University of Texas Health Science Center at Houston, Houston, TX, USA.
Cogn Psychol. 2010 Dec;61(4):333-42. doi: 10.1016/j.cogpsych.2010.07.001. Epub 2010 Aug 21.
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.
人们倾向于认为随机顺序事件中的连胜是罕见而引人注目的。当他们实际遇到连胜时，他们往往会认为潜在过程是非随机的。本文研究了伯努利试验序列中模式出现的时间，并表明在相同长度的所有模式中，连胜是其首次出现的延迟模式。本文认为，当时间至关重要时，模式出现的频率（平均时间，或频率）和模式首次出现的时间（等待时间）是不同的问题，具有不同的心理相关性。等待时间统计数据可以为人们期望概率事件时的心理距离提供定量衡量标准，这种衡量标准与人们对随机性的代表性和可用性启发式一致。我们讨论了一些最近的实证发现，并认为人们对随机序列的判断和生成可能受到他们对等待时间统计数据的实际经验的指导。
