In this paper we present a strategy for speeding up the estimation of expected maximum flows through reliable networks. Our strategy tries to minimize the repetition of computational effort while evaluating network states sampled using the crude Monte Carlo method. Computational experiments with this strategy on three types of randomly generated networks show that it reduces the number of flow augmentations required for evaluating the states in the sample by as much as 52% on average with a standard deviation of 7% compared to the conventional strategy. This leads to an average time saving of about 71% with a standard deviation of about 8%.