How do animal social skills influence evolution? Complex animal social behaviors require many cognitive skills including individual recognition and observational learning. For social systems to evolve, these abilities need to be transmitted genetically or culturally and supported by the evolution of underlying neural systems. Because animal skill sets are so varied, it seems best to describe animal cognitive behaviors as being a social calculus that can change with experience, which has evolved to match and facilitate the complexity of the social system where it arose. That is, acquiring and using social information in response to a rapidly changing complex world leads to social competence enabling success in essential behavioral interactions. Here, we describe the remarkable suite of social skills discovered in the African cichlid fish Astatotilapia burtoni, including an attention hierarchy, male deception, transitive inference, the mechanistic bases of social dominance, female mate choice and the neural control of female reproductive behavior. The social calculus of this species is presented as an example of a potential causal factor in the evolution of sophisticated social behavior necessary for the evolutionary success of their social system.