The analysis of horizontal mergers hinges on a tradeoff between unilateral effects and efficiency gains. The article examines the role of uncertainty (on the efficiency gains) in this tradeoff. Common wisdom is that the antitrust authorities should be very cautious about random gains. Our results show that dismissing efficiency gains on the sole ground that they are uncertain would not be theoretically founded. Indeed, the attitude towards uncertainty depends on the curvature of the social objective function. We exhibit a number of situations where the objective is convex in the efficiency gains, implying that competition authorities should welcome the risk for a given expectation of efficiency gains. Implications for empirical merger analysis are exposed.