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#3: Post edited by user avatar DNB‭ · 2021-08-20T23:17:49Z (over 3 years ago)
  • Alas, it isn't clear to me that** it becomes clear that the
  • probabilities are not 50-50 for the two unopened doors**. Had I never seen this exercise or problem, even if there were 1 **B**illion doors, I would "**stubbornly stick with their original choice**".
  • What am I misunderstanding? Am I just that witless? Rocketing the number of doors hasn't assisted me to intuit the Monty Hall Problem.
  • >To build correct intuition, let's consider an extreme case. Suppose that there are
  • a million doors, 999,999 of which contain goats and 1 of which has a car. After
  • the contestant's initial pick, Monty opens 999,998 doors with goats behind them
  • and others the choice to switch. In this extreme case, **it becomes clear that the
  • probabilities are not 50-50 for the two unopened doors; very few people would
  • stubbornly stick with their original choice**. The same is true for the three-door case.
  • Blitzstein. *Introduction to Probability* (2019 2 ed). p 71.
  • [The Time Everyone “Corrected” the World’s Smartest Woman](https://priceonomics.com/the-time-everyone-corrected-the-worlds-smartest/)
  • > Here’s another way to visualize this. Imagine that instead of three doors, Monty Hall presents you with 100 doors; behind 99 of them are goats, and behind one of them is the car. You select door #1, and your initial odds of winning the car are now 1/100:
  • >
  • > ![](https://pix-media.priceonomics-media.com/blog/907/doors1.png)
  • >
  • > Then, let’s suppose that Monty Hall opens 98 of the other doors, revealing a goat behind each one. Now you’re left with two choices: keep door #1, or switch to door #100:
  • >
  • > ![](https://pix-media.priceonomics-media.com/blog/907/doorsx-edout.png)
  • >
  • > When you select door #1, there is a 99/100 chance that the car is behind one of the other doors. The fact that Monty Hall reveals 98 goats does not change these initial odds -- it merely "shifts" that 99/100 chance to door #100. You can either stick with your original 1/100 odds pick, or switch to door #100, with a much higher probability of winning the car.
  • Alas, it isn't clear to me that **it becomes clear that the
  • probabilities are not 50-50 for the two unopened doors**. Had I never seen this exercise or problem, even if there were 1 **B**illion doors, I would "**stubbornly stick with their original choice**".
  • What am I misunderstanding? Am I just that witless? Rocketing the number of doors hasn't assisted me to intuit the Monty Hall Problem.
  • >To build correct intuition, let's consider an extreme case. Suppose that there are
  • a million doors, 999,999 of which contain goats and 1 of which has a car. After
  • the contestant's initial pick, Monty opens 999,998 doors with goats behind them
  • and others the choice to switch. In this extreme case, **it becomes clear that the
  • probabilities are not 50-50 for the two unopened doors; very few people would
  • stubbornly stick with their original choice**. The same is true for the three-door case.
  • Blitzstein. *Introduction to Probability* (2019 2 ed). p 71.
  • [The Time Everyone “Corrected” the World’s Smartest Woman](https://priceonomics.com/the-time-everyone-corrected-the-worlds-smartest/)
  • > Here’s another way to visualize this. Imagine that instead of three doors, Monty Hall presents you with 100 doors; behind 99 of them are goats, and behind one of them is the car. You select door #1, and your initial odds of winning the car are now 1/100:
  • >
  • > ![](https://pix-media.priceonomics-media.com/blog/907/doors1.png)
  • >
  • > Then, let’s suppose that Monty Hall opens 98 of the other doors, revealing a goat behind each one. Now you’re left with two choices: keep door #1, or switch to door #100:
  • >
  • > ![](https://pix-media.priceonomics-media.com/blog/907/doorsx-edout.png)
  • >
  • > When you select door #1, there is a 99/100 chance that the car is behind one of the other doors. The fact that Monty Hall reveals 98 goats does not change these initial odds -- it merely "shifts" that 99/100 chance to door #100. You can either stick with your original 1/100 odds pick, or switch to door #100, with a much higher probability of winning the car.
