But I don't think the two envelope paradox has anything to do with that practical impossibility. It is about the rules of symbol manipulation and modeling. Exa

But I don't think the two envelope paradox has anything to do with that practical impossibility. It is about the rules of symbol manipulation and modeling. Exactly this. The two envelopes paradox is a paradox only because using a fallacious argument leads to the wrong result, and the Wiki page proposes numerous resolutions to the problem as well. I like this way of stating it (from http://en.wikipedia.org/wiki/Two_envelopes_problem#Non-probabilistic_variant http://en.wikipedia.org/wiki/Two_envelopes_problem#Non-proba...): 1. Let the amount in the envelope chosen by the player be A. By swapping, the player may gain A or lose A/2. So the potential gain is strictly greater than the potential loss. 2. Let the amounts in the envelopes be X and 2X. Now by swapping, the player may gain X or lose X. So the potential gain is equal to the potential loss. In the first case, A and A/2 are actually referring to the same amount of money. You have to condition on what A is: If A is the larger value, the second envelope cannot contain 2A; A/2 is equal to the smaller amount. If A is the smaller amount, then the second envelope cannot contain A/2; A is equal to the smaller amount. So your potential gain and loss are both equal to the smaller amount of money, and you have no logical reason to swap.