Monty Hall Problem - Numberphile

Extended math version: • Monty Hall Problem (ex...
A version for Dummies: • Monty Hall Problem (be...
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This video features Lisa Goldberg, an adjunct professor in the Department of Statistics at University of California, Berkeley.
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[@maplewang1992]

Third option: you intentionally switch to the open door to guarantee that you get the goat

[@scrtmin7022]

How darE YOU DETECTIVE DIAZ I AM YOUR SUPERIOR OFFICER

[@lloydburden2341]

If you pick the car and switch you always lose. But if you pick a goat and switch you always win, since Monty is forced to eliminate the other goat from the game. But because you are twice more likely to pick a goat than a car in the first place, this means that you are twice more likely to be in a situation where switching wins you the game.

[@Motorsheep]

Another way to look at it is from Monty's perspective:

[@criscusack]

I always sum it up as: "In order to lose by switching, you have to have picked right at first. So you will lose by switching 1/3 of the time. So switch."

[@JNDlego57]

Before you comment saying its 50/50, read this.

[@jayparmo2284]

I didnt understand it until the 1 in 100 part. That made it incredibly clear to me.

[@Viva_Reverie]

I've heard explanations for this game too many times but I've only found a few which are super easy to understand, this is my preferred "Explanation":

[@dumitruene8883]

The explanation with 100 doors got rid of any misunderstandings I had about the answer of this problem. Thank you!

[@Lozzie74]

That was the best explanation of this that I’ve ever seen. I always accepted it was better to switch, but never fully grasped why. You explained this easily and gave me 100% clarity! To understand something is one thing, but to explain it so easily (and then use an improved example to prove it) is a whole other level. You are a master!

[@cdmcfall]

The brute force method is easiest for me to visualize. With three doors and three prizes (car, goat 1, goat 2), we can get the following possible combinations:

[@victoriahiggs6501]

switching can save you 15% or more on car insurance

[@SamueITan]

"The math thing isn't the problem, you just need to bone."

[@ryhs0]

for anyone confused still

[@ryanmunch464]

I’ve read or listened to many explanations of this problem and this is by far the most clear explanation. Thank you!

[@djsnowman06]

programed a simulation on my TI-83 plus. Ran a sample of 500 games, where the choice was always switched after a "goat" was removed. switching won 67.6%.

[@gamingbutnotreally6077]

Easiest explanation I could come up with is that this game is equivalent to you choosing a door, and then Monty asking you if you want to keep that door or if you want to switch to the other 2 doors and if the prize is in EITHER of those 2 doors you get the prize. Easy to see that you should always switch to the 2 doors option!

[@Dashi42100]

This is the first time I've ever seen the Monty Hall problem explained on a larger scale eg 1/100 vs 99/100. When you inflate to that scale, you get a gut feeling that the odds are in your favor to switch because the chance you picked the car on your first try is 1/100 which are extremely low odds. Extremely effective way to present the problem, and one I intend to use in future. Thank you!

[@napoleon3026]

In order for you to lose after switching you must have guessed the right door and that can only happen at 1/3 probability

[@prakashraj4519]

For those who still didn't get the intuition for this truth, think like this... the only way you win on swapping is by picking a wrong door, what is the probability of picking a wrong door? 2/3