Under uncertainty, firms risk bankruptcy. We ask, in symmetric duopoly with stochastic demand, what happens when one firm minimizes the probability of negative profits while the other maximizes expected profits. When fixed costs are small, a firm can reduce the likelihood of negative profits. However, under a large fixed cost, the chance of negative profits increases upon deviation from a profit‐maximizing strategy. In any event, if one firm adopts a safety‐first strategy, the other firm has higher profits and a better survival chance by maximizing expected profit. Finally, we compare a profit maximizing to a safety‐first strategy in relation to ownership and control in firms.