The Two-Envelope Paradox is an interesting puzzle about probability. You can read more about it at wikipedia, or join the discussion.
In short, there are two envelopes, A and B, and one contains twice as much money as the other. You're holding envelope A in your hands. Before looking in either envelopes A or B, does it make sense to switch to envelope B?
On the face of it, it seems that it doesn't matter whether you switch or not. However a "paradox" arises if you choose to think of the contents of envelope B as containing half or double that of A. Meaning you have even odds of doubling or halving your money. Under this assumption, it makes sense to switch, as you stand to gain more than you risk losing!
My explanation of the "paradox" is below if you're interested: