We examine a number of probabilistic choice models in which people might form their beliefs to play their strategies in a game theoretic setting in order to propose alternative equilibrium concepts to the Nash equilibrium. In particular, we evaluate the Blavatskyy model, Returns Based Beliefs (RBB) model, Quantal Response Equilibrium (QRE) model, Boundedly Rational Nash Equilibrium (BRNE) model and the Utility Proportional Beliefs (UPB) model. We outline the foundational axioms for these models and fully explicate them in terms of probabilistic actions, probabilistic beliefs and their epistemic characterizations. We test the model predictions using empirical data and show which models perform better under which conditions. We also extend the Blavatskyy model which was developed to consider games with two actions to cases where there are three or more actions. We provide a nuanced understanding of how different types of probabilistic choice models might predict better than others.