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Michael Stevens
PO Box 33168
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When he said “Hannah, pick a door” I got scared because that’s my name
Hannah is a very common Name so why bruh?
@@adwans1491 Because your first thought is often that he is speaking to you. Common reaction, and it's quite funny
@@ChristianRingdal :3 naaah
It's. Must be a funny moment
Lol
If the goat's behind the door long enough, there will be poop too.
@I Z if you like that stuff, a million dollars can still buy you more than enough
And a dead goat
There's guaranteed to be poop there unless you can do all of this in 5 seconds.
Oh Im 1000th like... So satisfying
I see this as an absolute win
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.
This is how I explain it too. When it's 2 out of 3 it can be hard to understand, but it works just the same with more options. Sticking with the first door is saying you'll take a 1 out of (however many options were initially available) chance, but switching is betting that you were wrong on the initial pick. It's definitely a no-brainer.
This is a great way to explain the idea, thanks.
This is how I've always explained it to people. Never fail to see their eyes light up with understanding when we switch the problem from 1/3 to 1/10k.
But imagine the door u picked first went next to the other door that hasn’t been opened yet, which one will u choose? Like that it seems like an equal 50/50… IDK still looks to me like it doesn’t matter if you switch
Wow, this is great. The more likely to be wrong on the first pick is what made it click for me as well. And then the way you put it's like "omg, duh, it's so obvious" :D
I think a better way of looking at it is to imagine if Monty didn't open ANY doors but instead asked you if you would be willing to give up your chosen door in exchange for being allowed to open up BOTH of the other doors. That is essentially what this problem and your choice comes down to. Him opening up the one door ahead of time is simply a distraction from that choice.
That's actually a perspective I hadn't heard or thought of before. Very good!
Indeed, great explanation!
While this is true, if somebody didn’t already understand why the Monty Hall problem isn’t 50/50 they would disagree with this visualization as they don’t see the opening of the door as a distraction but rather as increasing their odds. This way of thinking only helps to further visualize if you already understand how the problem effectively functions.
Oh damn
I agree it's a great explanation, but sadly in my experience doesn't work. I tried this explanation when I was trying to explain the Monty Hall problem to my dad, he still refused to accept it. He didn't even accept it when I increased the number of doors to a thousand with a one in a thousand chance of being correct first time, then Monty, knowing where the money is, opening 998 wrong doors. Dad still claimed his odds had increased to evens. My dad was a maths teacher.
Michael: WHATS UP DINGALINGS KZhead: *Demonetized*
KZhead killed vsauce. Really sad actually, I really enjoyed it before it was sub based
Grant Harlor why did KZhead kill vsauce
@@CorleoneSoup because it was an awesome channel then KZhead went and made it premium only. Didn't kill it off, just killed it for all the people that don't subscribe to KZhead.
Grant Harlor that was vsauce’s decision
@@glharlor i just found out that !!!!!!! this is not gud
"Oh hey this is a cool video to show to my fami-" "GRR BABY GRR"
Press pause before the ending.
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.
And your door pick is off limits for opening at the time of the host reveal
Well yes and no. The host knowing doesn't really change the benefit of switching. If the host didn't know, and picked the door with the money to open - you lose. If they open a random door, and it's poop, you have the same advantage of swapping since your new pick has better odds. Regardless of the host knowing, you always switch doors given the chance
@@MelodicTurtleMetal The Host knowing strongly determines the solution, as long as the Host can choose whether or not to open a door or not. If the Host must always open a door, the probability of winning when switching is the traditional 2/3. However, if the Host can choose to not open a door every time, the probability of winning when switching is somewhere between 0 and 1, depending on Host behavior. It is 0 if the host only opens a door only when your first choice was a win, and it is 1 if the host only opens a door when your first choice was a loss.
@@MelodicTurtleMetalIf the host doesn’t know, and you’ve made it to the point where you’ve gotten the chance to switch (the door opened had a goat), it actually is a 50/50, since getting to this point is conditional on the probability that the host didn’t open the car. It can be shown mathematically as well with a simple application of Bayes’ Theorem.
@@alienx33 can you provide that evidence? Feels like you have a 33% chance on first guess, and now a 50/50 chance IF you can continue. Or does the math take into account the random door being opened to have the car...
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
I thought Michael had fused with that table, now I'm disappointed.
Same
Michael may not have, but Aunt May did (shoutouts to SnapsCube dubs)
Cannot unsee
He tried to put his peepee in a hole on the table and now it's stuck
I already understand it, I am just here to watch Micheal lying on a table
Aren't we all?
I thought he would sit down after the first 30sec but noooooooooOoOOoOOOO
I'm here to envy Michael's epic beard.
I'm here to envy Michael's epic beard.
Same, and it was worth it.
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.
I thought about that as well. The part where Hannah picked a door could've been staged, but hopefully not. But when he picked the white marble and switched to the black in the bag, that was incredibly satisfying.
