“Your analogy doesn’t hold, because each spin of the roulette wheel is a separate trial, while choosing a door and then having the option to choose another are causally linked.”
No, they are not causally linked. It does not matter what door you choose, you don’t influence the outcome in any way at all. Ultimately, you have to choose between two doors. In fact, you don’t “choose” a door at first at all. Because there is always at least one goat behind a door you didn’t choose, you cannot influence the next action, which is for Monty to open a door with a goat. At that point it’s a choice between two doors.
At this point you’ve had this explained to you multiple times. May I suggest that if you don’t get it at this point, maybe be a bit of an empiricist and write a computer program to repeat the game many times and see what fraction switching wins? Or if you don’t have the skill to do that (in which case learning to program should be on your list of things to learn how to do. It is very helpful and forces certain forms of careful thinking) play the game out with a friend in real life.
If—and I mean do mean if, I wouldn’t want to spoil the empirical test—logical doesn’t understand the situation well enough to predict the correct outcome, there’s a good chance he won’t be able to program it into a computer correctly regardless of his programming skill. He’ll program the computer to perform his misinterpretation of the problem, and it will return the result he expects.
On the other hand, if he’s right about the Monty Hall problem and he programs it correctly… it will still return the result he expects.
Sure, but then the question becomes whether the other programmer got the program right...
My point is that if you don’t understand a situation, you can’t reliably write a good computer simulation of it. So if logical believes that (to use your first link) James Tauber is wrong about the Monty Hall problem, he has no reason to believe Tauber can program a good simulation of it. And even if he can read Python code, and has no problem with Tauber’s implementation, logical might well conclude that there was just some glitch in the code that he didn’t notice—which happens to programmers regrettably often.
I think implementing the game with a friend is the better option here, for ease of implementation and strength of evidence. That’s all :)
The thing you might be overlooking is that Monty does not open a door at random, he opens a door guaranteed to contain a goat. When I first heard this problem, I didn’t get it until that was explicitly pointed out to me.
If Monty opens a door at random (and the door could contain a car), then there is no causal link and therefore the probability would be as you describe.
“Your analogy doesn’t hold, because each spin of the roulette wheel is a separate trial, while choosing a door and then having the option to choose another are causally linked.”
No, they are not causally linked. It does not matter what door you choose, you don’t influence the outcome in any way at all. Ultimately, you have to choose between two doors. In fact, you don’t “choose” a door at first at all. Because there is always at least one goat behind a door you didn’t choose, you cannot influence the next action, which is for Monty to open a door with a goat. At that point it’s a choice between two doors.
At this point you’ve had this explained to you multiple times. May I suggest that if you don’t get it at this point, maybe be a bit of an empiricist and write a computer program to repeat the game many times and see what fraction switching wins? Or if you don’t have the skill to do that (in which case learning to program should be on your list of things to learn how to do. It is very helpful and forces certain forms of careful thinking) play the game out with a friend in real life.
If logical wants to play for real money I volunteer my services.
If—and I mean do mean if, I wouldn’t want to spoil the empirical test—logical doesn’t understand the situation well enough to predict the correct outcome, there’s a good chance he won’t be able to program it into a computer correctly regardless of his programming skill. He’ll program the computer to perform his misinterpretation of the problem, and it will return the result he expects.
On the other hand, if he’s right about the Monty Hall problem and he programs it correctly… it will still return the result he expects.
He could try one of many already-written programs if he lacks the skill to write one.
Sure, but then the question becomes whether the other programmer got the program right...
My point is that if you don’t understand a situation, you can’t reliably write a good computer simulation of it. So if logical believes that (to use your first link) James Tauber is wrong about the Monty Hall problem, he has no reason to believe Tauber can program a good simulation of it. And even if he can read Python code, and has no problem with Tauber’s implementation, logical might well conclude that there was just some glitch in the code that he didn’t notice—which happens to programmers regrettably often.
I think implementing the game with a friend is the better option here, for ease of implementation and strength of evidence. That’s all :)
The thing you might be overlooking is that Monty does not open a door at random, he opens a door guaranteed to contain a goat. When I first heard this problem, I didn’t get it until that was explicitly pointed out to me.
If Monty opens a door at random (and the door could contain a car), then there is no causal link and therefore the probability would be as you describe.