Rambling on 96 months ago.
Two identical envelopes, one containing twice as much money as the other are shuffled. You may open one then decide which one to keep.
You open one, which contains $20.
You are offered the chance to take the other envelope instead.
Common sense tells us that it doesn't matter, but consider this:
The other envelope contains either:
Since there is an equal chance you will gain more than you could potentially lose, doesn't it make more sense to take the other envelope?