You are told there are two envelopes. One contains twice as much money as the other one. You pick one but are allowed to change your mind after picking it. (You are equally likely to pick the one with less money as the one with more money.)
To figure out how much on average the other envelope should contain, one might average x/2 and 2x because one is equally likely to pick one as picking the other. Since this comes out to 5x/4, one might always change his or her mind. But wouldn't this end up with one never making up his or her mind?
Assume that there 100 people given 2$. Beside each is an spare envelope and half of the spare envelopes have 1$ and the other half has 4$. If everybody swiched, the average amount of money people would have is 2.50$. If nobody swiched, the average would be 2$. So it is better to switch.
In order for there to be no advantage, the difference between the 2$ and 4$ must be the same as 2$ to 1$ but it is obviously not.
Edited on December 15, 2006, 2:07 am
Edited on December 15, 2006, 2:09 am
Posted by Haruki
on 2006-12-15 02:05:32