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An adaptive dual control algorithm is presented for linear stochastic systems with constant but unknown parameters. The system parameters are assumed to belong to a finite set on which a prior probability distribution is available. The tool used to derive the algorithm is preposterior analysis: a probabilistic characterization of the future adaptation process allows the controller to take advantage of the dual effect. The resulting actively adaptive control called Model Adaptive Dual (MAD) control is compared to two passively adaptive control algorithms - the Heuristic Certainty Equivalence (HCE) and the Deshpande-Upadhyay-Lainiotis (DUL) model-weighted controllers. An analysis technique developed for the comparison of different controllers is used to show statistically significant improvement in the performance of the MAD algorithm over those of the HCE and DUL.