Gamblers have "hot hands" because they believe in the gambler's fallacy

WSJ

Gamblers are prone to two key fantasies. First, they tend to believe in the hot hand: If you're winning, you'll probably keep winning. Second, they often succumb to the "gambler's fallacy," or the belief that getting heads nine times in a row makes the chances of tails higher on the 10th try.

A new paper from Britain reports that the first of those fantasies is no fantasy at all—probably because gamblers believe in the second.

Scientists at University College London analyzed 565,915 bets on a variety of sports made by 776 online gamblers during 2010 [that's 729 sports bets a year each!] and found that the probability of winning was 48% (which is why bookmaking is profitable). But they also found that each time a bet was won, the probability of a bettor's next wager succeeding actually went up. Bettors with six wins in a row had an astounding 76% likelihood of success on the seventh bet—in other words, a hot hand.

Bettors on a losing streak displayed the same syndrome in reverse: With each loss, the likelihood of winning the next bet declined. After six consecutive losses, the probability of winning the next wager was just 23%.

How is this possible? According to the scientists, the answer is simple: Gamblers believe in the gambler's fallacy. The researchers noticed that, in their sample, bettors on a winning streak chose wagers with more favorable odds on subsequent bets, raising their chances of winning. It is hard to see why they would do this if they didn't believe their luck was likely to turn. Similarly, consecutive losers chose bets with worse odds, presumably because they believed themselves overdue for a change of fortune.

Winners and losers alike had embraced a fantasy about the nature of chance events that only made their luck less likely to change. Or, as the scientists put it, "The gamblers' fallacy created the hot hand." The paper says the findings could have implications for financial traders, who might respond to chance success by changing their risk preferences.

"Carry On Winning: The Gamblers' Fallacy Creates Hot Hand Effects in Online Gambling," Juemin Xu and Nigel Harvey, Cognition (May)