We empirically investigate the possibility that a decision maker prefers to avoid making a decision and instead delegates it to an external device, e.g., a coin flip. A large data set from the centralized clearinghouse for university admissions in Germany shows a choice pattern of applicants that is consistent with coin flipping and that entails substantial consequences for the matching outcome. In a series of experiments capturing the relevant features of university choice, participants often choose lotteries between allocations rather than certain allocations. This contradicts most theories of choice such as expected utility. A survey among university applicants links their choices to the experiments and confirms that the choice of random allocations is intentional.