The gambler’s fallacy prevails in lottery play

We use natural experiments in Haiti and Denmark to test recent theoretical predictions about how agents react to random events. Using player-level administrative data, we find that the average lottery player avoids numbers that recently won (the gambler’s fallacy). A small subset of players in each country exhibit the hot hand fallacy, and bet recent winners. We find no evidence of ‘streak switching,’ in which beliefs switch from the gambler’s fallacy to the hot hand fallacy as winning streaks grow. Follow-up survey data in Haiti indicate that almost all lottery players believe that some numbers are more likely to win than others, and that recent winning history is an important factor in subjective beliefs about numbers’ win probabilities.