We introduce a probabilistic version of the iterated factor method developed in our previous work. Let n be drawn uniformly from the set {1, 2, ..., M}. Define s(n) = floor( sqrt(log base 2 of n) / log(log base 2 of n) ), and t(n) = sqrt(log(log n)), and let ku2099 = floor(n / 2) with respect to s, meaning a construction related to the s-th iterated factor. As N tends to infinity, with Zu2099 distributed normally with mean 0 and variance 1, and under the condition thatPr[ ν(ku2099) ≤ s and |Zu2099| ≤ t ] tends to 1,we show the inequality ι(2u207f − 1) ≤ n − 1 + log base 2 of n + C·sqrt( log base 2 of n / log log base 2 of n ) holds for some absolute constant C > 0. This result surpasses the O(log n / log log n) barrier that is guaranteed under the classical Brauer method (Brauer, 1939). It may thus be viewed as an introduction of probabilistic methods into the theory of addition chains.