2 box problem

[NLSoldier]

I am almost positvie I have seen this in this forum before, but I did a few searches and can't find it. Can anyone either give me a link or a quick explanation of the solution. Thanks.


Two boxes are on a table in front of you. One box is clear; the other is
opaque. In the clear box is $1,000. The opaque box either contains
$1,000,000 or else it contains nothing. You have the option of taking
either both the opaque box and the clear box, or the opaque box only.
Before you choose, however, a perfect predictor has decided whether or not
to put the million dollars in the opaque box. The perfect predictor knows,
perfectly, what you are going to choose. If he predicts that you are going
to choose both boxes, he will put nothing in the opaque box, to punish your
greed. If, however, he predicts that you will take only the opaque box,
then he will put the million dollars in it.

What do you choose to do?

[Jacob_Gilliam]

I know about the predictor beforehand? I'll take just the opaque box. The predictor would know I was going to do this, and I get my money. Yay, me!

[Macdaddy Warsaw]

The money doesn't somehow drop through the bottom of the opaque box if you pick up both. Once you get there, is there a difference between choosing one box and both boxes? The money is either there or it isn't.

This is a tougher question than you make it out to be.

[Jacob_Gilliam]

But since I know the rules of the game, I would always take only the opaque box, and if the predictor was accurate, it would predict that I'm going to take the opaque box. Therefore, I win.

[NLSoldier]

[ QUOTE ]

The money doesn't somehow drop through the bottom of the opaque box if you pick up both. Once you get there, is there a difference between choosing one box and both boxes?

[/ QUOTE ]

This is what I was thinking but that seemed too simple to me. Is there more to it?

well you basically have an opportunity an extra 1,000 bucks if you can figure this riddle out...i'd probably be fine with a guaranteed 1,000,000...because i'm not that bright

...of course you would want to be 99.9% sure that you're right to try and take both boxes

[ QUOTE ]
[ QUOTE ]

The money doesn't somehow drop through the bottom of the opaque box if you pick up both. Once you get there, is there a difference between choosing one box and both boxes?

[/ QUOTE ]

This is what I was thinking but that seemed too simple to me. Is there more to it?

[/ QUOTE ]

there IS more to it...if you just take both since the money is already in there, then the PERFECT predicter would have predicted that and thus there would have been no 1,000,000 placed in the box

--this question is basically whether or not you think that the predicter is perfect or not

...somewhat like a free will question on if a true prediction can be turned wrong by a free will decision..very mind boggling..but probably not a question that has a deffinite answer

--if there is a deffinite answer i'd like to hear it
--you said the the answer was once posted in the forums??

[housenuts]

why risk 1 million just for an extra grand, when you can get a million guaranteed?

[NLSoldier]

[ QUOTE ]
why risk 1 million just for an extra grand, when you can get a million guaranteed?

[/ QUOTE ]

what is the clear box had 50k? I think that is how the problem is supposed to be. Not that it matters much.

[ QUOTE ]
[ QUOTE ]
why risk 1 million just for an extra grand, when you can get a million guaranteed?

[/ QUOTE ]

what is the clear box had 50k? I think that is how the problem is supposed to be. Not that it matters much.

[/ QUOTE ]

then you'd just need to be at least 95% sure you have it right..still probably not worth the risk though

Possibly the dumbest "choice" scenario ever.

You can take $1M guaranteed ro risk it to win $1000 more, but since the predictor is perfect, the risk is 100%. So, you are choosing whether you want $1M or $1k. Hmmm, yeah that's a tough problem.

[NLSoldier]

[ QUOTE ]
Possibly the dumbest "choice" scenario ever.

You can take $1M guaranteed ro risk it to win $1000 more, but since the predictor is perfect, the risk is 100%. So, you are choosing whether you want $1M or $1k. Hmmm, yeah that's a tough problem.

[/ QUOTE ]

But by the time you are ready to take the box, the predictor has already made his choice. Look at it this way. Say that the predictor is also a truth teller. And before you make your choice, he tells your friend whether he put the million in or not. Whether he did or not, your friend is going to tell you to take both boxes. Why wouldnt you listen to him?

[ QUOTE ]
[ QUOTE ]
Possibly the dumbest "choice" scenario ever.

You can take $1M guaranteed ro risk it to win $1000 more, but since the predictor is perfect, the risk is 100%. So, you are choosing whether you want $1M or $1k. Hmmm, yeah that's a tough problem.

[/ QUOTE ]

But by the time you are ready to take the box, the predictor has already made his choice. Look at it this way. Say that the predictor is also a truth teller. And before you make your choice, he tells your friend whether he put the million in or not. Whether he did or not, your friend is going to tell you to take both boxes. Why wouldnt you listen to him?

[/ QUOTE ]

So what if he made his choice, you said the mil is there if you take the 1 box. So take the mil.

[RJT]

Hint: It is an analogy.

[slickpoppa]

This question violates the laws of physics. There is no such thing as a perfect predictor according to the Heisenberg uncertainty principle.

[housenuts]

if it's a 50/50 chance there's no way you should take the risk unless there is at least 1 million in the other box as well.

oops: i guess you still get the other box which means you would get a million anyways.

hmmm, now i can't figure out math. assuming it was completely random 50/50.

how much would have to be in the other box to make choosing both of them +EV?

eg. if there was $500,000 and you chose both then 1/2 the time you'd have 1.5 million and the other 1/2 the time you'd have .5 million. hmmm, looks like i just figured out my own problem after trying to make some fancy formula.

so essentially if there was more than $500,000 in the other box it would be +EV to choose both. otherwise, especially if it's only 1k, it's very -EV

[slickpoppa]

[ QUOTE ]
This question violates the laws of physics. There is no such thing as a perfect predictor according to the Heisenberg uncertainty principle.

[/ QUOTE ]

And given that there is no such thing as a perfect predictor, you have absolutely nothing to lose by picking both boxes.

[Macdaddy Warsaw]

By the way, I think when I heard the question, the other box had 10k in it and the predictor was only right 99.9% of the time. Not perfect, but almost. If the predictor is actually perfect, I don't see anyway that you can avoid picking up just one box. If the predictor is even wrong 1 in 1000 times, you have to ask yourself when you enter the room if picking up both boxes doesn'change what's in the opaque one, why don't I pick up both.

I don't know, when I thought through this 2 years ago, I thought it become pretty evident that picking both boxes is the way to go. Not based on physics or math, or anything.

EDIT: And yes, I think it's more of a problem about free will or a predictable future than anything.

[jdl22]

Clearly the predictor doesn't ever put the money in since everyone takes both boxes. This situation has the flavor of the prisoners' dilemma.

[NLSoldier]

[ QUOTE ]
Clearly the predictor doesn't ever put the money in since everyone takes both boxes. This situation has the flavor of the prisoners' dilemma.

[/ QUOTE ]

I think its just the oppostie. I think the predictor puts the million in every time because no one ever has the balls to take both.

[Georgia Avenue]

I'll just take the clear box and donate the unopened opaque one to charity. Do you see why?