The Hot Hand Fallacy
Type: Probabilistic Fallacy
A gambler has had a streak of luck.
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 increase their wagers to take advantage of their good luck, they commit this fallacy. The fundamental mistake 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 previous bets.
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: failing to appreciate the fact that a random event is not affected by past wins or losses.
Ironically, the gambler's and hot hand fallacies can lead to contrary expectations about what will happen next: Suppose that a gambler bets on his lucky number, and wins several times in a row. The gambler's fallacy predicts that his 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.
Sibling Fallacy: The Gambler's Fallacy
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).