[extropy-chat] monty hall paradox again

[Rafal Smigrodzki]

----- Original Message ----- 
From: "Spike" <spike66 at comcast.net>
To: "'ExI chat list'" <extropy-chat at lists.extropy.org>
Sent: Sunday, May 23, 2004 12:34 PM
Subject: RE: [extropy-chat] monty hall paradox again


>
>  David wrote:
>
>
> > Call the larger envelope value LV,
> > the smaller envelope SV,
> > the minimum possible amount of zorgs is z.
> > and i is some integer.
> >
> > SV must be i * z.
> > But LV = 2 * SV , therefore SV can only increment in steps of 2z.
> >
> > This means that for any given range there are twice as many
> > possible SV values as there are LV values.
> > This means that the chance that the other envelope is the
> > smaller one is twice the chance that it is the larger one.
> >
> > expected value becomes 2/3 * 5 + 1/3 * 20 = 10.
>
> I am examining this argument carefully, for it is
> tempting indeed.  The phrase "for any given range" makes me
> squirm a little, for I fear that it incorrectly causes the zorg
> version of the puzzle to collapse to the less interesting
> real dollars version, which is solved by Eliezer's solution.
> The real dollars version is merely a poker match.
>
> On the other hand, I suppose that even with zorgs, there
> must me *some* finite range.  Do let me ponder, thereby
> dumping even more perfectly good life into this maddening
> time-sink.

### Quite simple - in a finite range, there is a maximum amount of zorgs, m.

Then for envelopes with x> (m-z)/2, you swap, for x<(m-z)/2 you stick, for x
= (m-z)/2 you stick, since swapping costs you effort.

For an infinite range, you complain to the donor that thinking about
infinite ranges give you a headache, and you don't want to play.

Rafal