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The fact that the host never shows the car is critical to the solution. You choose a door. There's a 2/3rd chance that the car is behind one of the other doors.
by salamanderman 5y ago
The fact that the host never shows the car is critical to the solution. You choose a door. There's a 2/3rd chance that the car is behind one of the other doors. Monty is kindly going to show which of the other two doors not to choose. ... The other way to think of it is, you choose a door, and then you're asked "would you like to keep what's behind your door, or would you like to have the sum of the other two doors?"
- shkkmo 5y agoNot at all. Once the door is opened, it doesn't matter if the host knew there was a goat behind it or not. Edit: The host's knowledge only matter if the host can choose not to open a door.
- salamanderman 5y agoIf the host opens the door with car, and asks you if you'd prefer to switch to the unopened door, then you have a 100% chance of being wrong, as the door with the car isn't one of the choices. But, sure, my second point still stands, that it's effectively asking if you want your door or the sum of the other two doors. But, to be clear, the question states that Monty opens the door with the goat. If you were to write a monte Carlo to test this empirically, you'd have to have your "Monty" choose the door with the goat.
- shkkmo 5y agoYou appear to have completely edited the comment I was replying to. My "not at all" does not apply to your comment as it currently reads, which is correct. On HN it is considered polite to append corrections rather than replace content that has become part of the discussion.