The famous problem goes like this:
A being (God, an alien, a supercomputer...) who can predict what humans will choose in a given circumstance. This being has to boxes to give to humans. Box A always holds $1,000 and Box B may or may not have $1,000,000.
The being then tells you:
You have two choices. One is to take both boxes and keep their contents. But if I expected you to do this, I have left B empty. You get only $1000.
Your other choice is to take only box B. If I expected you to do this, I have put a million dollars in B. You get it all.
The being puts the content on the boxes and then he leaves to have no contact whatsoever with you. You will have to make the choice the next day.
Well, obviously you should take only Box B, right? For if this is your choice, the Being has almost certainly predicted it and put $1 million in Box B. If you were to take both boxes, the Being would almost certainly have anticipated this and left Box B empty.
But wait a minute. The Being made his prediction yesterday. He either put $1 million in Box B, or he didn't. If it's there, it's not going to vanish just because you choose to take both boxes; if it's not there, it's not going to materialize suddenly just because you choose only Box B. Whatever the Being's prediction, you are guaranteed to end up $1,000 richer if you choose both boxes.
So, what would you choose and why?
What would you choose if Box A held $1 instead?
What if it held $900,000?
What if a friend could see the contents when you make your choice but can't communicate with you?
I take Box B.
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