Envelope Dilemma?

Similar to the Monty Hall question....

You are on a game show. In front of you are 2 envelopes, each containing an unknown amount of cash. You are told that 1 envelope has twice as much money as the other. You are now asked to choose an envelope. You choose one. It contains $50,000. Now you are told that you can keep the envelope you picked, or swap for the other one. Should you swap?

https://wizardofodds.com/askthewizard/145

Wanna take a look at the next question?

Do you advise playing the money line or the spread on your NFL picks or does it not matter one way or another? - Aaron Kelly from New York

hmm i haven't actually paid a lot of attention to his sports advice columns, but even so this answer seems to directly contradict his own published nfl appendix: https://wizardofodds.com/sports/sports_apx3.html

i think we need to press mr.shackleford for an explanation

Only if your greedy!

Your box has 50k. Therefore the other has either $25k or $100k. Thus the EV of your box is (125/2)=62.5k.

So yes you should swap

(Answered without checking WOO link -- so hopefully right!)

If the correct answer is to swap, then obviously you should have chosen the other envelope to begin with.

ooooo...pretty funny. Fezzik must have gotten his sense of humor back with his huge weekend!

i believe why this problem was named a paradox to begin with is that the mathematically correct answer will have you swapping the envelopes endlessly as long as you were given the option to do so

that aside, fezzik what are your thoughts on woo recommending you bet the dogs on ml?

It doesn't make a difference in this case if you swap or not.

In the real "lets make a deal" example you should always swap.


Sticking to this example only....(I am assuming the size of the envelope is the same and there is really a check in the envelope or something).

Since you are correct 50% of the time before hand then you are correct 50% of the time afterwards since there was no selection bias to begin with.

Unlike the "lets make a deal" example, with just 2 choices and no selection bias you were correct as much as wrong. In the "lets make a deal example", there was a selection bias due to the fact that one of the correct choices was removed for you. If you were right initially (which is only .33) and you switched then you had a .66 chance of getting the good prize.


David...The way you phrased the question I am saying it doesn't make a difference if you switch or not.

Ok now where is my prize? LOL.