Monty Hall Problem (best explanation) - Numberphile

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NUMBERPHILE

Videos by Brady Haran

[joaovitorjoaovitor]

This is the absolute best explanation of this problem. Never before had someone pointed out to me the value in the fact that Monty knows everything.

[catherinelastname]

This really clicked for me. Much better than the other video with “concentrated probability”.

There are three possibilities. One where your initial guess is correct, and switching makes you lose. Then two different possibilities where your initial guess is wrong, and switching means you win. Boom, 2/3 chance to win if you switch. Great video

[tanukigalpa]

FINALLY.
I think the issue is that when we talk about "concentration of probability", we shouldn't say that there is a 2/3 chance the car is in door 3, we REALLY should be saying there's a 2/3 chance there is a goat behind your door, so you should switch to avoid opening your likely goat door.

[_Doskii]

Omg, after so many years I finally understand it. I'm find it really odd that nobody could ever just have explained it to me in this way. Thank you.

[danielweber]

My math teacher made a helpful example back in the day. If you do the game with 100 doors and Monty opens 98 of them after your choice, it became clearer to us that your chance of having picked the correct door in the beginning is smaller than the likelihood of the other (last) door being the car.

[Rundvelt]

I think that if you drew out all the possibilities that would demonstrate the fact better.   For example.

Scenario 1:
Car / Goat / Goat

Scenario 2:
Goat / Car / Goat

Scenario 3:
Goat / Goat / Car

Let's say you pick the door on the left and do not switch.
Scenario 1:   Win
Scenario 2:  Lose
Scenario 3:  Lose

Let's say you pick the door on the left and switch doors.
Scenario 1:  Lose
Scenario 2:  Win
Scenario 3:  Win.

Not Switching = 1 win out of 3.
Switching = 2 wins out of 3.

Hard to make it any easier then this.

[VastChoirs]

This explanation FINALLY made sense to me where every other one sounded ridiculous. Thank you!!

[strayster]

Disagreed with the official explanation until I saw this video. I was wrong all along. Thank you for correcting me.

[KetoMelange]

Last video on this I went I get it"
Some time passed, forgot some stuff
This video I went I get it"
You could keep making these videos for eternity, I'd still be equally amazed each time.

[templarthade]

I GET IT! I FINALLY GET IT! THANK YOU!

[Darwins_Fink]

THIS video explained it properly. the last video said that the 1/3 chance of the opened-goat-door was 'added' to the not-chosen-door, which is kind of 'imprecise' and not very easy to understand.
With this video you explained all possible outcomes and showed that 2/3 of the time you get the car, if you switch. Well done

[nekogod]

There is a greater chance of picking the goat first time so it's better to swap.

[Viva_Reverie]

I commented on the first video pretty much explaining "If you switched while on a goat, you get the car (2/3), and if you switch when on the car, you get a goat (1/3)", similar to how this video explained it. Even then, I recall at least a couple of responses still not understanding that the third door plays a part xD

[ravenlord]

Yeah the key is this.  The player is picking randomly.  Monty Hall is NOT picking randomly.  So think of it this way:  Player picks door 1 (33% chance of being right).  Monty picks door 2 (0% chance of being right).  Door 3 must have 66% of being right.

[Mozicon]

Who says I want the car?  Maybe I want the goat.

[alexandrabender]

I read an entire Wikipedia article on this and didn’t understand where the 2/3 chance was but by 2:19 I understood. Great video and very clear explanation.

[EddyProca]

This is the explanation I posted on the other video. The other explanation with 100 doors just makes things too complicated for some people and is unnecessary when this simple explanation does the job.

[TheConfuzzledCat]

This video is still helping people like me ten years on. This never made sense to me before, and now it at least sort of does. Thank you so much!!

[nychold]

In this case, knowing is 2/3 the battle.  GI JOE!

[francus]

I recently discovered this problem. I've watched several videos and yours are by far the best ones. This specific video clarifies any doubt that I could had remaining. Great job.