. While local sampling has previously explained why people are unpredictable in standard cognitive tasks, here it also explains why human random sequences are not unpredictable enough.