We report on the results of an experiment with a statistical choice task involving the toss of a fair coin. In our experiment, participants had to decide whether they were willing to pay a price to switch from betting on the future performance of one player to betting on that of another player. The switch was from a player who had been previously less successful in betting on five coin flips to another one who had been more successful in the same task. We conducted a treatment with the Becker–DeGroot–Marschak mechanism and one in which participants were faced with a fixed price. In both cases, participants exhibit a strong bias towards placing their bets on players with a good guessing history in the coin toss task. Participants’ behaviour is compatible with prescriptive luck beliefs, that is, the idea that luck is a somehow deterministic and personal attribute.