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BGonline.org Forums
My favourite probability problem
Posted By: joe freedman In Response To: My favourite probability problem (playBunny)
Date: Friday, 28 August 2009, at 11:28 p.m.
jf: The predictor has already taken his action -- what you do cannot affect the result.
PB: And what action was that?
JF: Two actions, actually. The predictor made his prediction, and then predictor sealed the envelope, after either putting a check in it or not. Nothing you do can change either of those actions.
PB: Bob Koca mentioned that he thought it was perhaps more of a pholiosophical [sic] problem. Why? As I see it, it's because you have an entity that will have done something dependant on what you are about to do. If you do something differently then it will have anticipated that and acted accordingly.
JF: Oh, so this is supposed to be about determinism and free will? But in the end it doesn't matter -- there is no penalty for choosing the cash first, unless you think that action will magically remove the check from the envelope. But if you don't have free will, then your course of action is already determined, so there's no choice involved.
Looking at it differently, what if you think: The Predictor is always right, if I decline the cash, that means he will have predicted that I would decline the cash, which means I get the $1M. There are two fallacies there. First, the problem said that the Predictor is almost always right, not 100%. Second the prediction has already been made; your action cannot retroactively make it right. If the Predictor predicted that you would take the cash, then you won't get the $1M whether you take the cash or not. The most you can win is $1K. If the Predicator predicted that you would not take the cash, then the $1M is in the check and you can grab both. Of course, that will show the predictor to be wrong in this instance. If the Predictor were really always right, then you would be unable to act at variance with the prediction.
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