Remarkl
1 min readDec 25, 2024

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The important word in this version of the problem is "always." Without it, the answer becomes "Too little information." That word does not appear in the original version of the problem. Here's Wikipedia, quoting the version in Marilyn Vos Savant's article:

Suppose you're on a game show, and you're given the choice of three doors: Behind one door is a car; behind the others, goats. You pick a door, say No. 1, and the host, who knows what's behind the doors, opens another door, say No. 3, which has a goat. He then says to you, "Do you want to pick door No. 2?" Is it to your advantage to switch your choice?

In that version, you don't know that the host will always open a door with a goat. You know only that he has done so. Maybe he opens a second door only if you have picked the door with the car. Maybe he looks at his watch and, despite knowing what's behind each door, opens one door if the second hand is on an even number and the other if it isn't. If it's the car, you lose and go home. Only the "always" saves the problem, which raises the question of whether the problem stated here and the one stated by Marylin are the "same" problem.

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Remarkl
Remarkl

Written by Remarkl

Self-description is not privileged.

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