The Monty Hall Problem

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Michael Stevens
PO Box 33168
L.A. CA 90033

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***CREDITS***

Hosted by
Michael Stevens

Edited by
Hannah Canetti

Music from AudioNetwork

***VSAUCE LINKS***

[neil]

0:33 "But maybe it does"


_VSauce music starts playing_

[davidozab]

If the goat's behind the door long enough, there will be poop too.

[chrisbero]

This helped me grasp the real issue here, you probably picked the wrong door in the first place so you should switch. Let's say that there are not three, but ten thousand doors. You pick one at random and Monty Hall opens not one but 9, 998 of the remaining doors to reveal empty rooms. Now there are just two closed doors, your first choice and the one Monty did not already open. Now, you could look at the remaining closed doors and tell yourself that it is a fifty/fifty chance so you might as well stick with your first guess. However, there is only a 1/10, 000 chance you chose correctly the first time. There is thus a 9, 999/10, 000 chance that the other door Monty left closed is the winner. Because you almost never pick the correct door when up against 10, 000 choices, Monty opening all the other doors except one is telling you that THAT is the door with the prize behind it. Now 2/3 is not as obvious as 9, 999/10, 000, but the principle is the same -- the odds are you chose the wrong door which means Monty is showing you the correct one. Take it.

[worker-wfem]

The door you pick has a 1/3 chance of winning. That means the remaining 2 doors collectively have a 2/3 chance of winning. The host eliminates one of the doors meaning the remaining door you didn’t choose has that 2/3 chance of winning all to itself. So it’s better to switch

[girthman]

"A great analogy for the Monty Hall problem is this sack"

*reaches into pants*

[RYSyoutube]

Michael: if you pick the door with the poop, like the goat you would need to take it home, take care of it, feed it, all that poop stuff

*incredible*

[webbc]

Great explanation - the absolute key to this is that the host KNOWS where the money is and NEVER opens a door with the money. This fact is the crucial piece of the rules that makes this the case.

[beautanner]

I think it's cool that he did this in (apparently) one take, and ran the experiment at least twice in the video having it work out in the most pedagogically desirable outcomes both times.

[Hannahruda]

When he said “Hannah, pick a door” I got scared because that’s my name

[Reilers]

0:21 "Kevin's recent video"
Recent: More than 5 months ago

[evolutiagames]

There are 2 goat doors, and the host will always open a goat door. Therefore, switching will always result in the opposite of your first choice. There is a 2/3 probability of being wrong with your first choice, and therefore switching in either of those 2 cases results in switching to the winning door. 2/3 is the chance of winning *if you switch doors.*

[cameroncorrado]

Draw a tree of possible outcomes given every possible combination of choices, and it becomes clear that the mathematically correct choice is to switch.

[Luke_Freeman]

Michael Stevens is a committed man.

Micheal- "Let's do a whole episode laying on a table."
Hannah-

[GauravGRocks]

I don't know whether I should be scared for Michael or of Michael.

[AkshatSehgal]

This is the best, most intuitive, clear explanation I have seen of this puzzle. So, thank you for creating “yet another” video about it!

[MarcusTheDorkus]

I'd thought I'd heard enough explanations of the Monty Hall problem at this point, but I'm glad I watched this one. For some reason I never thought of it as simply as when you're using the always switch strategy, then if your choice of door at the start is wrong, you win. When put that way, the 2/3 odds are dead simple to see.

[mr_niceman]

I already understand it, I am just here to watch Micheal lying on a table

[YTzaecapone]

Me: *trying to watch something educational in front of parents*

Michael: HeY DiNGaLnGs!

[andreypopov]

The easiest way to explain it is this:
Imagine that you’ve played with 1000 doors instead of 3. And after you’ve chosen the door Monty Hall opens 998 other doors to show that all of them have goats in them, leaving only your and another one door closed. Would you then switch to the other door?
Yes, of course switch. Because you’ve had a 1/1000 chance of choosing the correct door in the beginning. And if you don’t switch - you’re still betting that you’ve won a 1/1000 chance by accident (or more likely - 999/1000% of losing), ignoring 998 doors that were opened. But since we know that Monty Hall cannot open the door with the Money - he HAD to leave the door with the Money closed. Door with the Money AND your first chosen door, that is the most probable scenario here. You will have 99, 9% of winning money if you switch the door in that example.
And if you think about it - in the original Monty Hall problem with 3 doors, Monty does the same thing: he opens ALL doors other than your and another one. Yes, you are not as guaranteed of winning as in the 1000 doors example, but you still are more probable to win if you switch doors.
Fun fact: when I was a student about 8 years ago I could not believe it wasn’t a 50/50 chance. So I asked a friend of mine to determine the probability by making a lot of blind tests. I’ve put a coin in one of 3 cups and asked my friend to choose, then revealed one empty cup and asked her to always switch the cup. Repeated that 100 times. If I was correct the result would more incline to 50% of choosing the other door. Like a coin toss. But we ended up with like 62/100 winning (or 64, I don’t really remember now). Much closer to a 66% than 50%. So this little “field test” proved me wrong =)
Took me a while to understand why I was wrong though))

[xX_cjpg_Xx]

Can we just appreciate that he got 11 minutes into this video in one cut and then proved how it works with the marbles