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there is no such thing as a $1000 dollar bill, so you would be crazy not to go with the closed box,... then there is always the rocket-testing smart idea of lifting the closed box to see if it weighs at all

What about kicking him in the nuts to see if he really predicts stuff ?
This would add new data and thus would improve the chance of a good decision-making.

The human doesn't make a choice here. The alien does. Or rather, the human, by being a two-box human or a one-box human, directs the alien to put the million in or not. You make the choice long before you enter the room, through all the actions of your life that will make you the predictable being the puzzle stipulates that you are.

You think the alien can't exist? Actually, we could almost do this today. There are drugs, like Versed, which inhibit your ability to store long term memories. I could give you Versed, pose the problem to you, see what you do and then wait until it wears off. You will have no memory of the puzzle. (When this was done to me, I remember the injection, but nothing after that, even though I talked to people.)

Anyway, I give you the drug again. (If it weren't an injected drug you would have no way of knowing this is the 2nd time, for for this hypothetical imagine you think the injections are for something else.)

Anyway, now I can predict what you will do very accurately. Probably not as accurately as the alien, but so well that the result is very similar. Those who are the sort who pick one box become millionaires, those who aren't, don't.

Now imagine something better than Versed, something I can give you without telling you, something that doesn't sedate you or generate other visible effects, something like the Men-in-black pen that just erases a segment of memory if you will. It's not as science fiction as it sounds, the drug I describe is real and is used in medical procedures where they want you to be awake but not remember the horror.

Now do you understand the problem better? You understood it better the last time I explained it to you...

I'd take the $1,000 bill: one just sold at auction for $2.3 million. This paradox just vanished thanks to simple economics.

http://www.chron.com/disp/story.mpl/metropolitan/4405479.html

-John

I believe that such being cannot exist, and therefore the problem is a logical impossibility, but for different reasons than Martin Gardner.

One thing I can decide to do is flip a coin to decide. In order to predict what I will do, the being has to be able to predict how the coin will land. In fact, I can use something harder to predict than a coin: I can use something truly unpredictable, governed by quantum mechanics: I'll set up a single radioactive atom and observe whether it decays or not in 1 half-life.

In such a circumstance, the being can never be better than 50-50 with me, no matter how smart s/he is, so the paradox goes away.

Take neither box. You neither gain nor lose anything, and you got to meet a super intelligent being from another galaxy. Try asking the alien some questions rather than taking his box (this works with women, too).

This is not even hard. To solve it, just invert the order of events. First you choose, then the alien decides what goes in the closed box. It doesn't really matter which comes first, but it is easier to see. The alien has 99.9 percent chance of knowing your decision accurately. If you are greedy, you have a .1 % chance of fooling him, with expected value of $1K + .001*$1000K = $2K. If you are not greedy, the alien still has a .1% chance of getting it wrong, so the expected value of that decision is .999*$1000K = $999K. $999K > $2K so the greedy thing to do is not be greedy (now there's a real paradox!)

You take the closed Boxed. Risk reward ratio. If the predictive power of the alien is 100% then if you take the closed box as you are guaranteed a million dollars. If his predictive power is not quite perfect, but highly accurate, you are most likely to get a million dollars if you take the closed box. If the Alien does have 100% predictive power and you take both boxes you are only getting a thousand dollars. If his predictive powers are only extraordinarily good, then if you take both boxes, most likely you will only end up with 1,000 with a very small chance of getting 1,001,000. If the predictive power is 100% and you take the closed box, you get the million which is the highest possible outcome. If his predictive power is only very good, then you still take the closed box, because you are more likely to end up with a million then either the small chance of getting nothing or 1,001,000. If there was a 999 chance in 1,000 of risking a 1,000 to gain a 1,000,000 who wouldn’t take those odd. Certainly beats Vegas or the Stock Market. Of course this all takes on faith that you believe the alien is telling the truth that he has predicted the last 999 in a row.

Quit thinking so hard. Take both boxes. Not only do you then have $1,000 , you also have TWO BOXES!!

An extra $1,000,000 would be nice, but again, you get TWO BOXES!! And of course the $1,000.

A great day any way you look at it.

Paradox?
All this proves is that the superior being knows we a basically materialistic species fsacinated by all forms of material gain. No matter what happens he knows we are going to take something. In the end, he knows that he is superior because we fell for the scam, $1000 or $1,000,000 and will either 1) know enough to avoid this planet in the future or 2) know he has a couple billion fish to fry when he sets us up for a bigger scam.
Besides, I want to go behind the green curtain and see who this "superior alien" really is. Sounds like Oz to me.

The test is executed exactly the same way _only_ if each and every one of the 999 person was told the same "he has run this experiment with 999 people before, and has been right every time." before choosing.

Think, if you'd been the first one tested, would the alien have said "999" or "0"? The test is only same if he says "999" to everyone because telling that will affect the outcome.

Now, only way for him to say "999" and not lie is to posses time machine. If he has time machine, he knows what you will choose because he went and watched beforehand your choice.

Thus, choosing the closed box will give you 1 million dollars if telling the number of participants is part of the test.

I reckon an alien box is worth well more than $1000 so I'd take a chance on the single box...