Consumers often lack information about how online services collect, use and protect their data. Therefore, transparency is viewed as an essential prerequisite to support consumers in making informed privacy decisions. So far, the literature has primarily studied the consequences of transparency in different data disclosure contexts. However, whether and when individuals actually prefer transparency about privacy risks when given a chance to avoid it remains an open research question. Thus, we investigate individuals’ choices between varying levels of transparency about uncertain losses of personal data. In a randomized controlled online experiment based on a between-subjects Ellsberg-type design, subjects repeatedly choose between a situation of risk, where a loss of personal data will occur with a known probability, and a situation of ambiguity, where a data loss will occur with an unknown probability. By eliciting subjects’ revealed preferences in a controlled environment, we provide novel insights into why and when individuals may avoid transparency about privacy risks. In particular, we investigate whether subjects exhibit ambiguity aversion as found for uncertain monetary losses by previous studies. Moreover, we vary the general probability of a data loss in the experiment to analyze whether transparency preferences are contingent on the loss probability. Altogether, these insights contribute to a better understanding of whether individuals actually make use of transparency about privacy risks and thus shed light on firms’ incentives to be transparent about their data use and the associated risks.