Standard economic models assume that the demand for expert predictions arises only under the conditions in which individuals are uncertain about the underlying process generating the data and there is a strong belief that past performances predict future performances. We set up the strongest possible test of these assumptions. In contrast to the theoretical suggestions made in the literature, people are willing to pay for predictions of truly random outcomes after witnessing only a short streak of accurate predictions live in the lab. We discuss potential explanations and implications of such irrational learning in the contexts of economics and finance.