Recent theoretical research has shown that the assumptionsthat both laypeople and researchers make about randomsequences can be erroneous. One strand of research showedthat the probability of non-occurrence of streaks of repeatedoutcomes (e.g., HHHHHH) is much higher than that for amore irregular sequence (e.g., HTTHTH) in short series ofcoin flips. This tallies with human judgments of theirlikelihood of occurrence, which have conventionally beencharacterized as inaccurate and heuristic-driven. Anotherstrand of research has shown that patterns of hits and missesin games like basketball, traditionally seen as evidence for theabsence of a hot-hand effect, actually support the presence ofthe effect. I argue that a useful way of conceptualizing thesetwo distinct phenomena is in terms of the distribution ofdifferent sequences of outcomes over time: Specifically, thatstreaks of a repeated outcome cluster whereas less regularpatterns are more evenly distributed.