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Cognitive biases · Probability

Gambler's fallacy

We expect random streaks to 'even out', as if chance had a memory.

What it is

The gambler’s fallacy is the belief that after a run of one outcome, the opposite outcome is “due”. For truly independent events, such as fair coin flips, dice rolls or lottery draws, past results do not change future odds. Chance has no memory.

An everyday example

Noah has played the same scratch-card game at the corner store for months without a big win. “I’ve lost so many times, I must be close,” he tells himself, and buys five cards instead of one.

Each card’s odds were fixed when it was printed. A long losing streak does not make the next card any more likely to win.

Why it happens

Tversky and Kahneman (1971) argued that people expect even small samples to look like the overall process that produced them. We know a fair coin lands heads about half the time, so we expect any short run to look roughly half and half. A streak of five heads feels “unbalanced”, and we expect tails to correct it.

In reality, balancing happens only over very large numbers of trials, and it happens by dilution, not correction.

How to counter it

  • Ask whether events are independent. Coin flips, roulette spins and lottery draws are. Many real-life events, like weather or a team’s form, are not, so think about which kind you face.
  • Say the odds out loud. “This draw is still 1 in 1,000, the same as last time.”
  • Don’t chase losses. If you gamble for fun, set a budget in advance and do not raise it after a losing run.
  • Watch for it in sequences of decisions. When reviewing many cases in a row, judge each one on its merits, not on how the last few went.

What the research shows

In Maryland’s daily numbers lottery, betting on a number dropped sharply right after it was drawn and took months to recover, consistent with players believing it was now less likely to come up (Clotfelter & Cook, 1993).

The pattern also appears among professionals. Chen, Moskowitz and Shue (2016) found that asylum judges, loan officers and baseball umpires were slightly less likely to make the same decision twice in a row than the merits of the cases would predict. The effect was stronger among less experienced decision makers and after longer streaks. The authors note that other explanations, such as contrast effects, cannot be fully ruled out.

Related biases

  • Illusion of control — We often feel we can steer outcomes that are mostly down to luck, especially when we get to make choices.
  • Conjunction fallacy — We rate a detailed story as more likely than a simpler one, even though logically it can't be.
  • Base-rate neglect — We focus on vivid details of a case and forget how common the outcome is overall.

Sources

  1. Tversky, A., & Kahneman, D. (1971). Belief in the law of small numbers. Psychological Bulletin, 76(2), 105–110. https://doi.org/10.1037/h0031322
  2. Clotfelter, C. T., & Cook, P. J. (1993). The "gambler's fallacy" in lottery play. Management Science, 39(12), 1521–1525. https://doi.org/10.1287/mnsc.39.12.1521
  3. 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. Quarterly Journal of Economics, 131(3), 1181–1242. https://doi.org/10.1093/qje/qjw017

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