In social contexts, we refer to strategic sophistication as the ability to adapt our own behavior based on the possible actions of others. In the current study, we explore the role of other-oriented attention and cognitive reflection in explaining heterogeneity in strategic sophistication. In two eye-tracking experiments, we registered eye movements of participants while playing matrix games of increasing relational complexity (2x2 and 3x3 matrices), and we analyzed individual gaze patterns to reveal the ongoing mechanisms of integration of own and others’ incentives in the current game representation. Moreover, participants completed the Cognitive Reflection Test (CRT), in addition to alternative measures of cognitive ability. In both classes of games, higher cognitive reflection levels specifically predict the ability to incorporate the counterpart’s incentives in the current model of the game, as well as higher levels of strategic sophistication. Conversely, players exhibiting low cognitive reflection tend to pay less attention to relevant transitions between the counterpart’s payoffs, and such incomplete visual analysis leads to out-of-equilibrium choices. Gaze patterns appear to completely mediate the relationship between cognitive reflection and strategic choices. Our results shed new light on the cognitive factors driving heterogeneity in strategic thinking and on theories of bounded rationality.