Can we just appreciate that he got 11 minutes into this video in one cut and then proved how it works with the marbles
Yes:)
Michael, reaching into his pants: "And it contains a sack"
said while he suggestively squirms on a table
Thats a big twinkie ;)
Demonetized
A ball sack
With... Somehow 3 balls🤔 Scarry!😱
"A great analogy for the Monty Hall problem is this sack" *reaches into pants*
A sack of balls, no less
After all, this is still a DONG
@@luiscarlosarenas9370 it's not online though
@@luiscarlosarenas9370 what is a DONG? Never heard about it
@@SophieJMore Do Online Now, Guys
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))
Yeah you were right when is played once it gives u a 50-50 when you run it exponentially then makes sense to switch
I still believe in 50/50. Let's say you have 3 doors and you picked door 1. Monty showed you that 2 is a zonk. You are saying switch because chances of winning would increase to 2/3 because each door has 1/3 chance. Since you have more information, the odds are in your favor... (I hope I got your perspective) ... You could make the same argument for door 1. Let’s say door 1 and door 2 have 2/3 chances and door 3 has 1/3 chance. If door number 2 is a zunk, from your perspective door 1 chances should improve to 2/3 as well. The problem is how you are grouping the data! Here’s my theory - From the start each door has 1/3(33.333%) chance. When the game show host reveals a zonk in door 2, the chances that the car is in door 1 and door 3 improved equally. Divide that zonk door 2 33.333% into two door 1 and door 2. 33.333 + (33.333/2) = 50% Both the remaining unopened doors chances improved to 50%. No harm no foul if you change doors because your chances of winning a car is the same (theatrical to switch doors)
@@jaymo2024 I literally just told you I did a physical test and got ~66%, not 50%. You can do it yourself at home. Just ask a friend to help you and take an hour of your time to make 100 tests
@@andreypopov3400 I am going to simulate this with code. 1 million contestants will stick with the original option after the zonk is revealed and 1 million contestants are will switch to the other option after the zonk is revealed. What I’m seeing is data bias but the computer doesn’t have bias. Now, would you stick with door 1 or switch
@@jaymo2024 Choose to always switch. There is no bias because there was no choice. I asked to pick the door randomly and always choose the other door. And got much closer to 66% than 50%.
Draw a tree of possible outcomes given every possible combination of choices, and it becomes clear that the mathematically correct choice is to switch.
THATS NOT TRUE. LITERALLY THAT IS THE EASIEST WAY TO PROVE THAT YOUR ASSERTION IS FALSE
@@UNABRIDGED_SCIENCE oh, sweetheart. It is true.
It’s an illusion because you can do it with door A and door B on the exact same set of doors meaning two doors out of three have a 2/3 chance of being right 4/3. Hmm that’s weird. That’s suspicious
@@drewidlifestyle7883 that just isn't how math works. But feel free to elaborate what you mean.
Who misses the iconic Vsauce tune when something trippy happens. I know this ain't Vsauce.
The actual song is called Moon Men by Jake Chudnow if you're interested
i wonder if its because of youtube's cancerous copyright & demonetization thing
John Nguyen Or is it? Here we go again
It was time for it to retire lol
The phrase that got me to understand was "2/3rds of the time you pick the wrong answer"
Yes!!!!!!
Back in the day, I got it with a similar problem, but it had 1,000,000 doors, and after I pick one, the host open 999,998 doors with a goat.. I could impossibly choose the correct door in the first go.
you can make it even clearer with 10 doors. you choose a door and after that the gamemaster opens all other doors with goats. then by 9/10 of the time you are wrong so the chance to win if you switch would be 9/10.
When it clicked for me was when he said that 2/3 of the time, the host opens one door *because the money is in the other door* .
@@MrHan-is1ko so, that one part in zero escape: zero time dilemma
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.*
Correct.
One more way to help simplify this: the host, in opening one of the incorrect doors, could also have just said, “you can have what is behind both of the doors you didn’t choose, or keep the one you have.”
That explains why one door has a probability of 1/3 while the other one has a probability of 2/3?
Why would I want goat?
@@AlinaAniretake Yes, goats are cute and all, especially when they're kids, but they smell and they're not worth a million bucks.😊
0:33 "But maybe it does" _VSauce music starts playing_
I should be "Or does it?"
Well no, but actually yes.
or does it? I am a bit worried that the real Michael was switched with a fake one by the youtube Red management
Haha
Take notes Michael
0:21 "Kevin's recent video" Recent: More than 5 months ago
It’s recent for a vsauce video
Actually it was uploaded in 2018 so more than 5 months
*more than a year ago
Literally came to the comments the second I heard that
@@LilPiga that's what they said to begin with
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.
for some reason i'm still not able to see how the unchosen door has more odds of being right. i've understood it's better to switch by the theory of having it up against say 10k doors (basically more than 3) because then the one door the host wouldn't open besides your choice must obviously have something (if it isnt reverse psychology). but I've never understood how switching will make your chances to win 66.67%
I first came across this in a Parade column in a newspaper over 30 years ago.I was shocked that mathematicians would write in explaining that it wouldn’t benefit you to switch.
It first it seems you are picking #1, the host is opening #2, and asking if you want #3 instead. Indeed in that scenario switching wouldn't help you, but since the host is not opening your door ever, and never opening the money door, the door he opens is giving you a lot of information.
Yes, and some of those mathematicians were PhD professors at top universities! Incredible.
I don't know whether I should be scared for Michael or of Michael.
I'm still scared of hannah from that texting magic video
i think this all began when he got locked up in this small room for 24h ^^
Both
Both. He'll snap sooner or later.
Shhhh, he's more scared of you than you of him.
Michael Stevens is a committed man. Micheal- "Let's do a whole episode laying on a table." Hannah- ".........Ok."
Micheal: "THERE'S MICE IN THE STUDIO!!! help" Hannah: -_-'
im on my side with this one
I misread your comment and thought you were saying that Michael should be committed.
he's committed alright but he can be whatever tf as long as he's happy,over there,and away from me
He flips around on the table just like the disk flips around on the mirror. Product placement...just properly targeted towards us geeks and subscribers. (I hesitate to say “followers”...semantics.) I give them credit for thinking outside the [curiosity] box.
