NationStates Jolt Archive

A Chaoist Mage claims to have the ability to predict one’s thoughts and actions days in advance, not with absolute perfection, but with a success rate of about 77%.Fnord
A Non-Prophet =POPE= agrees to take part in an unusual test of the Mage’s powers. The =POPE= does not care much about verifying or refuting the Mages psychic powers, but could really use some cash for additional Slacking. A TV program has provided the facilities and put up a large sum of money; all the Pope has to do is abide by the conditions of the experiment. On a table in front of him are two boxes: A and B. Fnord
Box A contains $15,000. Box B either contains a million dollars or is empty. The Non-Prophet =POPE= cannot see inside it. Of his own free will he must choose either to take box B only or to take both boxes. Those are the only options. The catch is this: Twenty-four hours ago, the Mage predicted what the =POPE= would choose. The Mage decided whether to put the million dollars in box B. If he predicted that the =POPE= would take only box B, he put the million dollars in it. If he foresaw him taking both boxes, he left box B empty.Fnord
The conditions of the test have been and will be enforced scrupulously. No type of trickery will be allowed. The =POPE= must analyze the situation and decide on the most profitable of the two options. Of course, the Chaoist Mage has anticipated this analysis. What should the Non-Prophet do - take both boxes or just B? Remember, the mage only claims 77% accuracy.Fnord

I curse the 100 character limit on poll options. It should have read:
Ifreann, what you've just said is one of the most insanely idiotic things we have ever heard. At no point in your rambling, incoherent response were you even close to anything that could be considered a rational thought. Everyone on this interweb is now dumber for having listened to it. We award you no points, and may Eris have mercy on your Fnord.

I also praise and offer to fellate the timewarp device.

So, theres no consequence to taking both boxes? Then he should take both everytimes as he will at least end up with $15,000 or at most 1,015,000. Who cares about proving a mage wrong on principle?

The only rational course of action is to take both boxes.

At the time you choose, either the second box contains $1 million or it doesn't - nothing you do can affect that.

Of course, if I really want to trick the mage, I flip a coin.

He should take box B only if he thinks the mage is right. If he is skeptical, he should take both.

Reasoning in white:

If the =POPE= believes in the mage's ability:

Assuming the =POPE= was going to choose Box B only:

There is a 77% chance the mage predicted right and put a million in Box B
and 23% chance that he was wrong and put nothing in it

Therefore: average winnings = 77%*$1,000,000+23%*0 = 770,000

Assuming the =POPE= was going to take both:

There is a 77% chance that the mage predicted right and left nothing in B
and a 23% chance he was wrong and put a million in Box B

Therefore: average winnings = 77%*$15,000+23%*1,015,000 = 245,000


If the =POPE= just makes his decision on profitability assuming the mage is bogus:

Average winnings for picking B only = 50%*1,000,000+50%*0 = 500,000

Average winnings for picking both = 50%*15,000+50%*1,015,000 = 515,000

Thus the =POPE= would pick both. But the mage anticipates this and puts nothing B, so the =POPE= only gets 15,000 for picking both.

Edit: Didn't account for if the =POPE= doesn't believe in the mage's abilities.

If it were me, I'd take both boxes. I figure that the mage is full of shit. I figure that the mage knows that most people think he is full of shit. Because people think he is full of shit, most people will take both boxes in order to get some money. Because he wants to seem right, he will predict that most people will take both boxes, so the million dollars will probably not be there. I'll take the 15 grand, if the mage is dumb enough to have put the million in as well, I could live with that. fnord

He should take box B only.

Reasoning in white:

Assuming the =POPE= was going to choose Box B only:

There is a 77% chance the mage predicted right and put a million in Box B
and 23% chance that he was wrong and put nothing in it

Therefore: average winnings = 77%*$1,000,000+23%*0 = 770,000

Assuming the =POPE= was going to take both:

There is a 77% chance that the mage predicted right and left nothing in B
and a 23% chance he was wrong and put a million in Box B

Therefore: average winnings = 77%*$15,000+23%*1,015,000 = 245,000


You'd believe some guy claiming he has 77% mind reading ability accuracy?

He should take box B only.

Reasoning in white:

Assuming the =POPE= was going to choose Box B only:

There is a 77% chance the mage predicted right and put a million in Box B
and 23% chance that he was wrong and put nothing in it

Therefore: average winnings = 77%*$1,000,000+23%*0 = 770,000

Assuming the =POPE= was going to take both:

There is a 77% chance that the mage predicted right and left nothing in B
and a 23% chance he was wrong and put a million in Box B

Therefore: average winnings = 77%*$15,000+23%*1,015,000 = 245,000

Wrong.

By choosing only box B, you're trying to create evidence that the prediction was accurate, but at the time of your selection the money's already in the box. Or it isn't. You can't change that.

I didn't read carefully enough. The =POPE= doesn't care if the mage is right or not. I already editted it.

Even if you do believe in his abilities, the fact remains that your decision cannot affect the contents of the boxes.

Sitting in front of you is 2 boxes. One of them contains $15,000. The other one might contain $1,000,000. The probability that the second box contains $1,000,000 is irrelevant, since it's not affected by which box you choose.

Therefore, you should always take both boxes.

Is this even a question? You take both. You can't lose anything for it.