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.