Discrimination (for instance, along the lines of race or gender) is often prohibited in auctions. This is legally enforced by preventing the seller from explicitly biasing the rules in favor of bidders from certain groups (for example, by subsidizing their bids). In this paper, we study the efficacy of this policy in the context of a single object, independent private value setting with heterogeneous bidders. We show that restricting the seller to a using an anonymous, sealed bid auction format (or, simply, a symmetric auction) imposes virtually no restriction on her ability to discriminate. Our results highlight that the discrepancy between the superficial impartiality of the auction rules and the resulting fairness of the outcome can be extreme.