| Topic Name: |
brainteaser |
| Message Name: |
"Switching Continually" |
| Date Posted: |
08/27/2002 |
| In Reply To: |
You are absolutely correct about the mathematics of the 'Monty Hall Problem', which is the common name for the three door (or envelope) problem.
I am not sure I am seeing your logic about the question in the original thread. Who gave the elegant derivation?
Could you explain to me exactly what you mean by "switch continually" ?
Thanks |
| Message: |
What I had intended to say was that in expectancy terms, switching will always be the right answer, *even* *though* this makes it right for *both* parties holding envelopes to switch. The reason is that the expectancy is a numeric average of the two envelopes (which is 1.25 'x', with 'x' being whatever you are currently holding). This sounds odd, but here is why it is the case. If one has a $10 bill, and the other a $20 bill, if the two people could combine their envelopes and share the money, they would each get $15. This is a *50%* increase for the person with the $10 bill, but only a *25%* decrease for the person with the $20 bill. In *percent* change terms, sharing effectively increases societal wealth. That said, the premise of this question is that you get x *or* y, not (x + y)/2. The "continual" piece of my explanation (which I see I didn't explain very well) is to say that if each person would want to switch, *both* would want to keep on switching, and the process would continue (until one was smart enough to suggest sharing the money).
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