[extropy-chat] monty hall paradox again

[Alejandro Dubrovsky]

On Wed, 2004-05-19 at 00:47 -0600, Alan Eliasen wrote:


> > I reason that there is a 50% chance the other envelope
> > contains 5 dollars and 50% chance it contains twenty,
> > so mathematical expectation value of the other envelope
> > is .50*5 + .50*20 = 12.50 so I would trade.  Same reasoning
> > applies if the first envelope contained 500 or 5000
> > dollars or a billion, all under the assumption that seems
> > so natural to me, that money is good, so more is
> > better and too damn much is just right.  You trade
> > 5 dollars for a 50% shot at 20.  Such a deal!
> 
>    The fact that this leads to a paradox is probably the tip-off that the
> reasoning isn't quite right.
> 
>    Say that the envelopes contain n and 2n dollars.  Then, you'll either pick
> the envelope that contains n or 2n on your first guess.
> 
>    Draw the payoff matrix for staying or switching:
> 
>    First pick  ---->  n    2n
> --------------------------------
>       Stay            n    2n
>      Switch          2n     n
> 
>    Projected earnings for either case is 3/2n, and no option (always staying,
> switching, whatever) improves that.
> 

So are you saying that once you opened the first envelope and it had
$10, you wouldn't switch?
alejandro