Sometimes people believe that a run of similar independent events will be broken (belief in the gambler's fallacy) but, other times, that such a run will continue (belief in the hot hand). Both of these opposite inductions have been explained as being due to belief in a law of small numbers. We argue that one factor that distinguishes these phenomena is people's beliefs about the randomness of the underlying process generating the events. We gave participants information about a streak of events but varied the scenarios in such a way that the mechanism generating the events should vary in how random the participants would judge it to be. A manipulation check confirmed our assumptions about the scenarios. We found that with less random scenarios, the participants were more likely to continue a streak.