One consequence of stimulus sampling theory is the prediction of probability matching as the asymptotic response probability. That is, subjects tend to choose each alternative with the frequency of its reinforcement. This study attempts to differentiate the conditions which lead to "matching" behavior from those which lead to "maximizing" and to develop a mathematical model for this behavior. The experimental results indicate that the prediction of probability matching does not obtain. Therefore, it would seem to be probable that the stimulus sampling theory which predicts this behavior also does not apply. One of the axioms of stimulus sampling theory has been generalized. An effect of this revision is to allow for the prediction of nonprobability matching behavior. This model has been fitted to the data previously gathered, and described the data far better than any previous stimulus sampling model. It is concluded that probability matching is not a general learning law as Estes proposed in 1957, but, rather, that it is a special case of a more general phenomenon, just as previous stimulus sampling models are special cases of the model developed here.