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Stumbling Intuition #1: The Monty Hall Problem

Debater Slayer

Debater Slayer

Vipassana
Staff member
Premium Member
Starting with this thread, I'm planning to initiate a series of threads about counterintuitive problems in mathematics (or programming, if I encounter suitable ones), both for fun and as an opportunity to engage my passion for math. :D

The original Monty Hall problem is worded thus:

440px-Monty_open_door.svg.png


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?
Click to expand...

Monty Hall problem - Wikipedia

I posted the Wikipedia article to properly cite my source for the above wording, but since it contains the answer to the problem, I recommend not clicking the link before you have come up with your answer!

Before posting your answer, take your time to analyze it! This problem is an example of a veridical paradox, and it is so counterintuitive that Paul Erdős, one of the most prolific mathematicians of the 20th century, wasn't convinced of the correct solution until he saw computer simulations demonstrating its correctness.

A veridical paradox produces a result that appears absurd, but is demonstrated to be true nonetheless.
Click to expand...

Paradox - Wikipedia

Also, please only post your answer in spoiler tags so that you don't potentially reveal the solution to others!

So, if Monty Hall asked you the above question, would you open the door you initially chose, or would you switch to the other one?
 
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VoidCat

VoidCat

Use any and all pronouns including neo and it/it's
Counterintuitive? I don't even know enough about math to guess the wrong answer that's not counterintuitive.
 
Debater Slayer

Debater Slayer

Vipassana
Staff member
Premium Member
VoidCat said:
Counterintuitive? I don't even know enough about math to guess the wrong answer that's not counterintuitive.
Click to expand...

Well, setting aside any math, would you choose to open the door you had initially picked, or would you switch to the other door?
 
VoidCat

VoidCat

Use any and all pronouns including neo and it/it's
Debater Slayer said:
Well, setting aside any math, would you choose to open the door you had initially picked, or would you switch to the other door?
Click to expand...
I can't drive. And I don't know how to care for a goat. It don't matter if I get a goat or a car I'm still getting something that I don't know what to do with. Might as well stick with the door i originally chose
 
amorphous_constellation

amorphous_constellation

Well-Known Member
I've read about that before, and I did not get it at first, and it is counterintuitive. Well the thing I'd like a simple, really simple breakdown of, is bayesian reasoning. If I understand a little more about that, then I'll feel like I accomplished something.
 
Debater Slayer

Debater Slayer

Vipassana
Staff member
Premium Member
ideogenous_mover said:
I've read about that before, and I did not get it at first, and it is counterintuitive. Well the thing I'd like a simple, really simple breakdown of, is bayesian reasoning. If I understand a little more about that, then I'll feel like I accomplished something.
Click to expand...

Sure! Would you like a general overview or a more in-depth explanation?
 
Subduction Zone

Subduction Zone

Veteran Member
I understand the Monty Hall Problem. I could also use a goat.

I am not going to switch because then my chances would remain two times out of three that I would win a goat. If I would switch the odds would be two out of three that I would win a car:(
 
Heyo

Heyo

Veteran Member
We Never Know said:
I would agree here. Once one door is eliminated its out of the equation. The two doors left leave a 50/50.
Click to expand...
One should think so. After all the chance of tails in a coin flip is 0.5, no matter what the previous outcome was. The events are independent. After the goat was revealed it is a new experiment with two possible outcomes, each with a 0.5 chance.
That's where the error lies.
 
Subduction Zone

Subduction Zone

Veteran Member
Heyo said:
One should think so. After all the chance of tails in a coin flip is 0.5, no matter what the previous outcome was. The events are independent. After the goat was revealed it is a new experiment with two possible outcomes, each with a 0.5 chance.
That's where the error lies.
Click to expand...
I disagree. I will not even put everything in the spoiler yet.
No. It is still the same experiment. I could try to give you the simple explanation why your odds of winning are 2/3 if you switch after the reveal of a goat
 
Stevicus

Stevicus

Veteran Member
Staff member
Premium Member
Debater Slayer said:
Starting with this thread, I'm planning to initiate a series of threads about counterintuitive problems in mathematics (or programming, if I encounter suitable ones), both for fun and as an opportunity to engage my passion for math. :D

The original Monty Hall problem is worded thus:



Monty Hall problem - Wikipedia

I posted the Wikipedia article to properly cite my source for the above wording, but since it contains the answer to the problem, I recommend not clicking the link before you have come up with your answer!

Before posting your answer, take your time to analyze it! This problem is an example of a veridical paradox, and it is so counterintuitive that Paul Erdős, one of the most prolific mathematicians of the 20th century, wasn't convinced of the correct solution until he saw computer simulations demonstrating its correctness.



Paradox - Wikipedia

Also, please only post your answer in spoiler tags so that you don't potentially reveal the solution to others!

So, if Monty Hall asked you the above question, would you open the door you initially chose, or would you switch to the other one?
Click to expand...

I used to watch "Let's Make a Deal" as a kid. I thought the Monty Hall Problem was about trying to decide what costume to wear when appearing on the show and hoping to win the Big Deal.
 
Shadow Wolf

Shadow Wolf

Certified People sTabber & Business Owner
This is something I studied when I began learning more into gambling odds to sharpen my poker game.
I personally find it more impossible to explain to others than it is counterintuitive. Even after running a simulation to demonstrate to people this does actually work in the end I've still ran into people who just will not accept it works that way even if they don't understand why. The numbers are right in front of them but still they deny it.:facepalm:
 
Subduction Zone

Subduction Zone

Veteran Member
Shadow Wolf said:
This is something I studied when I began learning more into gambling odds to sharpen my poker game.
I personally find it more impossible to explain to others than it is counterintuitive. Even after running a simulation to demonstrate to people this does actually work in the end I've still ran into people who just will not accept it works that way even if they don't understand why. The numbers are right in front of them but still they deny it.:facepalm:
Click to expand...
People often feel that they are investing in a choice and it can be hard to switch, even if the numbers tell them to.
 
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