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

We demonstrate that lottery markets can exhibit the “hot-hand" phenomenon, where past winning numbers tend to have greater share of the betting proportion in future draws, even though past and the future events are independent. This is surprising, as works by Clotfelter and Cook (1993) and Terrell (1994) have documented instead the presence of an opposite effect, the “gambler's fallacy", in the US lottery market, which means that the amount of money bet on a particular number falls after the number is drawn. Current literature also suggests that gambler's fallacy prevails when random numbers are generated by mechanical devices, such as in lottery games (e.g., Ayton and Fisher (2004), Burns and Corpus (2004), Caruso et al. (2010)). We use two sets of naturally occurred data to show that both the gambler's fallacy and hot-hand fallacy can exist in different types of lottery games. We then run online experimental studies that mimic lottery games with one, two, or three winning numbers. Our experiment results show that lottery game design leads to the differences in behaviors, in particular, while a single-prize game leads to strong presence of the gambler's fallacy, we observe a significantly increases  in hot-hand behaviors in multiple-prizes games with two or three winning numbers. Strong evidence show that participants tend to underestimate the chance of observing the same winning numbers in consecutive draws, and when confronted with unexpected repetitions, they are more likely to switch from their predisposed behavior (gambler's fallacy) to its counterpart (hot-hand fallacy).