I don't get it - in your example, if you pick the 5 envelope, then your next pick will be either 6 or 7 (depanding on what's left), so the minimal value of the right envelope is 11, not 8. no?

oh, now I get it. I misunderstood the question - you're not going for the optimal number of points, just more then your opponent. I think that a recurcieve solution for the optimal number exists, in a si,milar fashion to your original suggestion.