I just watched this and, while I've seen explanations of the Monty Hall problem before, this is the first one that made sense to me insofar as I ended the video with understanding. Your explanation of the rules of the game and the host's obligations and the fact that they reveal additional information (somewhere around the mid-point) caused the concept to click in my mind. I really appreciate that. Thank you.
basicly you switch the wrong answer 2/3s of time and get the correct answer vs the switching the correct answer 1/3 of the time for a incorrect answer
ITS IRRELEVANT SINCE THEY ARE ALL EQUAL OPPORTUNITIES. THE VIDEO POSTER IS BAD AT MATH
@@UNABRIDGED_SCIENCEno?
today we are going to discuss the monty hall problem _maybe its goat poop_
300th like!!!
A goat's friendship is worth much more than a million dollars
But think of how many goats you could buy if you had a million dollars. That's a lot of friendship you could buy! 😉
Money can be exchanged for goods and services
@@angelbear_og if you buy them, they're not really your friends
Bruh moments
@@grandexandi Good point. 😁
Basically it's not 50/50 because you're using host's knowledge of where the money is which gives you 33.3% more chance to win when you switch.
It’s an illusion. I understand the math but watch make it too contestants. They pick doors A and B. Door C opens they both agree to switch because they know the math says the other guy is a sucker their door had a 2/3 chance of being right. Now how do both doors have a 2/3 chance of being right? Or Contestant 1 picks Door A that means door B has a 2/3 chance of being right. Contestant 1 is sent off stage contestant 2 comes on stage and picks door A as well. What a sucker they only have a 1/3 chance of being right since it’s the same door. Obviously that’s false. How did the chances go up for the same exact door unless it’s an illusion.
@@drewidlifestyle7883 the problem with adding in a second contestant is that if both of them pick incorrectly monty cannot open any doors because the only remaining door would have a car behind it. You are fundamentally changing the way the game is played and expecting it to play out the same way. It clearly wouldn’t.
This is the only video that has made this make sense, thank you so much! I was so focused on the probability after the door was removed, it didn't occur to me to think of the probability beforehand!
Well that's the reason why we always calculate probability before playing any game, not in the middle of a single game.
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*
lol
just more proof that he's an alien. He doesn't poop so he doesn't understand it.
@Vsauce out of context compilation
The non-intellectuals always stick to the irrelevant details, because it's hard for them to discuss the whole point of something and it's easier for them to stick to the jokes, puns, irrelevant details.
@@force6769 is the poop smell that bad huh ?
Michael is the only one that'll create an educational video lying down on a table and still get 2.7m views with 100k+ likes
He was like fueling Vsauce memes.
I am fairly certain there are some anatomy based "videos" which will result in millions of views... even when done on a kitchen table.
Michael understands that he's making a rectangular video and does so intentionally, rather than just doing a thing and filming it. He knows the camera isn't a person that can look around, and does so well to make the best of that.
What about that educational video Nina Hartley made while lying on a table
No other clowns 🤡 out there ?
This is a really good explanation but the one that convinced me was the adding more doors explanation. Lets say you gave 1000 doors with 999 goats and 1 money door. You have a 1/1000 chance of getting the money. Same as the monty hall problem when you choose the host will open 998 doors with goats and you can choose between the one you chose and the one left. With more doors it becomes increasingly more obvious how the math behind the problem works its just hard to understand the three door one because it's not that large of a difference
It's helpful to group the "doors" together. Instead of doors, you have 3 boxes on stage, and one has a prize. When you choose a box, they move it down into the audience. It's easy to understand that there is a 1 in 3 chance the prize is in the audience and there is a 2 in 3 chance the prize is still on stage. Opening an empty box doesn't change the odds that the prize is on stage, so of course you should switch to the remaining box on stage
wrong, it does change the probability that it's on stage because you just revealed one of the chances as not containing it. It only works if you always open an empty box ( if the host knows where it is and never opens it)
"You'd have to take it home and take care of it, all that normal poop stuff."
You should feed your poop or I'll call peta
Poota?
@@mcmouskewitz1271 haha
@@mcmouskewitz1271 poota madre?
Michael lies on a table for 14 minutes
I mean... look at that table though!!
But what he said was true!
That's actually his normal state, he usually has to get off the table to film his videos.
It honestly turns me on
Actually it's about 12:07
This is the best, most intuitive, clear explanation I have seen of this puzzle. So, thank you for creating “yet another” video about it!
8:25 for anyone who’s a skeptic, that 30 second clip is all you need. The real curiosity in this is why people who try explaining seem to ALWAYS unnecessarily over complicate it. The door that you don’t choose has a higher probability of having the prize because there is a 2/3 chance that you chose the wrong door to begin with. The host then reveals another door that is not a winner, telling you 2 things: The door that you chose only has a 1/3 chance of having the prize. That you already knew going in. And the second: the door that the host does open has a zero percent chance of having them prize. Therefore, the remaining 2/3 probability lies with the remaining door.
For most people, this explanation won't help. They will simply insist that the new choice is between only two doors and you still have no information about which door holds the car. Getting people with that mindset to let go and rethink the problem in a different way is the real challenge here.
@@Hank254 I had that mindset until recently. It's not most people's fault. It's the fact that most proponents of the theory try to one-up each other with fancier and fancier explanations. It's presented as something complex, when it's actually damn simple. It's just a matter of being shown how the participants opening the doors have more information about what's behind then is immediately seen. Nice and simple!
@@matheuscarvalhais954 Feel free to test your theory... you can sort the comments by 'Newest First' and explain it to someone who comes in to say the video is wrong. Or, look down for a thread started 3 days ago by hc3657 and explain it to him. We will see how it goes :)
Me: *trying to watch something educational in front of parents* Michael: HeY DiNGaLnGs!
