How Experience Confirms the Gambler's Fallacy when Sample Size is Neglected

Abstract

The Gambler's Fallacy is the mistaken belief that random sequences have a systematic tendency towards reversal, i.e. that streaks of similar outcomes are more likely to end than continue. Despite broad empirical support for gambler´s fallacy beliefs, there exists little formal explanation of why such beliefs persist. We present a simple model in which an individual formulates his beliefs about the probability of success given recent success via repeated exposure to random sequences. For each sequence he focuses on the proportion of success given recent success and then updates his beliefs, but (partially) neglects sample size. This results in probability beliefs which, in the limit, are smal..