[NaobisDad]

thanks for the reply guys.

@econ: Depending on the amount of money in the envelope, someone might indeed use this information for switching which I expect to influence EVj. However, as I understand it, stated in the original problem, it's not a matter of psychology. If you are indeed allowed to estimate EV according to the method of argument 1, switching would always be +EV. And if you believe arguemtn 2 to be true, it wouldn't matter. It's therefore that I simplified the problem to always switching.

@Paul: we could simply play it, or write a program to play it out. Note that as stated you could play this game without ever really having to actively participate. So you could run a lot of trials. From your response it seems a bit like you believe that how you simulate the problem is going to matter. If this is the case, I'd like to hear those thoughts.

@Sam: Sam, you refer to the sampling method. But at this point I can't really deduce why you believe the manner of sampling is important. You said: "Assuming that X is chosen equally likely from the set of all positive integers is flat wrong. You're not allowed to assume that, because it doesn't make sense." Alright, if we then do not make that assumption, how would that impact the results?