There is another very cool puzzle that can be considered a followup which is:

There are two envelopes in which I, the host of the game, put two different natural numbers, chosen by any distribution I like, that you don't have access. The two envelopes are indistinguishable. You pick one of them (and since they are indistinguishable, this can be considered a fair coin flip). After that you open the envelope and see the number. You have a chance to switch your number for the hidden number. Then, this number is revealed and if you choose the greater you win, let's say a dollar, otherwise you pay a dollar.

Now, before everything I said happens, you must devise a strategy that guarantees that you have a greater than 1/2 chance of winning.

Some notes:

1- the problem may be extended for rational, or any set of constructive numbers. But if you want to think only in probabilities this is irrelevant, just an over formalism.

2- This may seem uncorrelated to the two envelopes puzzle at first, but it isn't.

3- I saw this problem first on EDITthis post on xkcd blag. Thanks for Vaniver for pointing out.