Judgment Error in Lottery Play: When the Hot-Hand Meets the Gambler’s Fallacy

We demonstrate that lottery players can be influenced to believe erroneously in the existence of “hot” numbers, where past winning numbers are perceived to have a greater probability of winning in future draws, even though past and the future events are independent. The existence of this “hot-hand” effect in lottery games is surprising, as works by Clotfelter and Cook (1993) and Terrell (1994) have documented instead the presence of the opposite effect, the “gambler’s fallacy”, in the US lottery market—which means that the amount of money bet on a particular number falls sharply after the number is drawn. We use two sets of lottery game data to show that both the gambler’s fallacy and hot-hand fallacy can prevail under different gaming environments, contingent on the design (e.g., prize structures) of the lottery games. We develop a quasi-Bayesian model that is consistent with our empirical findings to investigate the conditions in the environment that determine which fallacy dominates. Our results also provide a new explanation for the “lucky store” effect (Guryan and Kearney, 2008)—why players in the US believe that lightning will strike twice in the case of lottery vendors, but not in the case of lottery numbers.