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My favourite probability problem

Posted By: Keene
Date: Friday, 28 August 2009, at 10:07 p.m.

In Response To: My favourite probability problem (Matt Cohn-Geier)

The predictor is the problem here. He either correctly predicted that you would reject the $1k, or he correctly predicted that you would accept it. Therefore for your assumptions, the envelope is essentially undetermined, as you have not made a logical conclusion as to your actions yet. As soon as you make your logical conclusions about how to proceed, the envelope is no longer undetermined. It doesnt matter what point in time this happens at, The Predictor already assessed how you would proceed, and knows with almost certainty exactly what you will do. So you either goof it up, and get $1k, or you dont, and get the $1M.

Based on the logic of this, my goal is for his prediction to be that I rejected the envelope, so therefore I follow that reasoning set in order to get the $1M. The Predictor is almost certain that he knows exactly what I will do, with that in mind, the timeframe becomes irrelevant as whatever he predicted you would do is going to be accurate.

Take the timeline out of the equation, and it becomes a whole lot easier.

What if The Predictor put you in a room, no windows, and said 'Tell me once you have made your decision on whether to accept the $1k or not, then I will predict what you will do, and fill this envelope as appropriate'. Its the same problem, just re-arranged in timeline is all. Only now you have removed the 0 or 1 state, and made it flexible until you decide how to proceed.

I think the end result of this is almost no-one will get $1,001,000, some will get $1M, some will get $1k. The Predictor is almost always correct. Half of the time when he is wrong, someone will get the extra $1k, the other half, nothing.

I believe the way to get the $1M is to be absolutely certain of your action, no debate in your mind. That way the Predictor will have correctly predicted your course of action.

Is there an actual answer to this theoretical problem? Can I meet this Predictor guy?

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