In optimal stopping problems in which the player is free to choose the order of observation of the random variables as well as the stopping rule, it is shown that in general there is no function of all the moments of individual integrable random variables, nor any function of the first n moments of uniformly bounded random variables, which can determine the optimal ordering. On the other hand, several fairly general rules for identification of the optimal ordering based on individual distributions are given, and applications are made to several special classes of distributions.
