Yes, I like your simplification.
To amplify it and make the results explicit, Suppose my envelope strategy is to flip a fair coin andheads: R=$5 B=$10tails: R=$10 B=$5.
ThenE(R) = E(B) = $7.50E(B)/E(R) = E(B)/E(R) =1E(R/B) = E(B/R) = 1.25
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