Numerical superiority confers a competitive advantage during contests among animal groups, shaping patterns of resource access, and, by extension, fitness. However, relative group size does not always determine the winner of intergroup contests. Smaller, presumably weaker social groups often defeat their larger neighbors, but how and when they are able to do so remains poorly understood. Models of competition between individuals suggest that location may influence contest outcome. However, because of the logistical difficulties of studying intergroup interactions, previous studies have been unable to determine how contest location and group size interact to shape relationships among groups. We address this question by using an automated radio telemetry system to study intergroup interactions among six capuchin monkey (Cebus capucinus) social groups of varying sizes. We find that the odds of winning increase with relative group size; one additional group member increases the odds of winning an interaction by 10\%. However, this effect is not uniform across space; with each 100 m that a group moves away from the center of its home range, its odds of winning an interaction decrease by 31\%. We demonstrate that contest outcome depends on an interaction between group size and location, such that small groups can defeat much larger groups near the center of their home range. The tendency of resident groups to win contests may help explain how small groups persist in areas with intense intergroup competition.