Show HN: Monty's Gauntlet – Do You *Really* Understand the Monty Hall Problem?
9 points
1 month ago
| 2 comments
| tinkerdeck.com
| HN
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!

sfn42
1 month ago
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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.

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weepinbell
1 month ago
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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.

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