Why do we think a random event is more or less likely to occur if it happened several times in the past?

Gambler's Fallacy

, explained.
Bias

What is the Gambler’s fallacy?

The gambler’s fallacy describes our belief that the probability of a random event occurring in the future is influenced by previous instances of that type of event.

Illustration of a stick figure standing next to a table, holding dice in one hand. Above the figure's head is a large thought bubble labeled 'The Universe's Master Plan,' containing a colorful, swirling spiral. Inside the thought bubble, there is another bubble with the text 'It is time for her to roll a 6.' The image is titled 'Gambler's Fallacy.'

Where this bias occurs

Consider the following hypothetical: Jane loves playing Blackjack, and she’s pretty good at it. But for the last few days, she’s been on a losing streak. Jane has had a few losing streaks in her many years of gambling, and she’s noticed a pattern: they usually end the fifth trip to the casino, when she wins big.

Today is the fifth day of the losing streak she currently finds herself in. She goes into the casino with a grin, knowing that today is her day.

Many hours and many games of Blackjack later, Jane is defeated. She has lost an enormous amount of money. “How could this be?”, Jane asks herself. She always wins on the fifth day!

Jane’s belief that she would find success in the casino that day, and the dismay that followed her unforeseen failure, was a result of gambler’s fallacy. The pattern Jane saw in her gambling history led her to believe that there was a high probability that she would win playing Blackjack. The problem is, the two aren’t causally connected. The length of her past losing streaks has no bearing on how likely she is to end this losing streak.

Related Biases

Sources

  1. Stevenson and Mihnea C. Moldoveanu, H. (2014, August 01). The Power of Predictability. Retrieved July 08, 2020, from https://hbr.org/1995/07/the-power-of-predictability
  2. Tversky, A., & Kahneman, D. (1974). Judgment under Uncertainty: Heuristics and Biases. Science, 185(4157), 1124-1131. doi:10.1126/science.185.4157.1124
  3. Effectiviology. (n.d.). Retrieved July 05, 2020, from https://effectiviology.com/gamblers-fallacy/
  4. Effectiviology. (n.d.). Retrieved July 05, 2020, from https://effectiviology.com/gamblers-fallacy/
  5. Tversky, A., & Kahneman, D. (1974). Judgment under Uncertainty: Heuristics and Biases. Science, 185(4157), 1124-1131. doi:10.1126/science.185.4157.1124
  6. Effectiviology. (n.d.). Retrieved July 05, 2020, from https://effectiviology.com/gamblers-fallacy/
  7. Barron, G., & Leider, S. (2010). The role of experience in the Gambler's Fallacy. Journal of Behavioral Decision Making, 23(1), 117-129. doi:10.1002/bdm.676
  8. Croson, R., & Sundali, J. (2005). The Gambler’s Fallacy and the Hot Hand: Empirical Data from Casinos. Journal of Risk and Uncertainty, 30(3), 195-209. doi:10.1007/s11166-005-1153-2
  9. Owen, A. M. (2011). The Monte Carlo fallacy. Medical Journal of Australia, 195(7), 421-421. doi:10.5694/mja11.10937
  10. Constantinides, G. M. (1985). The Disposition to Sell Winners Too Early and Ride Losers Too Long: Theory and Evidence: Discussion. The Journal of Finance, 40(3), 791. doi:10.2307/2327803
  11. Croson, R., & Sundali, J. (2005). The Gambler’s Fallacy and the Hot Hand: Empirical Data from Casinos. Journal of Risk and Uncertainty, 30(3), 195-209. doi:10.1007/s11166-005-1153-2
  12. Chen, D. L., Moskowitz, T. J., & Shue, K. (2016). Decision Making Under the Gambler’s Fallacy: Evidence from Asylum Judges, Loan Officers, and Baseball Umpires. The Quarterly Journal of Economics, 131(3), 1181-1242. https://doi.org/10.1093/qje/qjw017
  13. Farmer, G. D., Warren, P. A., & Hahn, U. (2017). Who "believes" in the Gambler's Fallacy and why? Journal of experimental psychology. General, 146(1), 63–76. https://doi.org/10.1037/xge0000245
  14. Croson, R., & Sundali, J. (2005). The gambler’s fallacy and the hot hand: Empirical data from casinos. Journal of Risk and Uncertainty, 30(3), 195–209. https://doi.org/10.1007/s11166-005-1153-2 
  15. Belet, S., & Flegg, J. (2018, September 6). We’ve crunched the numbers in McDonald’s Monopoly challenge to find your chance of winning. The Conversation. https://theconversation.com/weve-crunched-the-numbers-in-mcdonalds-monopoly-challenge-to-find-your-chance-of-winning-102763
  16. Eliot, L. (2021, December 23). Using AI to overcome gambler's fallacy that pervades human judges. SSRN. https://doi.org/10.2139/ssrn.3992208

About the Authors

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Dan Pilat

Dan is a Co-Founder and Managing Director at The Decision Lab. He is a bestselling author of Intention - a book he wrote with Wiley on the mindful application of behavioral science in organizations. Dan has a background in organizational decision making, with a BComm in Decision & Information Systems from McGill University. He has worked on enterprise-level behavioral architecture at TD Securities and BMO Capital Markets, where he advised management on the implementation of systems processing billions of dollars per week. Driven by an appetite for the latest in technology, Dan created a course on business intelligence and lectured at McGill University, and has applied behavioral science to topics such as augmented and virtual reality.

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Dr. Sekoul Krastev

Sekoul is a Co-Founder and Managing Director at The Decision Lab. He is a bestselling author of Intention - a book he wrote with Wiley on the mindful application of behavioral science in organizations. A decision scientist with a PhD in Decision Neuroscience from McGill University, Sekoul's work has been featured in peer-reviewed journals and has been presented at conferences around the world. Sekoul previously advised management on innovation and engagement strategy at The Boston Consulting Group as well as on online media strategy at Google. He has a deep interest in the applications of behavioral science to new technology and has published on these topics in places such as the Huffington Post and Strategy & Business.

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