We consider life-cycle production optimization with the aid of the Ensemble Optimization (EnOpt) technique. Although the number of applications of EnOpt has increased, and the theoretical understanding, which is based on strong assumptions, has recently significantly improved, there is still ample room for further development of the underlying theory. Here we study the mathematics (or statistics) of EnOpt and show that it is a version of an already well-defined natural evolution strategy known as Gaussian Mutation. With increased focus on ensemble-based methods in reservoir history matching over the last decade, a natural description of uncertainty arises from the use of multiple realizations. Thus it is a logical step to incorporate this ensemble-based uncertainty description in life-cycle production optimization through defining the expected objective function value as the mean over all geological realizations. We show that the frequently advocated strategy of applying a different control parameter to each reservoir realization, as a means to incorporate geological uncertainty in optimization, delivers an unbiased estimate. However, it is more variance prone than the deterministic strategy of applying the entire ensemble of control parameters to each realization of reservoir models.