A fallacious "Gambler's Fallacy"? Commentary on Xu and Harvey (2014).

In their recent article in Cognition, Xu and Harvey (2014) suggested that people who placed wagers on an online gambling site demonstrated very different wagering preferences depending on whether they were on winning or losing streaks. Specifically, they reported that people on winning streaks were more likely to win their subsequent wagers because they chose increasingly "safer," higher-probability bets as the win streak continued. People on losing streaks were more likely to lose their subsequent wagers because they chose "riskier," lower-probability wagers as the losing streak progressed. The authors suggested that individuals on winning and losing streaks both fell prey to the Gambler's Fallacy. Specifically, individuals on winning streaks combatted their expectancy to lose soon by choosing higher-probability wagers (with lower payoffs). Conversely, people on losing streaks expected to win soon and thus preferred lower-probability wagers with higher payoffs. Though their paper is fascinating and contains a remarkable data set, we note that the statistical methods employed by Xu and Harvey are prone to a serious selection bias, such that participants on winning or losing streaks may have already been choosing safer and riskier wagers, respectively, prior to the beginning of their streaks. We suggest easy, intuitive analyses to determine whether the effects reported in Xu and Harvey (2014) are real.