Interesting Mathematical Paradox?

[PairTheBoard]

[ QUOTE ]
Do you then want to switch? The answer I arrived at is, yes, you do want to switch envelopes every time! I currently have $20. The other envelope muse have either twice as much or half as much- in other words, it must have either $40 or $10, ...


[/ QUOTE ]

Yes. However you Don't know that the probability is 50% for the $40 and 50% for the $10. Therefore you cannot draw the conclusion,

[ QUOTE ]
... so your EV by switching is $25 ($50 / 2).


[/ QUOTE ]

Just because there are two possibilties doesn't make them equally likely.

PairTheBoard