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mwengler comments on Solving the two envelopes problem - Less Wrong
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Yes, I like your simplification.
To amplify it and make the results explicit, Suppose my envelope strategy is to flip a fair coin and
heads: R=$5 B=$10
tails: R=$10 B=$5.
Then
E(R) = E(B) = $7.50
E(B)/E(R) = E(B)/E(R) =1
E(R/B) = E(B/R) = 1.25