Re: Two envelopes and game theory

On Tue, 27 Dec 2005 17:24:20 +0000, Christian Bau
<christian.bau@xxxxxxxxxxxxxxxxxxxx> wrote:

>In article <tkjjq1hgcgtrsjadg1catfsmrp38nihhmb@xxxxxxx>,
> quasi <quasi@xxxxxxxx> wrote:
>
>> On Wed, 21 Dec 2005 16:15:29 EST, Kees <kees@xxxxxxxxx> wrote:
>>
>> >>
>> >> "Kees" <kees@xxxxxxxxx> wrote
>> >>
>> >> >> Consider this more simple question:
>> >> >>
>> >> >> Is the strategy "switch the envelopes if you find
>> >> 1
>> >> >> or 2" better than the
>> >> >> strategy "switch the envelope if you find 1"?
>> >> >>
>> >> >> I think the answer is YES if the number of rounds
>> >> is
>> >> >> big but I find
>> >> >> difficult to figure out how to prove it and how to
>> >> >> relate the answer to the
>> >> >> number of rounds...
>> >> >>
>> >> >>
>> >> >
>> >> > assuming the game can be played as many time as we
>> >> want, the expectation
>> >> > of any strategy is infinity.
>> >>
>> >> The game consist of 100 rounds.
>> >>
>> >>
>> >
>> >OP was wondering about a strategy when n is big. My comment should hint that
>> >for large n all strategies almost equal. To make it precise: given two
>> >strategies let X be the ammount won after n step using strategy 1 and Y the
>> >ammount gained from strategy 2. Then X/Y tends to 1 as n tends to infintiy.
>>
>> All strategies are equal in terms of expected value.
>>
>> Even the obvious mandatory switch if the envelope contains 1 is
>> actually irrelevant to the expected value.
>
>Your mistake is to assume that we are looking for the strategy with the
>highest expected value. We are not.

You are looking at an old reply. That mistake was already admitted and
corrected.

quasi
.

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