Newcomb's paradox

Newcomb's paradox is a thought experiment in philosophy, specifically decision theory. The paradox goes as follows:

Imagine a super-intelligent entity known as Omega who can accurately predict what you do. You know that Omega has correctly predicted your choices many times in the past, and has never made an incorrect prediction about your choices. You also know that Omega has correctly predicted the choices of other people, many of whom are similar to you, in the particular situation about to be described.

There are two boxes: A and B. Box A is see-through and contains $1,000. Box B is opaque, and contains either $0 or $1,000,000. You may take both boxes, or only take box B.

Omega decides how much money to put into box B. If Omega believes that you will take both boxes, then it will put $0 in box B. If Omega believes that you will only take box B, then it will put $1,000,000 in box B.

Omega makes its prediction, puts the money in box B ($0 or $1,000,000), presents the boxes to you, and flies away. Omega does not tell you its prediction, and you do not know how much money Omega put in box B.

What do you do?

If you only choose box B, Omega would have likely predicted you doing this, and put $1,000,000 in that box. Since $1,000,000 is more than $1,000, only choosing box B would be the best choice.

Omega has already made her decision, so the amount of money in box B will not change based on the decision you make. No matter how much money is in box B, choosing both boxes would net you an extra $1,000, making it the best choice.