The Envelope Paradox is a mathematical / philosophical puzzle, variations of which date back to (at least) the mid 1950s.

You are given two indistinguishable envelopes, each containing money. One contains twice as much as the other. You may pick one envelope and keep the money it contains. Having chosen an envelope at will, but before inspecting it, you are given the chance to switch envelopes. Should you switch?

Source : Wikipedia

Despite the intuitive answer - that swapping would make no difference to your chances of picking the larger amount - a number of experts in mathematics and logic have proposed (widely differing) solutions to the puzzle, which appear to 'prove' that there is a distinct advantage in swapping. (example ref.)

Others maintain that the paradox is unsolvable :

A topological representation of the problem is presented that captures both finite and infinite cases, explicating intuitions underlying the arguments both that there is an advantage to switching and that there is not.

Source : Acta Analytica volume 25, pages 479–498

Also see : Lottery ticket swapsplugin-autotooltip__plain plugin-autotooltip_bigLottery ticket swaps

Because the results of (well constructed) lotteries are essentially random, no one ticket is any more likely to win than any other. However, several studies have shown that those who are in possession of a lottery ticket are usually very reluctant to swap it