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#1
08-08-2006, 01:30 PM
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Envelopes
Some friends and I had this debate at work the other day.
There are two envelopes in front of you. One contains twice as much money as the other. You choose an envelope and it contains $10. You are now given the option to switch envelopes. Do you switch? 
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#5
08-08-2006, 01:55 PM
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Re: Envelopes
I know a simple expected value calculation tells you that you gain $2.50. But have you really gained any new information?
Let's say the envelopes are A and B. You pick A and it has X dollars in it. The math tells you that you gain 0.25X by switching to envelope B. This same logic can be used to switch from B to A also. The fact that there is $10 in the envelope or the fact that the envelope is even opened at all is completely irrelevant. You see what I'm getting at? The math is telling me one thing, but it's very counterintuitive.
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#7
08-08-2006, 02:08 PM
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Re: Envelopes
[ QUOTE ]
we are on the same page. all i know is that i would pay $10 for a 50/50 chance at $20 and a 50/50 chance at $5. i can't explain why i seem to have an advantage vs. just choosing randomly. [/ QUOTE ] That's what I was thinking, but it's still just as random.
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#8
08-08-2006, 02:10 PM
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Re: Envelopes
[ QUOTE ]
The fact that there is $10 in the envelope or the fact that the envelope is even opened at all is completely irrelevant. You see what I'm getting at? The math is telling me one thing, but it's very counterintuitive. [/ QUOTE ] Hmm, consider this: One person picks one envelope, opens it, and then trades it for the other since it is +EV (he can make double while only losing half). The other simply takes whatever money's in the envelope he picks first. If they both did this a million times, would they not likely end up with the same amount of money? So, switching is then not really +EV, it only seems so? I am no good at math so maybe I'm missing something.
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#9
08-08-2006, 02:34 PM
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Re: Envelopes
i don't think you're missing anything. this is irritating me because it really, really, seems like i'm choosing between $20 and $5 with equal probability.
i guess what it boils down to is that i can't use my subjective probability measure of .5 to calculate my EV.
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#10
08-08-2006, 04:16 PM
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Re: Envelopes
I think its pretty normal to first, realize the obvious answer is 'switch,' and second, be confused by how it seems an obvious +EV move to switch, yet choosing randomly should be the same EV...right? This is called the Monty Hall problem, with a linky here
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