Chimpanzees, bonobos, and human foragers share a fission-fusion social system and a mating system of joint male resource defense polygyny. Within-community skew in male strength varies among and within species. In this study, we extend a mathematical model of within-group male coalition formation among primates to derive the conditions for between-community conflicts in the form of raids. We show that the main factor affecting the presence of successful raiding is the likelihood of major discrepancies in party strength, which are set by party size distributions (and thus community size) and the skew in strength. This study confirms the functional similarities between the raiding of chimpanzees and human foragers, and it supports the "imbalance of power" hypothesis for raiding. However, it also proposes two amendments to this model. First, the absence of raiding in bonobos may be attributable more to potential female involvement in defense against raids, which increases the size of defensive coalitions. Second, the model attributes some of the raiding in humans to major contrasts in instantaneous fighting ability created by surprise raids on unarmed victims; it also draws attention to the distinction between minor raids and major raids that involve multiple bands of the same community.