Suppose a decision maker (DM), in the language of Anscombe and Aumann (1963), has preferences over acts (horse-race lotteries) that satisfy the von Neumann and Morgenstern (1944) axioms for objective lotteries (constant acts) and Anscombe and Aumann's (1963) Axioms of Reversal of Order and Dominance. This DM may have preferences that accommodate ambiguity aversion. Suppose the DM can choose acts objectively randomly (by flipping her own fair coin, for instance). Suppose the DM is able to (has the willpower to) commit to her ex-ante choice of a possibly self-generated random act. Then there is no set of decision problems an analyst can give this DM in which the DM can be shown to be ambiguity-averse.