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My favourite probability problem

Posted By: joe freedman
Date: Saturday, 29 August 2009, at 3:16 a.m.

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

<You know that if you take the $1K you will very probably end up with $1K. You know that if you do not take the $1K you will very probably end up with $1M. Your expectation on taking the $1K is close to $1K, your expectation on not taking the $1K is close to $1M.

Can it be right to make a hugely -EV decision? Can it be right to take one course of action which very probably results in $1K and forgo the other course which very probably results in $1M?

If so, how do you explain it? >>

I do not accept either of these premises (on what will "probably" happen). My probability of winning the 1M is fixed, because the envelope either does or does not contain the check. So whether I disdain the grand and open the envelope first, or I grab the cash first, my odds of winning the 1M does not change, regardless of the prediction. The notion that the prediction should induce me to defy the laws of nature reminds me of the cartoon where a character makes the car go faster by pushing the speedometer needle. It works in cartoons.

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