The Hot Hand Fallacy

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

Sibling Fallacy: The Gambler's Fallacy

 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 it's name, gamblers also commit this 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 the gambler's fallacy, that is, the failure to appreciate statistical independence. Just as a fair gambling device does not remember its own past, it also does not remember a gambler's past. So, a gambler's odds of winning a current bet are not affected by whether the gambler has won or lost previous ones. Roulette wheels and dice do not have memories.

Exposure:

• Can you guess which of the following is a random sequence of coin flips: "H" is heads, "T" is tails?
1. H, T, T, H, H, H, T, T, H, H, H, H, H, T, T, H, H, T, T, H
2. H, T, T, H, H, T, T, H, H, T, H, H, T, T, H, T, H, T, T, H

The first sequence is random, despite the fact that there is a run of five heads in a row, and there are a total of a dozen heads but only eight tails. The second sequence is simply the first reversed, and two of the heads changed to tails in order to remove the five head streak and balance the numbers of heads and tails to ten apiece. If you thought the second sequence was random and the first not, you were probably making the mistake of thinking that a short random sequence should resemble a long one, that is, should have an equal number of heads and tails in this case. This has been called believing in "the law of small numbers", which is not a "law" at all, but the mistake of thinking that small random samples should closely resemble large ones.

Psychological research2 has shown that people tend to underestimate how "streaky" random sequences can be. As a result of the belief in the "law" of small numbers, people may be more inclined to be surprised by streaks such as the five heads in a row in the first sequence, above. This may lead them to think that some mysterious luck or power is at work when a streak occurs that either benefits or harms a gambler; in the former case, he is "hot" and in the latter "cold".

We all are lucky on some occasions and unlucky on others, but the problem with luck is that it can only be recognized in hindsight. The fact that you've been lucky or unlucky in the immediate past is no reason to think that the good or bad luck will continue in the future.

• Ironically, the gambler's and hot hand fallacies can lead to contrary expectations about what will happen next: Suppose that someone bets on a "lucky" number, and wins several times in a row. The gambler's fallacy predicts that the lucky number will be less likely than chance to come up on the next bet, but the hot hand fallacy predicts that the lucky number is more likely to come up. This means that both predictions cannot be true, despite the fact that many gamblers probably have committed both fallacies, even on the same day, though not at the same time. So, these two forms of argument cannot both be cogent, and in fact both are uncogent.
• The so-called "hot hand" in basketball and other sports may be a different phenomenon than that discussed here, though it is still controversial. Since basketball and other sports are games of skill, it's possible that psychological factors may lead players to hit or miss in streaks greater than would be accounted for by chance. This is not the case for most gambling games, such as roulette, which are games of chance rather than skill.3

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. 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
3. Thomas Gilovich, How We Know What Isn't So: The Fallibility of Human Reason in Everyday Life (1991), pp. 11-17
No one is safe from being a victim of this fallacy. Even players who play on mobile casinos such as the ones found on casinojuggler.com are sure that if luck struck once and they won a game, they're more likely to win again in the next game, and vice versa. It seems that this fallacy transcends the medium one uses in order to play casino games. However, it can be avoided by being aware of it and changing one's thought process while gambling.