[extropy-chat] monty hall paradox again

[David]

Spike wrote:

>> Could it really be that you don't realise? Could it be that you
>> do realise and some others don't and that you enjoy that?
>
>
> Oh I enjoy it, but no I do not realize. Read on.
>
>>> For that reason, there really is no reason to bother opening
>>> and looking in the envelope you chose first.
>>
>> Re-read what you wrote when you first outlined the hypothetical
>> at the top. It is only AFTER an envelope is chosen and opened
>> revealing that it contains 10 dollars that the messenger offers a
>> second trade. The messenger did not say from the outset that
>> whatever the first envelope contained the contents could be
>> exchanged after being determining for the contents of the other
>> envelope prior to their being determined. If that whats you
>> wanted the messenger to say thats a different hypothetical.
>>
>> How long has this list been discussing a twisted hypothetical? Brett
>
> Paatsch
>
> You may be onto something Brett. What difference does it make
> if the messenger tells you up front that after making a
> choice, you will be given the option of trading? The
> paradox doesn't seem to disappear if it is carefully
> explained up front, but do suggest a modification of
> the scenario if you can fix it.
>
> spike
>
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Lets make things worse :)
If you open the envelope to find 10 zorgs there are two possible
scenarios :
5:10 and you have the larger amount, and
10 :20 and you have the smaller.
Each of these has a 0.5 probability of being the scenario you are in.
Therefore there are four possible values to the envelopes :

5
10 (high)
10 (low)
20

giving an average value to an envelope of 11.25 zorgs.
At least that?s closer to 10 than 12.5 is. :)