Two Envelopes
June 2nd, 2007
You write down 2 numbers on 2 pieces of paper (one number on each piece). You put each paper in a sealed envelope. I choose one of the envelopes randomly and open it. I then carry out a certain procedure at the end of which I know with a probability greater than 1/2 whether I received the larger or the smaller of the numbers. I can do this even if when you initially wrote down the numbers, you knew my decision procedure!
How can I do that? What is my trick?
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November 8th, 2007 at 12:33 pm
There is anothe great riddle with two envelopes that you might know.
In one envelope I put some amount of money, and in the other one I put double that amount (you don’t know the amount). I shuffle the envelopes, and you select (randomly) one of them, which you open, and you observe the amount, say $10. Now, the other envelope holds $5 with probability 1/2 and $20 with probability 1/2. So the average value for the other envelope is $12.5, higher than the one you have. I offer now the possibility to change and take the other envelope. Would you do so? why, or why not?
Now, imagine you don’t open the envelope when you first choose it. Does anything change? (this envelope has x inside, and the other one has on average 1.25x. Or not?)