So there is 50% probability that the other one contains Z/2 and 50% that it has 2Z. Do you disagree with that statement? Yes! Well, in some circumstances. Unle

So there is 50% probability that the other one contains Z/2 and 50% that it has 2Z. Do you disagree with that statement? Yes! Well, in some circumstances. Unless you know how the values were placed into the envelope to begin with, how could you possibly assign a probability to it? I just found this great link today: http://lesswrong.com/lw/dy9/solving_the_two_envelopes_problem/ http://lesswrong.com/lw/dy9/solving_the_two_envelopes_proble... which basically resolves the problem I'm having by taking into account how the values get into the envelopes in the first place. If you have absolutely no knowledge of how the values got into the envelope in the first place then there's a 50/50 chance you got the higher value on your first pick, and a 50/50 chance you'll get the higher value on your second pick. You can't make a more informed decision unless you know how the values were initially chosen.