We experimentally show that game complexity systematically influences individuals’ strategic sophistication within a refined Ring Game framework. Our novel identification strategy for higher-order rationality enables us to examine three dimensions of complexity—Informational Complexity, Structural Complexity, and the Salience of Strategy—within a unified experimental setting. We are able to identify the ability bounds of players by controlling for subjects’ beliefs about others, requiring them to interact only with a computerized opponent. Our findings reveal that all three complexity dimensions significantly impact observed Level-k behaviour, albeit in distinct ways. Participants tend to exhibit higher levels of strategic sophistication when payoff matrix entropy is lower, when the Nash equilibrium requires more iterative reasoning, and when a salient dominant strategy is present. Moreover, prior experience with strategic games plays a crucial role in individuals’ ability to engage in iterative reasoning. These results highlight that strategic sophistication is neither an inherent nor a fixed trait but is instead shaped by the complexity of the decision environment and prior experience.