A self-fulfilling fallacy?

Post written by guest host Tom Stafford, a psychologist from the University of Sheffield who is a regular contributor to the Mind Hacks blog, for the BPS Research Digest.

Lady Luck is fickle, but many of us believe we can read her mood. A new study of one year's worth of bets made via an online betting site shows that gamblers' attempts to predict when their luck will turn has some unexpected consequences.

A common error in judging probabilities is known as the Gambler's Fallacy. This is the belief that independent chance events have an obligation to 'even themselves out' over the short term, so that a run of wins makes a loss more likely, and vice versa. An opposite error is the belief that a run of good luck predicts more good luck – when a basketball player succeeds in a number of successive shots, they are said to have a 'Hot Hand', meaning a better chance of succeeding with their next shot. While the hot hand might be possible in games of skill, it is a logical impossibility for truly chance events.

Juimin Xu and Nigel Harvey from University College London, set out to study the role these fallacies might play in a highly relevant real-world setting: real bets made by people gambling online. Most psychology studies use are carried out on undergraduate psychology students, who participate as an obligatory part of their course. Hardly the strongest motivation for taking part in a study. With Xu and Harvey's sample there's no doubt the participants were sincerely motivated in their behaviour: they placed bets worth around £100 million during the 365 days of 2010. If any group had the incentive to judge correctly about their luck, this is it.

The bets from this sample were analysed for runs of wins and losses, revealing a surprising pattern. Although the bets were from unrelated events, from football matches to horse racing, people who had a run of wins had a higher probability of winning their next bet. For example, gamblers who had a run of three wins had a probability of 0.67 of winning their next bet, compared to a probability of 0.45 for those who hadn't had such a winning streak. The researchers analysed streaks of up to six wins in a row and found that the probability of winning the next bet just went up and up. The effect also held for losing steaks, so that those who lost successive bets were also more likely to lose again. The effect didn't seem to be due to skill, since a control analysis showed that the average winnings for gamblers who had long streaks of luck were the same, or perhaps even slightly lower, than for those who didn't have long streaks. The result seems to contradict the gambler's fallacy, and even our reasonable faith that bet outcomes should be independent.

The answer to the mystery was revealed when Xu and Harvey analysed the odds of the bets placed by gamblers in the middle of a streak, and the amount they staked. Gamblers who won tended to take their next bet on a safer odds than the bet they had just won, with the reverse true for people on losing streaks. This, the researchers suggest, is because they believed in the gambler's fallacy and so expected their luck to turn. This had the paradoxical effect of creating luck for those who were already winning – because they then made bets they were more likely to win – and rubbing in the bad luck of those who were losing – because they made bets which they were less likely to win and so perpetuated their losing streak.

The study is great example of how a simple phenomenon – the gambler's fallacy – can have unpredicted outcomes when studied in a complex real-world environment. Don't get too carried away by the rewards of online gambling however, the paper contains this telling detail: of all the bets analysed in the study, 178,947 were won and 192,359 were lost – giving overall odds of winning at 0.48. Enough to ensure the betting site's profit margin, and to suggest that on average you're going to lose more than you stake. Unless you're lucky.

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Xu J, & Harvey N (2014). Carry on winning: The gamblers' fallacy creates hot hand effects in online gambling. Cognition, 131 (2), 173-80 PMID: 24549140