The outcomes of agonistic interactions modulate access to resources and thereby affect fitness. Success in agonistic encounters may depend on intrinsic physical and physiological performance, and on social experience. Here we test the hypothesis that previous experience will override physical strength in determining the outcome of fights in the freshwater crayfish Cherax dispar. Between unfamiliar opponents, greater chelae closing force significantly increases the chances of winning. However, even when the chelae of the original winners were disabled, the winners kept on winning against the same opponents after 30min and 24h. This winner effect disappeared when previous winners encountered unfamiliar individuals. Similarly, a previous loss did not affect the outcomes of subsequent encounters with unknown crayfish. We suggest that this prolonged recognition of individuals and their relative fighting ability is a mechanism that can reduce the number of agonistic encounters experienced by individuals.