The rule of three: How the third event signals the emergence of a streak

It is well established that people perceive streaks where they do not exist. However, little is known about what constitutes a streak in the mind of an observer. This paper proposes that the third repeat event in a sequence is pivotal to the subjective belief that a streak is occurring. In five studies, we find direct and indirect evidence that perceived streakiness plateaus with the third repeat outcome in a sequence. The evidence to support this rule of three comes from various domains, including: observation of randomly determined probabilistic outcomes, investment decisions in response to performance histories, and basketball shooting percentages.