Gambler's Fallacy

by

Ulrike Hahn

• LAST REVIEWED: 17 May 2016
• LAST MODIFIED: 29 November 2011
• DOI: 10.1093/obo/9780199828340-0027

Introduction

The Gambler’s Fallacy is a mistaken belief about sequences of random events. Observing, for example, a long run of “black” on the roulette wheel leads to an expectation that “red” is now more likely to occur on the next trial. In other words, the Gambler’s Fallacy is the belief that a “run” or “streak” of a given outcome lowers the probability of observing that outcome on the next trial. The Gambler’s Fallacy is one of several biases or errors found in people’s perceptions of randomness. For statistically independent events such as the outcomes of a coin toss or a roulette wheel, there is simply no connection between events; coins and roulette wheels have no memory, and there can consequently be no systematic connection between the outcomes on successive trials. Nevertheless, the Gambler’s Fallacy can feel intuitively quite compelling, even to the statistically minded, and while it has often been fashionable within psychology to highlight humans’ irrationality and cognitive frailty, understanding the nature of chance really requires knowledge of probability theory, combinatorics, and randomness. Without these tools, fallacious and non-fallacious beliefs about chance cannot reliably be distinguished (see Why the Gambler’s Fallacy is a Fallacy).There are presently no monographs or introductions specifically on the Gambler’s Fallacy, so an understanding of the topic must be assembled from a range of different sources.

Introductory Works

Very brief but accessible first descriptions of the Gambler’s Fallacy itself can be found in many texts, such as Gardner 1978, Hardman 2009, and Howell 2010.

• Gardner, Martin. 1978. Aha! Insight. New York: Freeman.

  Contains the most accessible introduction to the Gambler’s Fallacy there could ever be.

• Hardman, David. 2009. Judgment and decision making: Psychological perspectives. Malden, MA: Wiley-Blackwell.

  An introductory textbook on judgment decision making; this contains a brief and very general introduction to the Gambler’s Fallacy.

• Howell, David C. 2010. Statistical methods for psychology. 7th ed. Boston: Wadsworth.

  Most introductory statistics textbooks contain introductions to probability and combinatorics. For a readily accessible and widely available basic introduction, see chapter 5 of this book; this chapter also mentions the Gambler’s Fallacy (or “law of averages”).