There are about a million reasons to take the mystery box only.
The way I see it, take the mystery box and I will almost certainly get the $1,000,000. If not, and the computer is wrong, I have the pleasure of knowing I fooled a supercomputer.
Right; in the formulation of this paradox I originally heard, it is explicitly stated that you have sat in the audience for hundreds of these trials, and seen that the computer predicted correctly every fucking time.
Take whichever you like. There’s only $1K difference in the outcomes, after all. Whether there is $1M in the mystery box has already been set. The determining factor dictating the majority of the outcome is what the computer thought of you before you entered the room, not what you pick now.
The most obvious way to do it would be to have both boxes always empty when you come in, but if you take only the first box a mechanism places the million dollars under the second so the presenter can then lift it up and show everyone how the supercomputer is always right. Certainly easier to pull off than a perfectly predictive computer.
Another obvious way is that the people running the experiment have invented a means of viewing future events and have programmed the computer with this ability. It looks into the future, sees whether a person will choose one or two boxes, and then based on what it sees, it loads the opaque box accordingly.
In the real world if something happened like this it would obviously be a trick. Somehow between the point you make the choice and the reveal the million is surreptitiously inserted. In this case you’d be an idiot to be a 2-boxer.
That’s boring though. The thought experiment only works if you have faith that it is done on predictive ability alone, and that the box cannot change.
Fyi, professional actuary here. You have long since disproved your a priori of that being a fair die. It’ll roll 6 again.
Yup. In the real world, this is a trick. The die isn’t fair. It’s not predicting; it’s observing and reacting. So you should take one box, because the odds that you are the sucker being set up are … You know, unless you know those other people, the odds that you are the sucker are pretty good.
Does this mean I’m rejecting the hypothetical? Yes, it does. I just can’t bring myself to have perfect faith in a prediction, even in a hypothetical situation. So i should probably drop out of this discussion. But the comment above about Pascal’s wager was insightful. I think this is really a question about faith. And for good or ill, i lack faith.
You don’t know that. You just know it successfully predicted a thousand time, it could just choose “both boxes” all the time and been right (because why would anyone ever take one box?)
I don’t have problems considering hypotheticals if the hypothetical setter is clear about what parts are axiomatically true. In this case the setter is saying
“You walk into a room, there are 2 boxes. The 1st box has £1000, the 2nd box has an amount in it. I’m not telling you the amount, but I am telling you for a fact that the amount was fixed before you walked in. How many boxes do you want?”
Dead, you say … then please the BIG box for me
But why does that matter? It can’t go back in time. The options are take zero or a million, or take 1000 and zero or million. Taking both boxes will only increase the amount you take home there are no downsides.
I’m amazed why so many people voluntarily choose to take less money when there is no downside.
Me, too - that’s why I am shocked that there are any two boxers.
But why? Whether the computer is supernaturally good or just one line of code that says “print ‘They’ll take both boxes’”, the decision has been made your choice doesn’t effect it. You can choose to take a box that may contain a million dollars or a box that contains a thousand and box that may contain a million dollars. The logical choice is to take both because x+1000 is more than x+0.
But two boxers always get more money than one boxers. Taking one box is voluntarily taking less money for no reason.
Yes. You can’t change who you are, or how you make decisions after you enter the room. Or even if you can, it doesn’t matter.
How do you figure?
In the last 1,000 trials, two boxers always got $1,000 and one boxers always got $1,000,000. So ISTM that one boxers always get more money than one boxers.
I’m shocked that they are so sure it’s the best decision. I said it before (Do you take one box or two boxes? - #77 by Thumper668), but maybe it was missed:
If the amounts were $1 in the open box and $1000 in the mystery box I’ll bet there would be more one-boxers. Likewise, if it were $1,000,000 and $1,000,000,000 I would jump on the two-box bandwagon on the slim chance the computer was wrong.
And in the last 1,000 trials anyone who went with that logic for $1,000 while anyone who took the closed box alone for a million dollars.
But the one boxers would have got 1000 dollars more if they had chosen both boxes and the two boxers would have not got any more if they’d chosen one box. The money is in the box when they walked in the room, the decision does not make the second box empty or full.