Group‐beneficial behaviors have presented a long‐standing challenge for evolutionary theory because, although their benefits are available to all group members, their costs are borne by individuals. Consequently, an individual could benefit from “cheating” their group mates by not paying the costs while still reaping the benefits. There have been many proposed evolutionary mechanisms that could favor cooperation (and disfavor cheating) in particular circumstances. However, if cooperation is still favored in some circumstances, then we might expect evolution to favor strategic cooperation, where the level of contribution toward group‐beneficial behavior is varied in response to the social context. To uncover how and why individuals should contribute toward group‐beneficial behavior across social contexts, we model strategic cooperation as an evolutionary game where players can quantitatively adjust the amount they contribute toward group‐beneficial behavior. We find that the evolutionarily stable strategy (ESS) predicts, unsurprisingly, that players should contribute in relation to their relatedness to the group. However, we surprisingly find that players often contribute to cooperation in such a way that their fitness is inverse to their relatedness to the group such that those that contribute to cooperation end up with the same return from group‐beneficial behavior, essentially removing any potential advantage of higher relatedness. These results bring to light a paradox of group‐beneficial cooperation: groups do best when they contain highly related individuals, but those with the highest relatedness to the group will often have the lowest fitness within the group.