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It's great that you're so sure of yourself, just a shame that you're wrong. If the host picks randomly, your chances are in fact 50-50. Think of it this way: i

It's great that you're so sure of yourself, just a shame that you're wrong. If the host picks randomly, your chances are in fact 50-50. Think of it this way: imagine every time the hosts picks the car the universe resets. Now imagine you see the host picking a goat. There's a 2/3rds chance in your universe you picked the car, and a 1/3rds chance you picked a goat, and so switching would seem like the bad option. This actually cancels out the effects of the normal Monty Hall problem, and we are left with a 50-50 chance.

jVinc 5y ago
It's funny to me that there always seem to be an over representation of rude people among those who get this problem wrong. There is absolutely no need to attack my person. As for the problem, you are just plain wrong. We are talking about are regular old TV-quiz, there is not "universe resetting button" to save your logic. In the regular situation, the host always remove a goat. because otherwise the quiz show is kinda boring. But in the modified version we are considering where he just picks a door at random, then in 2 of the 6 possible outcomes for the door the host picks, he'll be removing the car. Now since the problem has the host showing the doors content, that should be the end of the game show. Who want's to see someone pondering if they should switch between a goat and another goat right? But that doesn't change the logic at all, because the conclusion of "you should always switch" isn't impacted in any way. 0% to 0% is just no change. And in the rest of the cases your'll go from 33% to 66%. Now of cause what would happen in your odd example where the host has a universe resetting button is that you don't have any choice at all, because no matter what the host will reset the universe until they maximize ratings, which might have you get the car or might have you not get the car, but there's no choice to be taken and the outcome that has maximum rating will always happen with 100%. That's why most stats problems avoid introducing "then the host resets the universe" in their problem description, it kind of ruins the whole point of calculating proabilities.
- listenallyall 5y ago
  I agree with you that "the universe resetting" is a dumb way to visualize or explain the problem. But if Mr. Hall opens the first door randomly (essential that it was a random choice), and it revealed a goat, then no, switching does not provide an advantage. You do not go from 33 to 67%. Instead, you are left with 2 options, both of which originally had a probability of 33% of containing a car, and which, now that the third option has been eliminated, are both currently 50%.
- dbt00 5y ago
  Think of it this way. In the original problem, there was a 1/3 chance of your original choice being the car, and a 2/3 chance of the other two. The host knowing which door to open gives you information without changing the odds, so there's still a 2/3 chance you picked wrong. When the host does not know which door to pick, there's a 1/3 chance that you picked right, a 1/3 chance that the host opens the door with the car, and a 1/3 chance that you should switch. The host opening the door with the car ends that branch, so you're left with 2/3 of the original probability, and your odds for either branch remaining are 50:50.
stale2002 5y ago
> imagine every time the hosts picks the car the universe resets Do you believe that we live in a universe that is reseting, every time Mr Monty hall opens a car? As in literally Mr Monty Hall. From the game show. In real life. Because the purpose of the question is to mimic the show.
- TchoBeer 5y ago
  You could also consider a case where they send in a new contestant every time the Random Monty Hall picks a car, and the result is the same.
  - stale2002 5y ago
    > You could also consider a case where they send in a new contestant every time the Random Monty Hall picks a car In the actual show, do you believe they are sending in a new contestant every time Monty hall picks are car? Do you think that is what is happening in the actual game show?
    - TchoBeer 5y ago
      No, obviously not. We're talking about expected values though, so it's a useful thought experiment.
      - stale2002 5y ago
        > We're talking about expected values though No, what people are talking about is the actual game show. They are doing a statistical analysis of how the actual game show works, in real life. So nobody is talking about a different, hypothetical situation, where the universe is reset, or the game show host brings out a new contestant every time. Instead people are talking about how the actual show works. And your scenarios that you bring up, are not relevant, and therefore wrong. > so it's a useful thought experiment. No, it is a different thought experience that applies to a different situation.

jVinc 5y ago

It's funny to me that there always seem to be an over representation of rude people among those who get this problem wrong. There is absolutely no need to attack my person. As for the problem, you are just plain wrong. We are talking about are regular old TV-quiz, there is not "universe resetting button" to save your logic. In the regular situation, the host always remove a goat. because otherwise the quiz show is kinda boring. But in the modified version we are considering where he just picks a door at random, then in 2 of the 6 possible outcomes for the door the host picks, he'll be removing the car. Now since the problem has the host showing the doors content, that should be the end of the game show. Who want's to see someone pondering if they should switch between a goat and another goat right? But that doesn't change the logic at all, because the conclusion of "you should always switch" isn't impacted in any way. 0% to 0% is just no change. And in the rest of the cases your'll go from 33% to 66%. Now of cause what would happen in your odd example where the host has a universe resetting button is that you don't have any choice at all, because no matter what the host will reset the universe until they maximize ratings, which might have you get the car or might have you not get the car, but there's no choice to be taken and the outcome that has maximum rating will always happen with 100%. That's why most stats problems avoid introducing "then the host resets the universe" in their problem description, it kind of ruins the whole point of calculating proabilities.

listenallyall 5y ago
I agree with you that "the universe resetting" is a dumb way to visualize or explain the problem. But if Mr. Hall opens the first door randomly (essential that it was a random choice), and it revealed a goat, then no, switching does not provide an advantage. You do not go from 33 to 67%. Instead, you are left with 2 options, both of which originally had a probability of 33% of containing a car, and which, now that the third option has been eliminated, are both currently 50%.
dbt00 5y ago
Think of it this way. In the original problem, there was a 1/3 chance of your original choice being the car, and a 2/3 chance of the other two. The host knowing which door to open gives you information without changing the odds, so there's still a 2/3 chance you picked wrong. When the host does not know which door to pick, there's a 1/3 chance that you picked right, a 1/3 chance that the host opens the door with the car, and a 1/3 chance that you should switch. The host opening the door with the car ends that branch, so you're left with 2/3 of the original probability, and your odds for either branch remaining are 50:50.

stale2002 5y ago

> imagine every time the hosts picks the car the universe resets Do you believe that we live in a universe that is reseting, every time Mr Monty hall opens a car? As in literally Mr Monty Hall. From the game show. In real life. Because the purpose of the question is to mimic the show.

TchoBeer 5y ago
You could also consider a case where they send in a new contestant every time the Random Monty Hall picks a car, and the result is the same.
- stale2002 5y ago
  > You could also consider a case where they send in a new contestant every time the Random Monty Hall picks a car In the actual show, do you believe they are sending in a new contestant every time Monty hall picks are car? Do you think that is what is happening in the actual game show?
  - TchoBeer 5y ago
    No, obviously not. We're talking about expected values though, so it's a useful thought experiment.
    - stale2002 5y ago
      > We're talking about expected values though No, what people are talking about is the actual game show. They are doing a statistical analysis of how the actual game show works, in real life. So nobody is talking about a different, hypothetical situation, where the universe is reset, or the game show host brings out a new contestant every time. Instead people are talking about how the actual show works. And your scenarios that you bring up, are not relevant, and therefore wrong. > so it's a useful thought experiment. No, it is a different thought experience that applies to a different situation.