Before an animal can evaluate the benefits and costs associated with a particular behavior, it must first assess them. Since perfect information is impossible to acquire, it has been suggested that animals use simple rules of thumb to acquire information. The use of rules, however, may lead to substantially inaccurate perceptions. In this article, we present the results of a dynamic optimization model developed to study the opportunity for the evolution of rules of thumb for predation hazard assessment. There are four main conclusions from this model. First, selection will not always favor perfect estimates, if one assumes there is some cost in acquiring accurate information. There is a zone of tolerance where inaccurate perceptions perform just as well as perfect knowledge of predation hazard. This implies that animals need not have perfect, only sufficient, information in order to behave optimally. Second, this zone of tolerance is generally shifted toward overestimating predation hazard: animals that overestimate hazard will have a lower mortality than animals that underestimate hazard. Third, animals should attempt to track fluctuating predation hazard rather than act on the average predation hazard. Finally, the model is robust: several simplying assumptions can be relaxed, and the same general conclusions are reached. We suggest instances where animals are using simple rules to assess predation hazard and outline an experimental protocol to study the use of rules of thumb for predation hazard assessment.