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.
|People who had a run of wins had a higher probability of winning their next bet|
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.
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
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.