===Another proposed solution===  
 Motion to include this in the main article...  its proposed by me. All in favour say "I"...  seriously though, please give me feedback: 

 First, take A to be the name of the envelope we choose first, and B to be the other envelope. Then take the quantities of money in A and B to be multiples of a quantity Q. Even if the quantity in A is known, Q is not. In this situation, there are two possible outcomes: 

 (I) A contains Q, B contains 2Q 
 (II) A contains 2Q, B contains Q 

 The question is whether we would stand to benefit, on average, by taking the money in B instead of our random first choice A. Both situations (I) and (II) are equally likely. In situation (I), we would gain Q by choosing B. In situation (II), we would lose Q by choosing B. Thus, the average gain would be zero: 

  

 The average proportion of B to A is irrelevant in the determination of whether to choose A or B. The entire line of reasoning in the problem is a red herring. It is true that the average proportion of B to A is greater than one, but it does not follow from that determination that the better option is to choose B. As such, the cause of the paradox is step 8. The statement at step 8 is untrue. 

 For Example: Assume one of the envelopes contains $100 and the other $50. The two possibilities are: 

 (I) A contains $50, B contains $100 
 (II) A contains $100, B contains $50 

 In (I), the quantity in B is twice the quantity in A. In (II), the quantity in B is half the quantity in A. It is easy to see that, on average, B does equal five fourths of whatever A is. But, the average B does not equal five fourths of the average A. They are in fact both equal to $75. Obviously if we are allowed to open A to find its value ($100 or $50), we would know which to choose. This is because we already know the value of Q, as defined above. Q = $50. 

 To put it simply, if you repeat the above event many, many times, each time recording the following: 

  

 then the average R will approach , and both the average A and the average B will approach $75. The value of the average R is totally irrelevant. What is relevant is that the average A equals the average B. This means that it makes no different which envelope you choose. On average, you will end up with the same amount of money, which is the expected result.