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# Deus Ex Machina

Best Answer k-man, 16 July 2013 - 07:26 PM

What a great puzzle!!!

Spoiler for my thinking
Go to the full post

14 replies to this topic

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Posted 14 July 2013 - 05:07 AM

Five years ago, your rich uncle secretly commissioned the construction of a supercomputer! The purpose of this binary behemoth (the "Very Good Predictor") was to predict, as accurately as possible, every action you would take over the course of these five years. It has managed to do so with 100% accuracy for its entire runtime.

Now, your uncle has approached you with this information, and an offer to participate in a game involving the supercomputer's final prediction.
He has placed two envelopes in a room: Envelope A and Envelope B.

Envelope B contains exactly 1,000 dollars.  Envelope A either contains 10,000, 10, or 0 dollars.  If the supercomputer correctly predicted your selection of Envelope A alone, it will contain \$0.  If the supercomputer correctly predicted your selection of both A and B then Envelope A contains only \$10.  Otherwise the supercomputer predicted that you would not choose A and told your uncle that he could safely put \$10,000 in the envelope (which he would oblige).

Now since this is essentially a contest between you and the supercomputer, if the supercomputer correctly predicts your choice, the amount selected is the amount you owe your uncle, otherwise you keep the amount in the envelopes (both).  The values in both envelopes is revealed once a selection is made.

What should you do?

Edited by BMAD, 14 July 2013 - 05:12 AM.

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### #2 phil1882

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Posted 14 July 2013 - 05:34 AM

Spoiler for

Edited by phil1882, 14 July 2013 - 05:34 AM.

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### #3 gavinksong

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Posted 14 July 2013 - 09:32 AM

Spoiler for

I think the amount you owe your uncle if the computer predicts correctly is the value of the money in both envelopes, not just envelope A - if I understood the problem correctly. Also, even if the computer is wrong, you're not guaranteed an additional 10,000 since it might still be empty.

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Posted 14 July 2013 - 01:58 PM

Spoiler for

I think the amount you owe your uncle if the computer predicts correctly is the value of the money in both envelopes, not just envelope A - if I understood the problem correctly. Also, even if the computer is wrong, you're not guaranteed an additional 10,000 since it might still be empty.

The computer was designed for/by the uncle to work in his benefit not yours, so it would do what it can to ensure your uncle makes his money.

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Posted 14 July 2013 - 01:59 PM

Spoiler for

if the computer is right that you would pick both, you pay your uncle 1010 not 10.

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### #6 gavinksong

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Posted 14 July 2013 - 03:52 PM

Spoiler for

I think the amount you owe your uncle if the computer predicts correctly is the value of the money in both envelopes, not just envelope A - if I understood the problem correctly. Also, even if the computer is wrong, you're not guaranteed an additional 10,000 since it might still be empty.

The computer was designed for/by the uncle to work in his benefit not yours, so it would do what it can to ensure your uncle makes his money.

If the computer is confident in its prediction, wouldn't it always put 10,000 in Envelope A (unless it thinks I won't pick Envelope A at all)?

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Posted 14 July 2013 - 04:27 PM

Computer's are not confident, they either compute an answer or they don't.  It would play the probabilities of the human selection.

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### #8 phil1882

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Posted 14 July 2013 - 07:30 PM

well i personally see no good resolution to the puzzle. either way you have a good chance of ending with 0.

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### #9 phil1882

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Posted 15 July 2013 - 02:22 PM

okay how about this, instead of making a selection myself i simply let chance decide. for example i flip a coin or roll a dice.

it would be pretty hard for a computer to guess the outcome of such a result. though i suppose it would also be hard for a computer to guess accurately my decisions over a 5 year period. i don't see a better answer though.

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### #10 gavinksong

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Posted 15 July 2013 - 03:33 PM

okay how about this, instead of making a selection myself i simply let chance decide. for example i flip a coin or roll a dice.

it would be pretty hard for a computer to guess the outcome of such a result. though i suppose it would also be hard for a computer to guess accurately my decisions over a 5 year period. i don't see a better answer though.

Hey, that's kinda clever. Props for thinking outside of the box. Still pretty risky though. Remember, the odds don't look good and you're looking to lose a lot of money to your uncle.