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The Hot Hand Fallacy

Taxonomy: Logical Fallacy > Formal Fallacy > Probabilistic Fallacy > The Hot Hand Fallacy1

Sibling Fallacy: The Gambler's Fallacy

Forms
A gambler has had a streak of good luck.
Therefore, the gambler is "hot" and the good luck will continue at a probability greater than chance.
A gambler has had a streak of bad luck.
Therefore, the gambler is "cold" and the bad luck will continue at a probability greater than chance.

Exposition:

This fallacy is committed every day in casinos around the world, whenever a gambler thinks he's "hot". When gamblers are on winning streaks, and keep betting or increasing their wagers to take advantage of their good luck, they commit this fallacy. Despite its name, gamblers also commit the fallacy when they think that they're "cold", and stop betting or decrease their wagers because they're on a losing streak. This is still the "hot hand" fallacy, because the logical mistake is the same.

The fundamental error is the same as in its sibling fallacy, the Gambler's Fallacy, namely, the failure to appreciate statistical independence. Two events are independent when the occurrence of one does not change the probability of the occurrence of the other2. For instance, if you roll a die and flip a coin at the same time, then whether the coin comes up heads or tails does not affect the number that comes up on the die. So, a roll of a die and flip of a coin are statistically independent events. In a fair gambling device, such as an unloaded die, the number that comes up in one roll of the die does not affect the number that comes up in a different roll, that is, the rolls of the die are probabilistically independent. This is what is meant by a "fair" gambling device.

Both the Hot Hand Fallacy and the Gambler's Fallacy are tempting mistakes to commit. How can you avoid doing so? One way to keep statistical independence in mind is by reminding yourself that fair gambling devices do not have memories. Coins and dice and roulette wheels do not remember what they've done in the past. Also, just as a fair gambling device does not remember its own past, it does not remember a gambler's past. So, a gambler's odds of winning a current bet are not affected by whether he or she has won or lost previous ones.

Exposure:

Notes:

  1. James Sundali & Rachel Croson, "Biases in Casino Betting: The Hot Hand and the Gambler's Fallacy", Judgment and Decision Making, Vol. 1, No. 1, (7/2006).
  2. Roger Porkess, The Harper Collins Dictionary of Statistics (1996), see under: "independent events". In probability theory, event E1 and event E2 are independent if and only if P(E1) = P(E1|E2), that is, the probability of E1 occurring is the same as the probability of it happening if E2 occurs. For more on probability theory, see the entry for Probabilistic Fallacy.
  3. Amos Tversky & Daniel Kahneman, "Belief in the Law of Small Numbers", in Judgment Under Uncertainty: Heuristics and Biases (1985), Kahneman, Paul Slovic & Tversky, editors, pp. 23-31.
  4. Thomas Gilovich, How We Know What Isn't So: The Fallibility of Human Reason in Everyday Life (1991), pp. 11-17.

Revised: 11/18/2020


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