Marilyn vos Savant and the Monty Hall Problem (2015)

The remaining doors are not random. The one you picked still has a 1/3 chance of winning, that doesn't change with opening another door. However switching doors is essentially the same as picking all the other doors at once, since the door with a goat is not opened, thus the 2/3.

Imagine the thing with 100 doors and imagine the host isn't opening any doors, but just telling you what's behind them and it becomes pretty obvious.

Judging by the hazing Marilyn vos Savant received for her resolution of the Monty Hall problem, it seems like Twitter's preferred style of commentary isn't all that new.

The explanation that worked for me was:

Suppose after you make your initial choice, instead of opening a door, Monty simply asks if you'd like to switch to BOTH the other two doors, such that you win if the prize is behind EITHER of them.

That switch is intuitively a great deal, giving you 2/3 odds. The only way you can lose is in the 1/3rd case where you already picked a winner. The original scenario is equivalent to this, since by revealing a goat Monty is allowing you to pick "the best of" the two doors.

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Often people who don't like this problem complain that actually Monty, with his knowledge of the winning door, may be trying to trick you into losing. Maybe he offers this trade conditionally based on whether you've already selected a winner. Of course, this wouldn't support the most common intuitive answer of "it's 50/50", either, making this a bad excuse. If we accept this behavior from Monty -- not stated in the problem -- it becomes a very uninteresting problem based on whether we are dealing with Evil Monty who only offers the trade when it's a bad one (stay wins 100% of the time), Friendly Monty who only offers the trade when it's a good one (switch wins 100% of the time), or somewhere in the middle. It has no analytical answer. So for this to be a solvable problem at all we must assume we are dealing with Fair Monty who offers the trade all the time, or at least, offers it at random times not based on the contestant's initial pick.

TFA also presents this intuitive argument.

She said this:.

Marva Watkins in Chicago, Illinois, writes: What is your real last name?

Marilyn responds: It's "vos Savant," which was my mother's maiden name and is my own legal name. (My mother's maiden name is just as real as my father's boyhood name.) My maternal grandfather was Giuseppe vos Savant. Coincidentally, he married a woman named Maria Savant, my maternal grandmother. Growing up, I never thought about "Savant" being a word, too. I'm sure that people with the name "Miller" don't think about it, either! By the way, my mother changed her surname to my father's surname when she got married, which was traditional at the time. I use her name, and my brother uses his name.

https://parade.com/418148/marilynvossavant/marilyns-surname/