Thanks for the thanks!

I like the $x and $2x analysis of the original problem. One way of using it makes me think of quantum physics. If we assume that one envelope has $X and the other $2x, then the expected value of the chosen envelope is $1.5x, which is also the value of the other envelope. So there's no point in switching.

One might think of the two "logical envelopes" (the one with $X and the one with $2X) as being in superposition, their values being only probabilities until the "wave is collapsed" by inspection of both envelopes. (Opening one envelope tells us nothing about its status as $X or $2X, absent the iterative info described in the latter part of the article.)

Are the envelopes entangled? Let's move the second envelope a zillion miles away. If the game host tells you that the envelope you chose is the one containing $X, the value of the other envelope "instantly" becomes $2x, in defiance of the simultaneity principle. Thus arises the famous EPR (Envelope Picking Routine) paradox, previously attributed to Messrs. Einstein, Podolsky and Rosen.

Of course, quantum mechanics is weirder than that, I think. I don't really understand it.