The class of symmetric path-independent models with experimenter-controlled events is considered in conjunction with two-choice probability learning experiments. Various refinements of the notion of probability matching are defined, and the incidence of these properties within this class is studied. It is shown that the linear models are the only models of this class that predict a certain phenomenon that we call stationary probability matching. It is also shown that models within this class that possess an additional property called marginal constancy predict approximate probability matching.