Myto
For some reason, I've been noticing this mistake more and more lately.
The fact is, there are theories of QM that do not assume that entanglement happens faster than light. The Many Worlds theory is one that has no need for such hypothesis. And more generally, since you need to send the results via a classical (no faster than light) communication method, there's no way to be sure that the entanglement has happened faster than light.
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.
And once more, I'm talking about the problem as given, not some other problem. It is a self contained math / logic problem.
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?
By the way, once you make that assumption, those other scenarios you presented are also excluded.
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.
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.