In a show, you are given two closed envelopes containing positive sums of money. It is known that one envelope contains twice as much as the other.
You may choose one envelope and keep the money it contains. You pick one envelope at random, open it and see an amount of c. At this moment, the host offers you to switch to the other envelope. The common sense tells that whether you switch or not, on the average you will have the same. Nevertheless, you can reason as follows.

With equal probabilities, the other envelope contains either 2c or c/2. Hence, if you switch, then the mean amount you will get is 2c·

So, you should switch.
Moreover, this conclusion does not depend on c. Hence, you should switch even not opening the envelope. Then, you can repeat the same argument with respect to the envelope you have switched to, and consequently, you should switch back. So, we have come to the absurdity that you should swap envelopes infinitely long. Where is a mistake in the above reasoning?