The envelope dilemma & who wants to be a millionare

[KSakuraba]

While ago there was this discussion about the paradox with two envelopes with different amount of money and the EV of changing the one you choosed to the other one. The more obvious version of it was (for those who haven't heard) when you have three envelopes and one has money,you choose one, one of the two remaining with no money is dumped an after that it is clearly +EV to change your envelope to the remaining one.
This made me think about the "Who want's to be a millionare" and it's 50-50-choice...so if you have no idea to the answer of the question, is it possible to just choose one in your mind and then take the 50-50,if the computer dumps your choice then you can curse your luck but if your choice stays, is it profitable to change your choice to the other answer remaining...based on the envelope-thinking?
I hope i made my point in understandable way, this really has been bothering me... /images/graemlins/tongue.gif

[Jordan Olsommer]

[ QUOTE ]
so if you have no idea to the answer of the question, is it possible to just choose one in your mind and then take the 50-50,if the computer dumps your choice then you can curse your luck but if your choice stays, is it profitable to change your choice to the other answer remaining...based on the envelope-thinking?

[/ QUOTE ]

It makes no difference. The reason switching is +EV in the Monty Hall Problem is because Monty works around your choice to begin with. If you said "My first choice is A, now give me the 50-50" and Regis or whoever removed two incorrect answers from the three remaining, then you would switch every time - in doing so, you'd end up at the correct answer 3/4ths of the time (because only 1/4th of the time do you pick the correct answer randomly, and therefore only 1/4th of the time do you switch from the correct answer to an incorrect one)

But with the 50/50 in the Millionaire game as it is, it makes no difference whatsoever if you "switch" from your choice or not.