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Show HN: Monty's Gauntlet – Do You *Really* Understand the Monty Hall Problem? (tinkerdeck.com)
9 points by weepinbell 11 months ago | hide | past | favorite | 3 comments
A variant of the Monty Hall problem (the 7th one on this quiz) went semi-viral a couple months ago. For me at least, I may be able to walk through the reasoning of the original problem, and I may be able to convince myself it's correct, but it's very hard to build an intuition for why it's correct that feels truly sound.

So I thought it'd be interesting to have a quiz to contort the original problem in as many ways as possible to challenge my understanding and intuition. Try it out!



The one where Monty trips over a cord and opens a random door seems wrong to me. According to the explanation Monty doesn't give you additional information by accidentally revealing a goat, but it seems to me he gives exactly the same amount of information as he would by intentionally revealing a goat.

And the reasoning remains the same - when you pick a door you have 1/3 chance to pick the car, meaning the two other doors have a 2/3 chance to contain it. When he reveals a goat, my door is still 1/3 and the other one is still 2/3, so I should switch just like when he intentionally reveals the goat.


I believe the origin is here and explains it in a lot of detail: https://probability.ca/jeff/writing/montyfall.pdf

I should add the credit line, looks like I left it off for that one, though I think the general concept is pretty common.

One possible intuition is that when Monty opens a goat door in the original problem, the fact that he didn't open the other non-chosen door gives evidence that that door has a car (because it's more likely he doesn't open if it does have a car than if it has a goat).

In the "Monty Fall" variant, it's equally likely that he opens it whether it has a car or not. So the fact that it wasn't opened doesn't give you additional evidence for what's inside it.


Great quiz and really pushed me to understand probabilities better. Amazing take and i had a lot of fun!




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