We study multiple-prize contests where the set of prizes to be awarded is a random variable. We determine the unique symmetric Nash equilibrium of the contest game. We analyze the equilibrium outcome from the perspective of a contest designer aiming at maximizing the aggregate contest expenditure. We show that the aggregate contest expenditure is decreasing in the risk on the number of prizes (in the sense of second-order stochastic dominance) and is increasing in the number of contestants. Accordingly, a contest designer aiming at maximizing the aggregate contest expenditure should always reveal the number of prizes to be awarded and open the contest game to all potential contestants.