SwayTooCrayy 😂😂
😂 😂 😂
Did you watch Michael frolic on the table in a dark room in front of your parents?
9:20 Pull the sack out
@@yourself3195 that contain...not just one...not two (the usual)...but THREE marbles...
Never thought I'd see Michael lay on a table and pull a sack out of his pants on KZhead.
He also pulled one out
With 3 balls
and say “hey ding a lings”
Only on youtube?
@@heck2993 What, you've never seen Michael on Brazzers?
WHEN FIRST CHOSEN, The chance of any door being right was 33%. So total = 100%. When one door is removed, the chance of the chosen door being the right choice is still 33% so the chance of the remaining door being right must be 100%-33%=66%.
Yup. Every time you pick a goat, which is 2/3 of the time, the host will be forced to open the other door with the goat, meaning the door the host didn't open is the one with the money. So yeah, 2/3 of the time, the door the host didn't open has the money, so you have a better chance of winning by switching.
But only if it's clear that he really was forced to open the door. Usually, that is not mentioned and should not be assumed.
@@insignificantfool8592 Of course it has to be assumed, ya dingus. Why would he open the door with money and ask if the player wants to switch? Think before speaking.
@@_P2M_ in order to steer the contestant away from the winning door, is the obvious reason.
@@insignificantfool8592 HUH??? How is showing the contestant the door with the money steering them away from the money? If he opens the door with the money, the contestant already lost, because you can't switch to the door the host opened. There'd be no dilemma. There'd be no point in switching or staying. Is your head functioning properly?
@@_P2M_ I never said he would show the door with the money. I gave a plausible reason for offering a switch.
2017: Michaels head 2018: Michaels head and shoulders 2019: All of Michael 2020: Michael invisible
2016: Michael invisible 2020: Michael's true form
2020: Inside Michael
2019: Michael's sack
the only next logical step is: 2020: naked Michael
2021: Micheals nuts
2017: Vsauce is a science channel 2019: Vsauce is a meme channel. Plus, it's mostly DONG content
Actually it's Ding now
DONG? What's DONG? This channel is and has always been called D!NG...
And certainly didn’t change it’s name because it was deemed inappropriate for monetisation
@@janikeuskirchen this channel was and should have still been DONG
@@thearmyofiron r/woooosh
In a sentence: "Switching doors is a bet that your original choice (only 1/3 chance of being right) was actually wrong, and that's a good bet."
Yes:)
no
The reason you gave at the beginning for presenting "yet another" explanation is so true. Wise, even! And you really did help me with this. Especially when you began using the marbles-in-a-bag version. Then it became so clear--very nearly intuitive!
"Fewer people want poop-some still will-but the point is you're supposed to want the money."
"You have to take the poop home, you have to take care of it."
Eric K and feed it like normal poop stuff
en.wikipedia.org/wiki/Coprophilia
@@maksphoto78 i'm 100% positive that link details information that i am not in need of.
Peter G nothing wrong with a little turd munching bro
The fact that he's lying on a table actually makes it more interesting
At first, I thought he was IN the table.
D C I did too
I agree much better than standing.
Yes that’s right
but its way more difficult for him and you notice him struggling multiple times
When explaining this I like to elaborate and say let’s do it with 10 doors. One has money behind it, 10% chance of picking money, remove 8 doors with goats behind them, and you’ll win 90% of the time if you switch to the remaining door. People for some reason don’t understand the small scale of 3 doors when I explain this to them. But you did a great job explaining it 👍
Yes:)
I understood that problem only when I tried to build a simulation on python. So I thought how could I imitate that change of the chosen door and it came to my mind that: 1. If you chose the right door and changed your door later -- you 100% got the wrong door. 2. If you chose the poop door and changer your door later -- you 100% got the right door. AND: as there are 2\3 poop doors, your overall chances to get the right door by changing your decision are 2/3.
except the problem lies in the database in round 1 you aren't choosing which door is the right one you are choosing which door the host opens. ppl like to think of these problems as if they have control. it's reinforced bias. as part 1 of the question has nothing to do with part 2
@@LIAuNXeNON sorry, but I didn't get at all what you meant
@@MrFackoffline when choosing in the first round you are 33% certain that any door is correct but you are 133% certain that at least 1 of the 2 remaining doors is incorrect that 33% chance is the additional information that never gets conciderate when this is brought up especially by computers.
Trying to solve the Monty Hall situation using Python… you see where this is going
This video is weird 1. "What's up dingalings" 2. Goat poop 3. Lying on a table the whole video 4. The ending
I read your comment before the poop part and when i saw it , i was like man why the hell this guy is still on the table ?And Poop?C'mon
Do you know who this is? Being the weirdest nerd possible is his thing.
@@amanthapliyal2636 Do you know who this guy is?
And a Sack
Colin Apex charmander in the back staring the whole time
9:22 - Michael squirms across the table top moaning before pulling out his sack and proceeding to tell us about how he is going to pull one out.
...and (not unexpected) plot twist: His sack has 3 balls; surprise, one of them is black.
This is why we need context.
@@WokerThanThou it just gets better by the fact he got a hole 2 white ones out of it.
Pulling out his sack and showing us his marbles ;)
And called us dingalings tf?
Your original pick has 33% chance of being right. The other 2 door each have 33% chance of being right, for a total of 66%. But the nice host eliminates one of of those 2 doors, so that last possible door contains the entire 66% chance. So you are twice as likely to win if you switch.
