Roulette wheel

The Hot Hand Fallacy

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

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 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:

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.

Source: 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).

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.