We propose a new model of cooperators' advantage depending neither on supplementary incentives nor on cooperators' capacity to recognize, and play selectively with, other cooperators. It depends, rather, on players' making the play-no play decision by the heuristic of projecting their own “cooperate-defect” choices onto potential partners. Cooperators offer to play more often, and fellow cooperators will more often accept their offer. When certain boundary conditions are met, this results in a higher expected payoff for cooperators than for defectors. Empirical support for this heuristic is suggested by expectations data from related social dilemma experiments. Moreover, its use can be justified in Bayesean terms. Our model brings behavioral decision theory's “cognitive miser” paradigm to bear on interdisciplinary concern with the evolution of cooperative behavior and shows how, if other mechanisms provide a suitable “initial kick,” cooperation can evolve in the absence of iteration and in large, mobile societies.