"The other 2 door each have 33% chance of being right, for a total of 66%." They already are either 0 and 2/3, or 2/3 and 0.
This is the first time the monty hall problem has really "clicked" for me. 1/3 of the time you will pick the door with the money, and when you switch you will lose the game. However, the other 2/3 of the time you will pick the door without the money. In these cases, the host will remove the other door without the money, meaning that the only door that you can switch to is the door with the money behind it. Therefore, if you follow this strategy, you will win 2/3 of the time. Thanks for this explanation!
Yeah. Even throughout this video it wasn't until that specific point was brought up that it really snapped into place
Let's say the car is behind door 1. You pick one, switching results in a loss. Let's say the car is behind door 2. You pick one, switching results in a win. Let's say the car is behind door 3. You pick one, switching results in a win. Expanding this retains the same ratio. Switching always is better 66.6% compared to 33.3%.
No, it’s actually less, because u need to count on the first pick, the count is simple, the first choice is 2/3 of getting one with poop, and then 2/3 picking the the money, so doing that strategy is 2/3*2/3=4/9, and that’s about 44% chance of winning
@@cuca_str4151 No, 2/3 chance you choose the poop. Then, if you switch, given that you chose poop, 100% chance of getting the money. P(Poop initially)*P(Money|Poop initially and Switch) = 2/3*1 = 2/3.
Another way to look at it: most of the time you choose incorrectly, therfore most of the time, the host tells you EXACTLY where the money is. You have a 1/3 chance of the host being unhelpful.
This video perfectly describes why Michael is just the internet's dad, trying to make educational topics interesting by trying to imitate how kids talk and do things.
Youre more likely to pick wrong than right (1/3 compared to 2/3) so you have better chances to switch to a "right" door than to stay on an unlikely right initial door.
Yes:)
No. This is false. The first part of the game is actually irrelevant, since the game show host will ask this question regardless of them picking the right or wrong door at pick #1. No matter how you play round #1, you will always be left with only 2 of 3 doors, leaving this all in a 50/50.
@@LinusMellstrand-ej5od that is false. Your initial choice is what determines the outcome of your second choice. So you cannot ignore your initial choice.
@@WilliamCacilhas Yeah I've learned that now hehe.
I could wrap my head around this '2/3 - 50/50' pseudo paradox when I extended the game to 100 doors. When you see, that your initial chance is just 1/100 and the hpst opens the other 98 doors, the remaining door gets the accumulative chance from all other doors, hence it's a 99/100 chance.
4:51 No, that's a $ on a yellow background. That's demonetization.
Poop > demonetization
You can't spell demonetization without demon btw
It's a schlatt coin
Alternate title for the video: Michael writhes around on a table for 14 minutes talking about goat poop
One of the better suggestions I've seen in a while.
Shut up furry
If you are a furry, you are not a human, therefore you can be hunted during hunting season. So, do that, less furries the better.
@Aryaman Rajaputra Umm no
So many edgy kids here ! People can comment anything they want. Can't believe people like you kids are okay with Adolf Hitler profile picture.
I like to think at this problem like this: We have two groups of doors: group A and group B. Group A contains the door you chose. Group B contains the other two doors. Because group A has one door that means that there is a 1/3 chance of containing the winning door. The chance of the winning door being in group B is therefore 2/3. We can as well say that group B has a 2/3 chance of containing the winning door because it contains two out of the three doors. The door that have been initially chosen is always going to be in group A and it's always going to have a 1/3 probably of being the winning door. So far so good. But now, let's assume that you can change the door you want to open, but no door has yet been opened. This means that if you switch to a door in group B, there is (1/2)*(2/3) or a 1/3 chance of choosing the winning door. So far, all the odds are equal. But when one of the doors in group B, is opened, which isn't the winning door, that means that if you switch to a door in group B, there is a (1/1)*(2/3) or 2/3 chance of winning.
Your math is missing a scenario. If I choose A he can open B1 or B2, giving me an extra scenario where staying wins (2/4).
I have struggled wrapping my head around this for so long and I would argue for hours about it with anyone that would listen but you today have made the arguement that I needed to finally wrap my head around it
michael : “ you want the black marble” me : “ i want the black marble”
You : " i want the black marble" Me : " _i_ want the black marble"
@@DuringDark Host : "You want the door with the money behind it." Ding : "I wan't the Vsauce with a table under it."
The Force can have a strong influence on the weak-minded.
Lol
i want taco
Why doesn't he just ask youtube for the password to vsauce?
They don't have it. The password will be encrypted. However it would be totally possible for them to set a new temporary password, as the password hash is still ultimately stored in a centralised database.
Jay Welsh couldn’t he just reset his password
@@amoose8256 not if he doesn't have access to the recovery email/account. But even in such a case, the database admins at Google could just change his recovery email record in the database directly (similar complexity to just straight up changing the password hash and salt in the database - very straightforward process for someone with DB write access to execute).
@@alasdairhurst I know that, but for all intents and purposes I thought my comment would make sense to more readers if they read "encrypted" compared to "hashed". I understand that the difference between encryption and hashing is that hashing a a unidirectional/one-way/non-reversable function, as opposed to encryption being bidirectional/two-way/reversible function (provided the decryption key is available).
What are talking about? Who lost password and for what...?
There’s 2/3 chance the money is behind one of the two doors you didn’t pick. The host removes one. The remaining door has 2/3 chance of money all by itself.
Yours is probably the simplest, clearest, and best way of explaining the solution that we've ever heard. Nice going.
@@KpxUrz5745 I appreciate your recognition fellow human
@@KpxUrz5745 Not really. A SIMPLER explanation is you're trading one door for TWO.
