[extropy-chat] Re: monty hall paradox again: reds and green gorfs

[Rafal Smigrodzki]

----- Original Message ----- 
From: "Alejandro Dubrovsky" <alito at organicrobot.com>
To: "ExI chat list" <extropy-chat at lists.extropy.org>
Sent: Friday, May 21, 2004 5:46 PM
Subject: RE: [extropy-chat] Re: monty hall paradox again: reds and green
gorfs


> On Fri, 2004-05-21 at 11:35 -0700, "Hal Finney" wrote:
>
> > If you change the rules to say that there could be any value in the
> > envelope less than one billion dollars, then the correct strategy is
> > to switch if the value you see is less than half a billion, else don't
> > switch.  This is simple and logical and no one will disagree with it.
>
> *Raises hand* I do.  The problem is not so easily dealt with.  I was
> thinking of doing a simulation today until i realised the ridiculousness
> of what i was about to program:
> two agents,  two envelopes.   both get the same envelope (50:50
> probability of getting each envelope), but now one agent sits, and one
> swaps.
> ie, summarised:
> Agent1 = Envelope1
> Agent2 = Envelope2
>
> There's no way that this can lead to any difference between the agents'
> outcome (unless some magic happens when i first assign Envelope1 to
> Agent2 and then set it to Envelope2).
>
> Sticking or swaping makes no difference.  The hard bit is how to get rid
> of the double or half argument after opening the first one.  Probability
> of holding the bigger envelope then seems to get modified to 2/3 as soon
> as you open it.  How!?
>
### Is there a connection between the estimate of the relative size of
reward and the probability of holding the larger envelope? I don't see it.

Talking about relative reward sizes tends to obscure the issue. Note that
the absolute size of expected swapping reward if you hold the smaller
envelope is equal to the absolute size of swapping loss if you hold the
larger envelope, and both situations are assumed equally likely to occur -
isn't this a sufficient reason to stop fiddling with these envelopes?

Rafal