Perception of randomness: On the time of streaks |
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| Institution: | 1. Institute of Neurology and Center for Neuropsychological Research of the Policlinico Gemelli, Catholic University of Rome, Italy;2. Department of Neurology, Campus Bio-Medico University, Rome, Italy;3. IRCCS Fondazione Santa Lucia, Department of Clinical and Behavioral Neurology, Rome, Italy;1. Department of Mathematical Sciences, Michigan Technological University, Houghton, MI 49931, United States;2. Department of Epidemiology and Biostatistics, State University of New York, Albany, NY 12144, United States;1. Department of Psychology, Kobe University, Kobe, Japan;2. Department of Integrative Physiology, National Institute for Physiological Sciences, Okazaki, Japan;1. Resident, Department of Orthodontics, College of Dentistry, University of Illinois Chicago;2. Assistant Professor, Department of Electrical and Computer Engineering, College of Dentistry, University of Illinois Chicago;3. Clinical Assistant Professor, Department of Orthodontics, College of Dentistry, University of Illinois Chicago;4. Program Director, Clinic Director, Professor of Orthodontics, Department of Orthodontics, College of Dentistry, University of Illinois Chicago;6. Department Head of Orthodontics, Brodie Craniofacial Endowed Chair, Professor, Department of Orthodontics, College of Dentistry, University of Illinois Chicago;5. Professor and Department Head, Department of Oral and Maxillofacial Surgery, UIH Medical Center, Department of Oral and Maxillofacial Surgery, College of Dentistry, University of Illinois Chicago;1. Indiana University, Department of Psychological and Brain Sciences, Bloomington, IN 47405-7007, USA;2. City, University of London, Department of Psychology, London EC1V 0HB, UK |
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| Abstract: | People tend to think that streaks in random sequential events are rare and remarkable. When they actually encounter streaks, they tend to consider the underlying process as non-random. The present paper examines the time of pattern occurrences in sequences of Bernoulli trials, and shows that among all patterns of the same length, a streak is the most delayed pattern for its first occurrence. It is argued that when time is of essence, how often a pattern is to occur (mean time, or, frequency) and when a pattern is to first occur (waiting time) are different questions and bear different psychological relevance. The waiting time statistics may provide a quantitative measure to the psychological distance when people are expecting a probabilistic event, and such measure is consistent with both of the representativeness and availability heuristics in people’s perception of randomness. We discuss some of the recent empirical findings and suggest that people’s judgment and generation of random sequences may be guided by their actual experiences of the waiting time statistics. |
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