@@jakejones5736 Sorry, that makes no sense.
@@KpxUrz5745Sure it does. What the host is effectively doing is giving you BOTH of the other doors. This is because if the prize is behind ANY of the two doors... you WIN! You already know for certain that there is going to be a loser behind one of the doors, right? So that being the case, you could never win by switching unless what I said above is correct. Same holds true for lottery tickets. Right after you purchase a ticket, if the clerk offered to trade yours for TWO, would you accept the offer?
Whenever I come across folks who struggle with the math, I always extend the scenario out and say, "There are a BILLION doors in front of you with poop behind all of them but one, which has a million dollars!. Pick a door." I then take away ALL the doors except the one they chose and another door (say No. 171). I then ask them if they want to change the door they chose. Believe it or not, some people still insist it's still "50/50" :D
Yup, we see people like that all the time in here. There are a lot of people who think they understand probability but they really don't have a clue. To them, a choice between two options is the definition of 50/50. That is set in stone to them and it is a complete waste of time to try to help them move beyond it.
Does the world need another Monty Hall video ? Michael "Well, no, but actually yes."
Ramash440 belka did nothing wrong
Surprisingly helpful. I've known of this since I was a kid but never really understood how it works until now.
Or...does it?
There's actually very few possible outcomes, so let's just list them all: 1) You pick a door with a goat. You don't switch. You get the goat. 2) You pick the other goat door. You don't switch. You get the goat. 3) You pick the money door. You don't switch. You get the money. 4) You pick the goat door. You switch. You get the money. 5) You pick the other goat door. You switch. You get the money. 6) You pick the money door. You switch. You get a goat. Those are all the possible outcomes. Of the three not-switching outcomes, only one got you the money. 1/3 chance. Of the three switching outcomes, two of them got you the money. 2/3 chance. You have a 1/3 chance of winning if you don't switch, and a 2/3 chance of winning if you do switch. So there you go.
I think that is better than most peoples explanations
Oooo i like that
I love this explanation
(again this explains why it works but for most people will not explain to them why they felt it was intuitive)
Did you just out explain vsauce?
Just my go at explaining if it helps anyone... A - If you pick money the first time, you shouldn't switch because the other doors are both goats. B - If you pick goat, you've got a goat, then Monty shows you the other goat. The remaining "switch" door is the money. Monty always shows you a goat, since one of the 2 doors you didn't choose will have a goat behind it, so he opens that one to show you. So if your initial choice was a goat, you should switch, because Monty shows you the other goat before he asks you to switch or not. The other door can only be the money. But, you have no idea if your choice is the money or goat. Your chance of picking "money" back at the start is 1/3, all 3 doors closed, random chance, 1 in 3. Your chance of picking "goat" at the start is 2 in 3, cos there's 2 goat doors. If you initially chose a goat door, and switch, then you win, see "B". If you initially chose the money door, and switch, you lose, see "A". But since you have a 2/3 chance of choosing a goat at the start, that means 2/3 of the time the correct choice is "switch". See "B". If you chose the money door to start with, switching loses the money, but the chances are, 2/3 to 1/3, that you didn't choose the money door. So the odds say "switch" and you'll be twice as likely to win. I've repeated some points a bit here just to give some hooks for people to grab onto, if it helps understand it. Though Michael did a thorough job himself.
Summary is what you chose is probably wrong, plus the fact the host will always reveal another wrong one, further confirming your wrong initial choice, so the remaining is most probably the right one so always switch to that to maximize winning. Best non visual breakdown & explaining further, you only have 1/3 chance of choosing the car door, so switching has a bigger winning rate of 2/3. the host will ALWAYS remove a goat door which gives the change of choice (switching) an additional 1/3 (total of 2/3) compared to your initial choice of 1/3. this solution only works if the host ALWAYS removes a goat door. if the host doesn't open any doors then this will truly be a 1/3 chance of winning regardless if the host asks you to change your choice or not.
That's right because the other 2/3 doesn't just disappear. The equation must ALWAYS add up to 1. In other words, if there are initially three doors, then a win is 1/3 (one out of three). If there are initially two doors, then a win is 1/2 (one out of two). And if there is only one door, then it's obviously 1/1. Number of doors times the win fraction will ALWAYS equal one. This is why claiming a 50/50 chance, meaning 1/2, is incorrect because there are THREE doors. And 1/2 x 3 does NOT equal one.
my favorite way of understanding this very quickly and easily is this: There are 100 doors. one has money, the rest have goats. the game is played the exact same way, but rather that revealing one goat, the host reveals 98. so here's how the game goes - you pick a door (1/100 chance you got the money), the host reveals 98 of the goat doors, leaving one left. stick or switch? well lets reasonably assume you didn't get the 1/100 chance. the door he leaves MUST be the money. you switch.
Pin this genius
@@adrianputala9212 all credits to my maths teacher
pin this math teacher
Wut
This is actually the way the great mathematician Pal Erdös understood it back in the day after repeated failed attempts.
I agree with everything thing this video has to offer. The solution is solid, the table seems to be a good choice of support substrate, swapping goats for poop. 10/10.
he is the goat
Unpicked two doors have 2/3 chance combined. The host removes one door but the total probability is still 2/3.
Yes. That's because only one of these two doors have 2/3 chances of having a car behind, while the other door has 0% chance of having a car behind.
@@max5250 It's 2/3 and 1/3.
@@jakejones5736 Wrong. One door player picked holds a car with 1/3 odds. Two doors host got, hold a car with 2/3 and 0 odds respectively.
