The money in 2 evelopes \"paradox\"
I don't know if this has been discussed here before.
here's the paradox ...
Suppose you're given 2 envelopes with money in them and you are told that one contains twice as much as the other (let's say they're cheques and therefore weight is not an issue). You pick one and open it up to reveal a $100 cheque. You are now offered the opportunity to switch envelopes.
Is switching +EV?
Argument 1: It's +EV to switch. You had a 50/50 chance of picking the high or low envelope so there's a 50% chance that the other envelope is the high and a 50% chance it's the low. Therefore, EV of switch = 0.5*(+100) + 0.5*(-50) = +25.
Argument 2: It's EV neutral. If always switching was a +EV strategy then it would be more profitable to choose envelope A first and then switch to B then to just choose envelope B and not switch.
Who's right?
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