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My favourite probability problem

Posted By: Stein Kulseth
Date: Friday, 28 August 2009, at 8:55 a.m.

Seeing as these generate some interest, I can't stop myself from adding my favourite, the Newcomb paradox:

You are to receive a gift from an entity known as The Predictor (man, machine or alien ...). You know the following facts with certainty:

  • The Predictor is completely honest
  • The Predictor is able to predict the future actions of any human to near-certainty, at least well above 99% success rate
  • The Predictor's predictions are based on it's current observations only. (Eg. while it may conceivably be able to scan and register the state of every synapse in your brain - it cannot do time travel, it cannot change its predictions after the fact, nor can it force you to act in any way you would not do yourself in order to make its predictions)

    • Note that it does not matter how you know these things - invent your own encapsulating story if you wish.

    Now the Predictor gives you an envelope marked and lets you know that it contains either a $1,000,000 cheque or nothing. This envelope and its contents are now yours. In addition, before you open the envelope, you may decide to receive an additional $1,000 in cash, or you may choose to turn down this offer.

    The catch: The Predictor lets you know that it put the $1,000,000 in the envelope if and only if it predicted that you would plainly turn down the offer for the extra $1,000, without resorting to any other measures than thinking about it (that is: no trying to peek in the envelope, no coin tossing, no hedge bets etc. etc.)

    Now what should you do in order to get the most money?

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