You participate in a game show where you must choose between 3 doors. Behind 2 doors is a goat, but behind 1 door is a car. You pick a door, say door no. 1, but before you open the door, the host opens another door, say door no. 3, which has the car behind it. "Oops," says the host.
You lose.
The odds only change if what's behind the doors are fixed ahead of time.
If the host chooses a door, the game show rolls 1 out of ndoors chance of car behind it, and then puts the car or goat behind it before opening it then the odds don't change at all even if the host didn't know.
Switching your choice is the classical hidden-information answer, staying with your first choice is the quantum changes when-observed answer.
Yeah, but the assumption is that there is a right door. You're changing the fundamental rules of the problem and saying "guys, when you say the whole thing works differently, it works differently!" That's true, but it's not exactly insightful or useful.
You're saying your assumption is a fundamental rule... really? The insightful thing here is don't confuse assumptions with rules.
It's an entertainment show that's giving away free cars for advertisement. If they give contestants 50/50 they lower their prize payout, or if they give 2/3 odds maybe they get more audience investment. Maybe it's more work for them to keep giving out goats than cars because they have to train them to be calm on set. I have no idea how game shows prioritize these things.
Okay, man.
Anyway, here's the actual question:
I bolded the parts where it explicitly says it works the way I told you it works.
Source
Ok well in that phrasing of the problem you're right, the show has put the goat/car behind the doors ahead of time.
I don't know that's how it works on the Price Is Right or other actual game show. I would assume so, but they could set it up differently for the reasons I mentioned.
edit: although that still doesn't mean you should switch doors - that relies on the assumption that the host always opens another door (not stated in the problem) and didn't just offer you the choice (like "is that your final answer?" in Who Wants To Be A Millionaire) because he knows you picked the car.
You can see this in Savant's second follow-up article where she says "remembering that the original answer defines certain conditions, the most significant of which is that the host always opens a losing door on purpose". This is certainly not defined in the original question, which is entirely phrased about a single event and says nothing about "always". Instead of writing how she was right based on her assumptions, and they right with their assumptions, she's retconning the problem definition so only she's right.
Yup.
If everything is fake and gay, it doesn't matter if you switch or not, the funniest outcome will happen, if someone has their hand in it. i.e., you switch, and the car was "always" behind the door you initially chose. Oops, you lost!
It's also pointless, though, because if everything is in flux, your choice doesn't matter. So the fixed version is the only one that really makes sense, if the "problem" is expected to be solved.
It could be worse. You could open a door and there be 3 doors behind it.
It doesn't have to be 'fake and gay'.
Typically in regulated gambling, like with slots, they tell you your odds of winning. Slot machine doesn't know what the roll will be before you roll it.
Same principle. The game show may give all contestants a 50/50 chance of winning regardless of what doors they pick.
In which case it doesn't matter. The only way the problem makes sense is if the prizes are already fixed.
It's a game show. In what way does giving out free cars make sense other than as entertainment?