@@max5250 Mistook the "other" door to mean the contestant's door, so we're clear on that. But regarding your contestant having 1/2 odds, that means the total is 7/6. Consider: 1/2=3/6 and 2/3=4/6. Thus, 3/6+4/6+0=7/6!
@@jakejones5736 My mistake, I wrote 1/2 instead of 1/3 (corrected it now). As for you reply to me: You are talking about total odds (1/3 odds of a player's doors, and 2/3 odds of two host's doors), while I was talking only about odds behind two host's doors. (I was basically explaining that these two doors are not holding a car 1/3 odds each door, but one single door holds a car with entire 2/3 odds, while the other doors doesn't hold a car for sure, since a goat is behind it).
I'd summarize as: Your first choice has a 1/3 chance to be correct and by switching after the poop elimination your flipping that first choice over to 2/3's effectively exploiting your original choices chance of being wrong.
“There’s an analogy that makes this more clear” *reaches for his sack*
@James Goner rofl thats a killer
*pulls out his marbles*
How am I supposed to understand this while I’m being distracted by how THICC Michael is
No one can take you seriously when you use dumb made-up "words" like that.
@@SteveFrenchWoodNStuff Are you taking the piss?
@@SteveFrenchWoodNStuff Fun fact: all words are made-up :D
Lyrog I understood that reference
Wood 'n' Stuff w/ Steve French go make some wood
Seems intuitive. You pick 1 of 3. Then one is eliminated, but never the correct one. 1/3 you chose correctly, an incorrect is eliminated, and an incorrect remains. 2/3 you chose incorrectly, host eliminates the only other incorrect, making the last door the correct one. Your initial choice forces the host's hand. If you were wrong, which you are 2/3 of the time, the host must tell you which door is correct by eliminating the other wrong door. Simple. Just remember that none of the actions are independent. His choice depends on yours.
This is the best explanation of this conundrum because Micheal gives the intricate details other videos leave out.
The easiest way to understand is that if you pick incorrectly, switching will automatically get you the money. And you pick incorrectly 2/3 of the time, so switching gets you the money 2/3 of the time (whenever you pick wrong)
This really explains it intuitively
Honestly, that 3 second explanation was all that was needed for most people to understand
imagine the same situation but with 100 doors. You pick one, they remove 98 doors and give you the choice to switch. Would you switch now? For you to be better off not switching, you would have had to pick the right door out of 100 (1%). Do you have the confidence that you choose the right door?
This is the only thing I’ve seen that makes it understandable for me. Thank you!
This doesn't explain why switching automatically means you win if you picked incorrectly, though, which is the only thing that trips people up
"Kevin's recent video about paradoxes" - Apr 24, 2018
мяMαcкσ his calendar is a bit off. Why do you think vsauce1 is so empty? To him it is still 2018
He lost sense of time in that isolation chamber
I loved you left it uncut and completely proved the point with the marble example!
The crucial thing to understand is that the only "chance" step in the entire game, is the first choice of the first door. Everything else is set at the beginning and isn't remotely chance related. So, when you first choose, the chance of picking the $ door is 1/3, and the chance that $ is behind the other doors is 2/3. If you can get to the other two doors then your chances would be 2/3. Great, you switch, and if there was any $ there, you get it. You're not flipping a coin to decide whether to switch. You always switch. The "game" is, in fact, that you pick a door and win if the $ is behind one of the other two doors. (If you think of the game as being the pre-written plan that you pick a door and the host shows you which other door to not pick of the two and you switch. None of that is a probability after picking the first door, it's all known data.)
Best explanation I've heard: Imagine there were 100 doors instead of 3. 99 of them have goats and one has the money. You pick one door, and the host opens 98 doors to reveal goats, leaving only one other door closed. It should be DEAD OBVIOUS that it's the money door. The only way it won't be the money door is if you picked the money door initially, which is only a 1 in 100 chance.
Exactly. This is the best explanation. Idk what's so hard about this problem that Michael - freaking MICHAEL - needs to mull over it.
HS teacher here. I go for BIG numbers... 1 000 000 002 doors. Then to make them pay attention I emphasize that the 2 is important. After all the explanation I admit that the 2 is important 'cause I don't wanna say that the host opens 999 999 998. It's just easier to say "a billion". haha
@@Xanade I just go with 100 because it turns everything into percentages, which we're all used to.
I like how you think
@@jerrykoh9692 Calm down, he's not some math genius
This problem can be thought through an exaggeration: Imagine there were 100 doors instead - behind them are 1 case with a million dollars and 99 poops. If you now choose a door and Monty Hall opens 98 doors with poop, leaving your door and one other door, either of which has the money, it's obvious that you should switch since initially picking the money was so unlikely. EDIT:Wow I'm surprised this got so many likes and sparked such a rich discussion :D
Tarmo Taipale That helps, but that doesn't necessarily imply anything about the case with 3 doors. Of course, we know they do turn out to have the same reasoning, but this example alone does not prove that. I think the best way to see this is via case analysis. Case 1: I pick any of the doors with the poop -> Monty Hall opens the other door containing poop -> I win by switching. Case 2: I pick the one door with the money -> Monty Hall opens one door with poop -> I lose by switching. Case 1 is twice as probable as case 2, so you should assume that case 1 is the case you're currently in. That guarantees the highest chance of success.
@@angelmendez-rivera351 yeah it's true that the 100 door case doesn't prove anything about the 3 door case, however the point was to give some intuitive perspective to make sense of why switching is better than keeping the original choice (instead of both choices being equally good which is what some people what intuitively think). The difference is more apparent when we have 100 doors instead of 3, even though the logic is similar in both cases.
