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Gambler’s Fallacy: Next One’s A Winner!

Have You Ever?

You and your friends are playing a board game, and you are one space away from victory;  three game pieces are in your home base, anxiously awaiting the rolling of a “one” to move the last piece in and secure a win. On your next turn, you roll a five. The next turn, a four. The next turn, a two. After eight turns, your friends are closing in on your lead, and you have yet to roll a one. You think to yourself, “Ok, it’s been eight turns since I’ve rolled a one. It has to be next!”

Explanation

Each number on the die has a ⅙ probability of being rolled. After a slew of losses-- or undesirable rolls-- why would this probability change and favor the rolling of a 1? It wouldn't. But, we think it will because of the Gambler’s fallacy. We believe that a certain outcome, such as rolling a one, is overdue because of previous circumstances, like the string of bad rolls. In actuality, these events are independent. 

Definition: Gambler’s Fallacy

The Gambler’s fallacy is the belief that a random event or outcome with a fixed probability will be more or less likely to occur with an increased number of trials. Studies have shown that the strength of this belief increases as the number of trials increases. 

History

The Gambler’s fallacy was first introduced to literature in 1796 in Laplace’s A Philosophical Essay on Probabilities, illustrated through a father’s prediction for the sex of his unborn child. Given his assumption that males and females are born in a 50/50 ratio, the man inferred a previous high male birth rate in a neighboring village would indicate a future high female birth rate in his village. Laplace claimed this illogical conclusion was made based on personal experience, and not objective statistical reasoning. The sex of previous children does not determine the sex of subsequent children as these events are statistically independent, with each sex having an equal probability.  

A noteworthy instance of the Gambler’s fallacy took place in Monte Carlo in 1913. After a roulette ball fell on black twenty-six consecutive times, people rushed to collectively bet millions on the roulette ball falling on red next. The casino-goers were so certain red would come up next given the inconceivable streak of black, but instead, they collectively lost millions when it, again, fell on black. Their enormous loss can be attributed to the Gambler’s fallacy-- they thought red was “due” to appear, even though there was no such guarantee. 

The Gambler’s fallacy is the result of a heightened sense of self-efficacy. Imbued with the belief that predicting outcomes of purely random events is viable, people often ignore basic statistics to determine outcomes of said events. Studies show people with higher IQs tend to fall victim to the Gambler’s fallacy more often than those with lower IQs. People with higher IQs instinctively seek out patterns and overthink many situations, thus leaving them vulnerable to the Gambler’s fallacy.

Applying It

Investors in stock often fall victim to the Gambler’s fallacy. After a consistent, upward trend in the market, many expect that share prices are due to fall, and thus they sell their shares. Day-to-day fluctuations in share prices are assumed to be generally random, but the Gambler's fallacy tricks some into thinking they are predictable. 

The Gambler’s fallacy also occurs when judges decide on cases. Studies show a judge is more likely to deny someone asylum after issuing several previous acceptances. While this is not prediction-based, it still epitomizes the principle of the Gambler’s fallacy: after a streak of one outcome, a different outcome is “overdue.” Each case should be considered independently given that they’re presented to the judge in a random order, but it’s clear many judges let the Gambler’s fallacy negatively influence their decision-making. 

It’s important to recognize how and when the Gambler’s fallacy influences decision-making and predictions. It can unknowingly guide decisions made by people in positions of power in high-stakes situations, such as the courtroom, the stock market, and the lottery. These choices can have lasting effects on the greater population, even determining whether individuals live or die. If you think a decision has been unfairly made on account of the Gambler’s fallacy, it’s crucial to speak up about it and bring justice to the situation. 

Think Further

  1. Can you think of a real-world situation where you personally might fall victim to the Gambler’s fallacy?
  2. How can you reduce your vulnerability to the Gambler’s fallacy?
  3. Aside from the judge example, how might the Gambler’s fallacy negatively affect someone in the context of social justice?

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  1. 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
  2. Robson, D. (2020, February 17). The simple maths error that can lead to bankruptcy. BBC. https://www.bbc.com/worklife/article/20200217-the-simple-maths-error-that-can-lead-to-bankruptcy 
  3. Chen, D. L., Moskowitz, T. J., & Shue, K. (2014). Decision-Making Under the Gambler’s Fallacy: Evidence from Asylum Judges, Loan Officers, and Baseball Umpires. SSRN Electronic Journal. doi:10.2139/ssrn.2635524
  4. Laplace, P. S. (1902). A philosophical essay on probabilities. New York: J. Wiley & Sons.