Thefefore, Monty could be using the strategy of "if the player chose the car door, open a goat door and give the option to switch. Otherwise don't give the option to switch and the player wins the goat." In that case switching is a losing strategy.
Sometimes you have to use common sense, and I think every instance of the monty hall problem I've seen was sufficiently explicit (without being absurd), and the confusion was always around the math and probability and never around semantics or trickery.
The fact is that the argument I have presented demonstrates that the problem as given is flawed and does not have a unique answer. Most people don't understand this and substitute the correct version of the problem in their mind, and then proceed to solve that by arguing about the probabilities. Of course the probabilities are what the problem is "supposed" to be about.
You seem to be finding flaws where there are none. You are suggesting there is subtle unspoken trickery hidden in the problem (just as in my example) but nothing about the problem suggests that should be the case.
What if the host lets you choose to switch every game but if you make the right choice he says you are wrong without opening the door and the game is just over? What if he says the door you chose is eliminated and the remaining door is your prize if you chose correctly? What if you win and then he says you have to play best 2 out of 3 to really win, and if you win again he says 3 out of 5, and keeps moving the goalposts until you lose?
Suggesting the problem is flawed because you can imagine up fringe scenarios that are not explicitly excluded does not seem like a useful criticism.
By the way, once you make that assumption, those other scenarios you presented are also excluded.
> By the way, once you make that assumption, those other scenarios you presented are also excluded.
Even more of a reason that "flaw" shouldn't even be considered.
There is no hidden trickery and no reason to assume the game isn't fair.
In A, Monty Hall behaves like you think: always opens a goat door, always gives the option to switch.
In B, he behaves like I described: opens a goat door and gives the option to switch, but only when the player has chosen the car door. Otherwise he does not let you switch.
And then we find ourselves in this situation:
> 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?
At this point, how do you know you are in world A and not B (or some other world)? What in this problem as given here allows you to determine that?
If it was the first time the show ever aired, you could be in a situation where you didn't know whether it was A or B. But in the problem as normally posed, you have time to watch the show for months to years, and you know how Monty behaves.
And once more, I'm talking about the problem as given, not some other problem. It is a self contained math / logic problem.
I bet you could take any problem of similar nature from anywhere and scrutinize hard enough and find some gimmick that lets you claim similar claims about it, but I don't think that's useful or noteworthy.
At the end of the day we all rely on common sense and common assumptions about these kinds of things. It may be true that some don't have the same shared experience to draw upon and lead them to the same understanding as others, but that doesn't make the problem flawed. It just means people understand things differently.
If a significant number of people brought up this issue then my opinion might change, but as I said, this is the only time I've heard of this particular complaint (and I've been enjoying posing this problem to people for decades now), and that means, in my opinion, there is no grounds to claim your misunderstanding as some objective flaw in the wording or presentation of the problem.
If it's about popularity instead of logical argument, of course I'm not the only one who thinks this. There was a really good blog post that laid it out but I can't find it currently. Instead, here's a scientific paper I found just now, the introduction contains the same argument I'm making. And it's far from the only place which agrees.
https://link.springer.com/article/10.1186/2195-5468-2-2
> The problem posed in this way may lead to a lot of controversy, mainly because we do not know whether the behavior of the host had anything to do with your first choice or not.
> Perhaps the host would open a door with a goat only when your first choice was right. In this case, it was not a good choice to change doors.
EDIT: Also several people have pointed this same thing out elsewhere in this thread.