Many theories in cognitive science assume that people possess a repertoire of strategies or a "toolbox" from which they choose depending on the situation. This approach suffers from the problem that the number of assumed strategies is often not constrained and may be extended post-hoc to improve the fit to the data. This makes it difficult to rigorously test and compare strategy repertoire models. To prevent this "strategy sprawl", a criterion is necessary to decide how many strategies a toolbox should include. Here, Bayesian statistics provide a powerful tool to evaluate toolboxes of different sizes based on their marginal likelihoods. The present work illustrates how such a Bayesian approach can be implemented and demonstrates its applicability by means of parameter recovery studies. Our approach also makes the novel contribution of showing how Bayesian statistics allow testing the strategy repertoire theory against alternative decision theories.