Suboptimality of Probability Matching: A Formal Characterization, a Graphical Analysis and an Impulse Balance Interpretation

We characterize the suboptimality of probability matching in prediction tasks with an arbitrary (finite) number of equally rewarded, independent and identically distributed outcomes and an arbitrary number of repetitions, for deterministic, randomized and history-dependent guessing. The characterization gives the condition under which probability matching attains the maximal expected payoff and quantifies the loss it entails otherwise. For the common case of binary prediction tasks, we also provide a graphical representation of the result. Finally, we relate probability matching to impulse balance equilibrium theory and show when probability matching is consistent with its predictions.