Re: Interesting Mathematical Paradox?
Right. I'm sweeping it under the rug with the word "probably". If the situation were like with your brother then seeing the amount in the envelope does give you more information. I'm not exactly sure what information it might give in general.
However, here's the sense in which I think my statement has validity. Suppose many different people are offered such envelopes. Each of them wagers $100 that they have the smaller envelope. Each of them ignores the amount they see in their envelope and continues their $100 bet. At 2-1 odds they will on average make money on their $100 bets. But they will not on average make money from the Envelope Switch. This I think is at the heart of the psychological conundrum.
PairTheBoard
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