alt Hacker NewsI regret opening this can of worms called Monty Hall.
But anyway I'll link the relevant section from Wikipedia:
https://en.wikipedia.org/wiki/Monty_Hall_problem#Other_host_...
> The version of the Monty Hall problem published in Parade in 1990 did not specifically state that the host would always open another door, or always offer a choice to switch, or even never open the door revealing the car. However, Savant made it clear in her second follow-up column that the intended host's behavior could only be what led to the 2/3 probability she gave as her original answer. (emphasis mine)
My point was that when people ask this question, they often word it like the very 1990 version did, lefting out this critical statement (which Savant considered needed as well, therefore she clarified in the follow-up column), making the question ambiguous.
(Although Savant also said "Very few (out of people who said is 2/3 is wrong) raised questions about ambiguity"... so perhaps people are actually just bad at probablity...?)
Just be glad that you didn't go for the 2 envelopes problem which was her next. Vos Savant was wrong about that one, and few people like the real answer.
The problem is that you're presented with two envelopes with 2 real numbers inside. You randomly select one, then look, and try to guess if you got the larger number. It doesn't seem like you can do better than even, but you can!
Unfortunately everyone hates the answer. Which is that you make up a random number and pretend it is the other one. Your odds of being right are
50% + (probability of choosing between the numbers) / 2
Which can always be strictly bigger than 50%. (Though possibly by only a little amount.)
Special case. If those numbers and yours were all independently randomly chosen from the same distribution, you'll be right 2/3 of the time.