Re:Two envelopes problem
by johnrob on Tuesday May 31, 2022 @11:07AM
(#31570401)
Sounds like a misuse of relative return (growth rate). If you gain 100% today, then lose 50% tomorrow, you are back where you started. Absolute numbers give you the correct answer: x -> 2x is a gain of x, 2x -> x is a loss of x, so expected value is zero (x is a hard number not a ratio).
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Re:Two envelopes problem
by metacritic12 on Tuesday May 31, 2022 @11:11AM
(#31570453)
Exactly! The logic of "the average of +100% and -50% is positive" only applies if the denominator is the same. In this case it isn't.
The relative percentage "rule of thumb" doesn't even feel like a primitive in math. It seems wrong to reason from that.
why isn't this listed in wikipedia as an answer.
Re:Two envelopes problem
by whatshisface on Tuesday May 31, 2022 @12:07PM
(#31571237)
Because if the larger envelope is changed to contain four times as many dollars, then /2 vs. *4 points back towards swapping indefinitely.
Re:Two envelopes problem
by MrBlueIncognito on Tuesday May 31, 2022 @12:53PM
(#31571829)
If one envelope contains 4 times the money of the other envelope, then by swapping you either gain 3x or lose 3x, where x is the amount of money in the smaller envelope. Even in this case, the average return is +3x -3x = 0.
It is, it's the one where you treat both as having the same expected value