The two-envelope paradox

Over the weekend, I received an email from Moshe Sniedovich in Melbourne. He will probably be flattered to be described as one of the world's outstanding O.R. scientists, but that is my opinion. His great strength is to be able to look at accepted wisdom and question it, taking what is sometimes described as "A sideways look". Anyway, his email alerted me to his developing web directory entitled "Decision-Making Under Severe Uncertainty". The URL is

decision-making.moshe-online.com

It is well worth browsing through, especially if (like me) you have a streak of skepticism at the pronouncements of experts.

Today I browsed the article he has written about the two-envelope paradox.

I have just left on your desk two indistinguishable envelopes, each con-
taining some money. I do not know how much money is involved, except
that one envelope contains exactly twice as much as the other.
You can select an envelope, open it, and either keep the money you find
in it – no questions asked – or swap envelopes and keep the money you
find in the other envelope, in which case the money in the first envelope
that you opened will self-destruct.

What should you do? According to the paradoxical analysis, you should always swap, as this will increase the expected amount you will gain. But, in a delightful essay/paper, Moshe explains the mathematics behind this situation. Enjoy!