#2: Post edited by user avatar DNB‭ · 2021-08-07T04:26:36Z (over 3 years ago)
  • Alas, it isn't clear to me that** it becomes clear that the
  • probabilities are not 50-50 for the two unopened doors**. Had I never seen this exercise or problem, even if there were 1 **B**illion doors, I would "**stubbornly stick with their original choice**".
  • What am I misunderstanding? Am I just that witless? Rocketing the number of doors hasn't assisted me to intuit the Monty Hall Problem.
  • >To build correct intuition, let's consider an extreme case. Suppose that there are
  • a million doors, 999,999 of which contain goats and 1 of which has a car. After
  • the contestant's initial pick, Monty opens 999,998 doors with goats behind them
  • and others the choice to switch. In this extreme case, **it becomes clear that the
  • probabilities are not 50-50 for the two unopened doors; very few people would
  • stubbornly stick with their original choice**. The same is true for the three-door case.
  • Blitzstein. *Introduction to Probability* (2019 2 ed). p 71.
  • Alas, it isn't clear to me that** it becomes clear that the
  • probabilities are not 50-50 for the two unopened doors**. Had I never seen this exercise or problem, even if there were 1 **B**illion doors, I would "**stubbornly stick with their original choice**".
  • What am I misunderstanding? Am I just that witless? Rocketing the number of doors hasn't assisted me to intuit the Monty Hall Problem.
  • >To build correct intuition, let's consider an extreme case. Suppose that there are
  • a million doors, 999,999 of which contain goats and 1 of which has a car. After
  • the contestant's initial pick, Monty opens 999,998 doors with goats behind them
  • and others the choice to switch. In this extreme case, **it becomes clear that the
  • probabilities are not 50-50 for the two unopened doors; very few people would
  • stubbornly stick with their original choice**. The same is true for the three-door case.
  • Blitzstein. *Introduction to Probability* (2019 2 ed). p 71.
  • [The Time Everyone “Corrected” the World’s Smartest Woman](https://priceonomics.com/the-time-everyone-corrected-the-worlds-smartest/)
  • > Here’s another way to visualize this. Imagine that instead of three doors, Monty Hall presents you with 100 doors; behind 99 of them are goats, and behind one of them is the car. You select door #1, and your initial odds of winning the car are now 1/100:
  • >
  • > ![](https://pix-media.priceonomics-media.com/blog/907/doors1.png)
  • >
  • > Then, let’s suppose that Monty Hall opens 98 of the other doors, revealing a goat behind each one. Now you’re left with two choices: keep door #1, or switch to door #100:
  • >
  • > ![](https://pix-media.priceonomics-media.com/blog/907/doorsx-edout.png)
  • >
  • > When you select door #1, there is a 99/100 chance that the car is behind one of the other doors. The fact that Monty Hall reveals 98 goats does not change these initial odds -- it merely "shifts" that 99/100 chance to door #100. You can either stick with your original 1/100 odds pick, or switch to door #100, with a much higher probability of winning the car.
#1: Initial revision by user avatar DNB‭ · 2021-08-05T04:27:25Z (over 3 years ago)
Why would skyrocketing the numbers of doors help laypeople intuit the Monty Hall Problem? 
Alas, it isn't clear to me that** it becomes clear that the
probabilities are not 50-50 for the two unopened doors**. Had I never seen this exercise or problem, even if there were 1 **B**illion doors, I would "**stubbornly stick with their original choice**".

What am I misunderstanding? Am I just that witless? Rocketing the number of doors hasn't assisted me to intuit the Monty Hall Problem. 

>To build correct intuition, let's consider an extreme case. Suppose that there are
a million doors, 999,999 of which contain goats and 1 of which has a car. After
the contestant's initial pick, Monty opens 999,998 doors with goats behind them
and others the choice to switch. In this extreme case, **it becomes clear that the
probabilities are not 50-50 for the two unopened doors; very few people would
stubbornly stick with their original choice**. The same is true for the three-door case.

Blitzstein. *Introduction to Probability* (2019 2 ed). p 71.