Computational models of intuition typically focus on describing cognitive implementations of intuitive decision-making. In this commentary, we highlight several ways in which formal models can be used to consider a different perspective: the evolutionary and social origins of intuition. Why should intuitions have come to function as they do? We consider three case studies that demonstrate how introducing evolutionary game theory into the psychological study of intuition can help answer questions about the origins of intuitive processes. These case studies demonstrate why we should expect (i) intuition to persist within a population even when other forms of cognition perform better; (ii) intuition to favor cooperation rather than selfishness; and (iii) intuitive cooperators to be trusted more than people who cooperate after carefully calculating costs and benefits.