Study 1 used two scenarios depicting provocations to investigate whether prisoners' willingness to engage in physical aggression would vary according to the perceived fighting ability (Resource Holding Power [RHP]) of the opponent. RHP was operationalized in terms of three levels of the size, number of allies, and reputation. The sample (both sexes; N=1,253) was taken from a range of British prisons. Unexpectedly, the prisoners said that they would be less likely to attack a weaker opponent than an equally matched one. The predicted decline from equally matched to more formidable opponents was found only under some conditions. A further sample of male prisoners (N=260), completed a similar provocation scenario, with response options covering fear, several forms of aggression, the importance of the provocation for reputation, and that the provocation was unimportant. Fear increased with RHP as predicted. Lower physical aggression to a low RHP opponent was again found, and it was associated with a lesser impact on reputation of an insult from this source. There was also a lower likelihood of responding with physical aggression to a high RHP opponent, as originally predicted. Implications of the findings for motivational theories of aggression are discussed, and also the applicability to humans of concepts from game theory models of the evolution of fighting strategies.