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by aaroninsf 1195 days ago
I've always found the Monty Hall problem a poor example to teach with, because the "wrong" answer is only wrong if you make some (often unarticulated) assumptions.

There are reasonable alternative interpretations in which the generally accepted answer ("always switch") is demonstrably false.

This problem is exacerbated (perhaps specific to) those who have no idea who "Monty Hall" was and what the game show(?) was... as best I can tell the unarticulated assumption is axiomatic in the original context(?).
2 comments
lmm 1195 days ago
The unarticulated assumption is not actually true in the original gameshow. Monty didn't always offer the chance to switch, and it's not at all clear whether he did so more or less often when the contestant had picked the correct door.
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japaniard 1195 days ago
What unarticulated assumption needs to be made for switching to be incorrect?
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bombcar 1195 days ago
I believe the key is that he ALWAYS shows a goat.

You have to know that for it to work. If sometimes he just does nothing and you have no chance to switch, the math “trick” fails.

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mahathu 1195 days ago
The assumption is that Monte will only reveal the one of the two unopened doors that has the goat behind it, as opposed to picking a door at random (which may be the car or may be the door the participant chose, which itself may or may not be the "car door").

The distinction is at which point Monte, assuming he has perfect knowledge, decides which door to reveal.

In the former, the chance to win is 2/3, in the other 1/2. However in any case, always (always meaning: in each condition, not in each repetition of the experiment, as this is irrelevant) switching is better than never switching, as there your chance to win is only 1/3.

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japaniard 1194 days ago
How is it an "assumption" that Monte reveals a goat? Doesn't the question explicitly state that Monte opened one of the other two doors to reveal a goat?

Are there versions of the question where Monte doesn't reveal a goat behind his door or chooses the same door as you?

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mahathu 1194 days ago
Yeah, here:

https://en.wikipedia.org/wiki/Monty_Hall_problem#Other_host_...

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