Randomness in binary sequences: Conceptualizing and connecting two recent developments


Recent theoretical research has shown that the assumptions that both laypeople and researchers make about random sequences can be erroneous. One strand of research showed that the probability of non-occurrence of streaks of repeated outcomes (e.g., HHHHHH) is much higher than that for a more irregular sequence (e.g., HTTHTH) in short series of coin flips. This tallies with human judgments of their likelihood of occurrence, which have conventionally been characterized as inaccurate and heuristic-driven. Another strand of research has shown that patterns of hits and misses in games like basketball, traditionally seen as evidence for the absence of a hot-hand effect, actually support the presence of the effect. I argue that a useful way of conceptualizing these two distinct phenomena is in terms of the distribution of different sequences of outcomes over time: Specifically, that streaks of a repeated outcome cluster whereas less regular patterns are more evenly distributed.

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