I posted the following as an answer on this thread:

http://stats.stackexchange.com/questions/95694/two-envelope-problem-revisited/122757#122757

I realise this is old hat to many, but please bear with / be gentle if possible... Essentially my experience of playing with this puzzle is that it generates sub-puzzles which sometimes (or even often) loop back to the main one. So, with that in mind, here's what I asked:

Step 1 as stated by the OP in the link above. Step 2 as originally stated, but it is made explicit that a coin toss was used to fill the second envelope using the double or half rule. Step 3 both are sealed and the amounts are unknown to the player, but it is also stated that a coin toss was used and the player is told which envelope contains the original amount, so the amount that started the process.

It seems clear they should choose the envelope created by tossing the coin. The process of putting the money in the envelopes in a given way and the information about which envelope contains the starting amount makes it identical to Step 1, in content, it seems.

BUT: when the player holds the envelope created by tossing the coin and focuses on the amount it contains, or when they open it and see an actual amount, the other envelope appears 'better' - it is double or half with equal probability (coin toss used, let's not forget). So, in two steps (Steps 2 and 3) we have gone from a clear expectation of gain, which I think we all agree is correct, to the two envelope paradox. Where is the false step?

Perhaps, to begin to answer my own question, the false step is in my claim that the player can reasonably worry that the envelope he didn't choose is double or half with equal probability. Sure, a coin toss was used, but perhaps the prior question to consider is how was the original amount determined and what does the value in the envelope that is opened tell us about this? I have read over the mathematical treatments of this. I guess they always seem slightly unconvincing. What if I just boldly say: 'I thought of an original amount'? I can do this. If it helps, let's say I say the amounts are all whole number powers of two (including negative whole number powers), so envelope pairs differ by one number in the powers. In this case I just boldly assert that I thought of a whole number then flipped a coin to add or subtract one from this.

EDIT (ADD). This may help to clarify my point / puzzle: what I called Step one above, in other words what the OP on the other thread called Problem one, is just a coin flip to double or halve an amount. The player should take this as there is an expected gain of 1.25 times the original amount. Problem 3 or Step 3, as I formulated it above, is to take an amount, put it in an envelope, then flip a coin to double or halve that amount and put the resulting sum in another envelope. The player is offered both envelopes sealed and told which is which. It seems obvious that he should take the one resulting from the coin flip as, following the logic of the first situation, its expected value is 1.25 times the amount in the other envelope.

Here's the rub / question: the player opens the envelope and sees an amount. At this point should he start worrying about his choice, and if he shouldn't, why not? Suppose he sees 250 on opening. The logic of the way the envelopes were created seems to mean he should think that the expected value of the other envelope is 200. It can't be 200 of course, it can only be 125 or 500. So, is he supposed to think that there was a 4/5 chance that the original sum was 125 and a 1/5 chance that it was 500?