Tarmo Taipale I don't agree that it's more apparent. And neither do most of my students.
I don’t know why these dinguses are disagreeing with this exaggerated example. It is the same logic and explains it better...
Sin Because it isn't better. Morons don't get to say otherwise.
I had a statistics class where we went over a very similar problem, except there were five choices instead of three, and the person revealing an unchosen option didn't know which was the desirable one. We reached the same conclusion that switching was better, but 8 months later I'm realizing that we were taught wrong.
It matters not whether the one doing to revealing knows what is behind the door. What matters is process of elimination, you now know what was behind that door and therefore it is no longer an option. Since it is no longer a factor, your probably just improved to 0.25 instead of 0.2, but only if you switch! Therefore, You should switch to capitalize on this fact. To not switch, would be to accept 1/5 odds instead of improving to 1/4.
@@jj4791 No, it is crucial for the host to know which door has a prize. Otherwise the host might have opened the door with a prize, his decision is random, therefore the probabilities would not change. You can use Bayes formula to check it.
Wow, this was mind-bending... Just figured it out but explaining this to others would be beyond me. Great job!
2:24 "you gotta take the poop home take care of it feed it and all that normal poop stuff"
Why was nobody else talking about this lmao
Was searching for this comment ....
That would be a good quote to quote mine
You're telling me the Monty Hall problem was this easy to understand? Wow I've seen such a good explanation
This is the first explanation I've seen that wasn't smug.
Ye, I am amazed no annoying probability tables
It's never been especially complicated. The way the human mind works, however, we tend to overlook crucial information -- even when we're scrutinizing and trying to ascertain every possible detail. Sometimes that makes us more susceptible to missing the obvious. When you simplify it, the Monty Hall Problem is ridiculously and deceptively easy to understand. What's crazy to me is that mathematicians and statisticians have more than likely argued over the problem for decades at this point lol
i thought he did a mediocre job. I've seen better explanations.
Ooo an area11 fan
I always thought of it as "you're more likely to have picked wrong, so Monty is more likely to not want you to switch, therefore you should always switch"
at first i wasnt getting it all too much but then he did the scenerio with the marbles and i was like "I GET IT NOW!" that is a very good way of explaining how it will be more in your favor to switch!
So nobody going to talk about how he called us ding-a-lings? No? Okay lol
And here I thought he learned his lesson when he _totally did not rename this channel from its previous name and it's association with an innuendo_
Yeah. I would much rather be a dong-a-long.
This is not the first time he’s done that
It's not the first time he does that
This is not the first time he does that
The best example I've seen that makes understanding the gain in information when Monty opens a door really intuitive is this: Imagine there are 1000 doors, $1 000 000 behind one of them, goats behind the other 999 doors. You pick one of them, obviously not really expecting to pick the right one. Then Monty opens *998* of the remaining doors, guaranteeing that the money is not behind any of them. After rounding up the 998 rowdy goats, there is the door you picked and one other door _mysteriously singled out_ from the other 999. Now it feels pretty obvious to me that switching is a good idea. The 3 door problem is the same thing but the information gain is less obvious because it's not as big.
Wow.
Dude. Should have scrolled to your comment earlier and I would have saved 14 minutes of my life! Amazing explanation!!!
Amazingly, some people don't get even this sort of explanation; or rather, they don't see how it applies to the original problem.
Ah I just posted something similar and then saw this. Good job!
I think its easier to say, you get it wrong 2/3 of the time. So if you switch, you will be getting it right 2/3 of the time.
This was a good explanation. I think a revealing way to think about it is to imagine the problem with a hundred doors, you pick one then the host opens 98 of the remaining doors.
Yeah it's simple. The first door you choose has 1/3 of having the $. The remaining 2 doors (together) have 2/3 chance of having the $. After the host eliminates one of those 2 doors, the last door now has the 2/3 probability all for itself. So switching to it would be the smart thing to do.
"Fewer people want poop. Some people still want it" Words to live by.
I thought everyone wanted the poop! Man, my parents taught me wrong.
Ayy 100 likes
I want hot swedish teen girl model poop
Ratemypoo.com
Use the poop as fertilizer to grow the stalks, then sell the crops and soon enough you will earn a million dollars
0:20 “including Kevins recent video” video is from April 2018.
That's recent in Vsauce time
Time is relative. But that's another video.
Or perhaps this is an april fools joke
were talking vsause time here
I always looked at it as this: The total possible outcomes you have 50% of winning. However, the ACT of switching you have a 67% rate of success, because for your first choice is 67% likely to have been wrong.
As someone who has learned quite a bit about probability, I find this problem quite intuitive: since the initially chosen door cannot be opened by the presenter, we don't get any additional information about it as opposed to the other door which could have been opened. By the way, there are tons of paradoxical facts that can be proved by mathematics! Here's one that's easy to prove, but hard to understand: if you toss a perfectly normal/balanced coin indefinitely, the probability of getting tails once followed by heads twice is higher than getting heads twice followed by tails once! (You can easily find a demonstration online)
Want one that's even CRAZIER? This one is mind-blowing : Tails-Tails-Heads is more likely than Tails-Heads-Heads 🤯 !
@@Fascry_ Surely you meant about the first instance?
@@Stubbari My English is not perfect, but if I understood correctly here is my answer: yes, I am talking about the probability of getting one permutation before the other
2/3 of the time, it works every time. - Brian Fantana, “Anchorman” 1st: Contestant makes undesirable choice 2/3 of the time. 2nd: Host displays undesirable choice every time.
"I am 100% sure he's probably the guy" - Adrian Monk.
you misquoted brian fantana.. its 60%