# Thread: [Wednesday] Big brain exercises

1. ## [Wednesday] Big brain exercises

Been reading up on the Monty Hall problem, and it's more than a bit confusing. But it was made a bit easier when pointing out the standard assumptions: that the game master has certain behaviors that they need to perform, which are not random. As I understand it, the solution is not "you have a 2/3 chance of winning the prize if you switch doors", but "the game master has a 2/3 chance of actively avoiding opening the door with the car, therefore you should pick the door he did not". The game master's door choice is biased by yours.

2. Originally Posted by Nordstern
Been reading up on the Monty Hall problem, and it's more than a bit confusing. But it was made a bit easier when pointing out the standard assumptions: that the game master has certain behaviors that they need to perform, which are not random. As I understand it, the solution is not "you have a 2/3 chance of winning the prize if you switch doors", but "the game master has a 2/3 chance of actively avoiding opening the door with the car, therefore you should pick the door he did not". The game master's door choice is biased by yours.
Sticking with your original choice after one door is removed has exactly the same odds as switching door. Because deciding not to switch is as much a choice as switching and is made after the third door has been discarded therefore sharing the same 1/2 chance.

3. Originally Posted by tulip
Originally Posted by Nordstern
Been reading up on the Monty Hall problem, and it's more than a bit confusing. But it was made a bit easier when pointing out the standard assumptions: that the game master has certain behaviors that they need to perform, which are not random. As I understand it, the solution is not "you have a 2/3 chance of winning the prize if you switch doors", but "the game master has a 2/3 chance of actively avoiding opening the door with the car, therefore you should pick the door he did not". The game master's door choice is biased by yours.
Sticking with your original choice after one door is removed has exactly the same odds as switching door. Because deciding not to switch is as much a choice as switching and is made after the third door has been discarded therefore sharing the same 1/2 chance.
It's been proven both mathematically and experimentally that switching is the best strategy.

4. I find it strange that people think this as strange.

5. Originally Posted by tulip
Originally Posted by Nordstern
Been reading up on the Monty Hall problem, and it's more than a bit confusing. But it was made a bit easier when pointing out the standard assumptions: that the game master has certain behaviors that they need to perform, which are not random. As I understand it, the solution is not "you have a 2/3 chance of winning the prize if you switch doors", but "the game master has a 2/3 chance of actively avoiding opening the door with the car, therefore you should pick the door he did not". The game master's door choice is biased by yours.
Sticking with your original choice after one door is removed has exactly the same odds as switching door. Because deciding not to switch is as much a choice as switching and is made after the third door has been discarded therefore sharing the same 1/2 chance.
A common misconception (one that I had) based on the assumption that everything in this scenario is random, perpetuated by the fact that Savant didn't explicitly state some basic facts:

The host must always open a door that was not picked by the contestant.
The host must always open a door to reveal a goat and never the car.
The host must always offer the chance to switch between the originally chosen door and the remaining closed door.

These were implied when the thought experiment stated that the host knows what's behind each door and always opens a door for a goat. This is therefore not random behavior.

It's confusing at first, but read the Wikipedia article thoroughly and you'll understand.

6. Originally Posted by Nordstern
Originally Posted by tulip
Originally Posted by Nordstern
Been reading up on the Monty Hall problem, and it's more than a bit confusing. But it was made a bit easier when pointing out the standard assumptions: that the game master has certain behaviors that they need to perform, which are not random. As I understand it, the solution is not "you have a 2/3 chance of winning the prize if you switch doors", but "the game master has a 2/3 chance of actively avoiding opening the door with the car, therefore you should pick the door he did not". The game master's door choice is biased by yours.
Sticking with your original choice after one door is removed has exactly the same odds as switching door. Because deciding not to switch is as much a choice as switching and is made after the third door has been discarded therefore sharing the same 1/2 chance.
A common misconception (one that I had) based on the assumption that everything in this scenario is random, perpetuated by the fact that Savant didn't explicitly state some basic facts:

The host must always open a door that was not picked by the contestant.
The host must always open a door to reveal a goat and never the car.
The host must always offer the chance to switch between the originally chosen door and the remaining closed door.

These were implied when the thought experiment stated that the host knows what's behind each door and always opens a door for a goat. This is therefore not random behavior.

It's confusing at first, but read the Wikipedia article thoroughly and you'll understand.

iŽll save you some time, this is the relevant passage:
Using the switching strategy, winning or losing thus only depends on whether the contestant has initially chosen a goat (2/3 probability) or the car (1/3 probability). The fact that the host subsequently reveals a goat in one of the unchosen doors changes nothing about the initial probability.

7. OK, I thought I was right, then I thought I was thick, now I see just how counter-intuitive it is.

8. The thought that made me finally get it back in the day was imagining 10k doors or whatever in the beginning. You pick a door, host opens all doors except the one you picked and one other. Would you switch or not? (obviously yes, same with three doors just a lot less obvious)

9. Thats easy, but a bit sad, but a story much repeated over history.
See, they were a group rebelling against the establishment in the 70s and became so successful that they slipped into *being* the establishment.
Leading to some prominent figures even supporting Brexit, while actually living abroad due to tax reasons.

Wait
Sorry, thats the MontyPython problem..
never mind.

10. I'm impressed the forum is still alive. Also hello!

11. Originally Posted by Jolin
I'm impressed the forum is still alive. Also hello!
It's weird, isn't it?

12. Originally Posted by Jolin
I'm impressed the forum is still alive. Also hello!
Hello there!

There are a couple of us who won't let it die. And honestly, although the contributions have dried out, all in all it's very civilized and insightful.

13. Originally Posted by Jolin
I'm impressed the forum is still alive. Also hello!
Is it though?

14. Originally Posted by Dorvil Barranis
Originally Posted by Jolin
I'm impressed the forum is still alive. Also hello!
Is it though?

15. i'm still around, FHC lives confirmed.

16. Originally Posted by epictetus
The thought that made me finally get it back in the day was imagining 10k doors or whatever in the beginning. You pick a door, host opens all doors except the one you picked and one other. Would you switch or not? (obviously yes, same with three doors just a lot less obvious)
Thats a great way of explaining it

17. Originally Posted by Jolin
I'm impressed the forum is still alive. Also hello!
Alive and kickin' you might say. Just noticed this gem from the forum's start page:

Most users ever online was 7,557, August 3 2023 at 07:35:22 PM.
The spam bots held their annual meeting here that day, I guess.

18. Originally Posted by Hel OWeen
Originally Posted by Jolin
I'm impressed the forum is still alive. Also hello!
Alive and kickin' you might say. Just noticed this gem from the forum's start page:

Most users ever online was 7,557, August 3 2023 at 07:35:22 PM.
The spam bots held their annual meeting here that day, I guess.
Nah, there's probably just a horde of us ancient lurkers, waiting for the day the drama llama awaken again...

19. Originally Posted by Vicomt
Originally Posted by Hel OWeen
Originally Posted by Jolin
I'm impressed the forum is still alive. Also hello!
Alive and kickin' you might say. Just noticed this gem from the forum's start page:

Most users ever online was 7,557, August 3 2023 at 07:35:22 PM.
The spam bots held their annual meeting here that day, I guess.
Nah, there's probably just a horde of us ancient lurkers, waiting for the day the drama llama awaken again...
I'm here for the games section and the Political threads!

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