The method of exact relaxation (ER) makes it possible to accelerate and stabilize the convergence of single-point iterative methods, but in multidimensional cases there exists 'sphere of idling', if hit by a value delivered by the basic algorithm, ER leaves the value unchanged despite computational expenses have already been done. From the other hand, a volume of the sphere is null. Therefore, deterministic estimates of the effectiveness of ER is not satisfactory. Closer to real computational processes there is efficiency estimate by mathematical expectation under this or that hypothesis about probabilistic distribution of the result of the basic algorithm. Received formulas show high efficiency of ER.