Distinctively Mathematical Explanations of Game Outcomes

The debate on distinctively mathematical explanations relies heavily on examples such as strawberry distribution and bridge crossing.I argue that 'task-based' examples do not explain physical facts; rather, they explain outcomes of abstract games that follow predefined rules.The impossibility of these tasks stems from obeying the games' rules.Modality holds due to the way the explanandum is formulated, rather than due to nomological or mathematical constraints.I develop an account of these examples as mathematical explanations of game outcomes rather than distinctively mathematical explanations of physical facts, where mathematical models enable unification and counterfactual reasoning about game outcomes across instantiations, providing explanatory power.I then show how this account can provide insights on the range of valid counterfactual inferences enabled by these explanations.