The integrated assessment literature frequently replicates uncertainty by averaging Monte Carlo runs of deterministic models. This Monte Carlo analysis is, in essence, an averaged sensitivity analyses. The approach resolves all uncertainty before the first time period, drawing parameters from a distribution before initiating a given model run. This paper analyzes how closely a Monte Carlo based derivation of optimal policies is to the truly optimal policy, in which the decision maker acknowledges the full set of possible future trajectories in every period. Our analysis uses a stochastic dynamic programming version of the widespread integrated assessment model DICE, and focuses on damage uncertainty. We show that the optimizing Monte Carlo approach is not only off in magnitude, but can even lead to a wrong sign of the uncertainty effect. Moreover, it can lead to contradictory policy advice, suggesting a more stringent climate policy in terms of the abatement rate and a less stringent one in terms of the expenditure on abatement.