The Law of Large Numbers and Beliefs about Luck: An Asymmetry in Recognition of the Risks and Benefits of Chance

Three studies (n = 655) examined beliefs about chance, focusing on participants’ recognition of some implications of the principle that small samples are more subject to chance fluctuation. Participants consistently demonstrated an asymmetry in their views about luck. Although they tended to recognize the possible decrements of chance fluctuation, they consistently failed to appreciate its potential benefits, especially in a context in which the outcome was largely contingent on factors under their personal control. Participants preferred a 100 question exam to a 10 question exam, correctly believing that an atypically low score was more likely with fewer questions. In contrast, they failed to recognize that an atypically high score was also more likely with fewer questions, and preferred the long exam even when there was no possible detriment from a low score and a potential benefit from a high one. This asymmetry was reduced, although not eliminated, in a ball drawing task in which the outcome was entirely chance determined. Results suggest that people associate chance fluctuation with bad luck more than with good luck, and are therefore reluctant to exchange control for the possible benefits of chance.