In this paper we aim to investigate how the complexity of a decision-task may change an agents strategic behaviour as a result of increased cognitive fatigue. In this framework, complexity is defined as a function of the number of outcomes in a lottery. Using Bayesian inference techniques, we quantitatively specify and estimate adaptive toolbox models of cognition, which we rigorously test against popular expectation based models; modified to account for complexity aversion. We find that for the majority of the subjects, a toolbox model performs best both in-sample, and with regards to its predictive capacity out-of-sample, suggesting that individuals result to heuristics when the complexity of a task overwhelms their cognitive load.