Newcomb's Paradox

A highly superior being from another part of the galaxy presents you with two boxes, one open and one closed. In the open box there is a thousand-dollar bill. In the closed box there is either one million dollars or there is nothing. You are to choose between taking both boxes or taking the closed box only. Of course there's a catch.

The being claims that she is able to predict what any human being will decide to do. If she predicted you would take only the closed box, then she placed a million dollars in it. But if she predicted you would take both boxes, she left the closed box empty. Furthermore, she has run this experiment with 9,999 people before, and has been right every time.

The paradox is that there is a convincing argument in favour of the two box solution, ie that you must get $1,000 more, as well as for the one box option, ie that it is nearly certain that the superior being has divined your choice and hence will reward you for taking just one.

Solution