Calculating the expected value of information (VOI) for sequences of observations under uncertainty is intractable, as branching trees of potential outcomes of sets of observations must be considered in the general case [11]. We address the combinatorial challenge of computing ideal observational policies in situations where long sequences of weak evidential updates may have to be considered. We introduce and validate the use of Monte Carlo procedures for computing VOI with such long evidential sequences. We evaluate the procedure on a synthetic dataset and on a challenging citizenscience problem and demonstrate how it can effectively cut through the intractability of the combinatorial space.