what if you want the goat?

@TedManney

8 жыл бұрын

What do you think?

@julianfuchs9253

8 жыл бұрын

stay

@Agirlswierdworld

7 жыл бұрын

not necessarily...I'm syrian and my people could care less.

@Keenankid11

7 жыл бұрын

dont switch

@kale2514

6 жыл бұрын

LOL

How dare you Detective Diaz, I am yoUR SUPERIOR OFFICER!

@sakonan4883

4 жыл бұрын

BOOOOOONE

@brodie_c

4 жыл бұрын

BBBBBBOOOONEEEEE

@aminhaekal5709

4 жыл бұрын

@@sakonan4883 whatever happens in my bedroom is none of your concern

@jyotsnapanicker8111

3 жыл бұрын

@@brodie_c Don't ever speak to me like that again.

@shahdalkasas101

3 жыл бұрын

Boonneee😂😂

This FINALLY makes sense. I couldn’t wrap my head around why the probability wasn’t 50/50 on new information. But it turns out that it is more likely you randomly picked a goat, and therefore the host has to show the door with the other goat. And then the unselected one would have the car 2/3 of the time. In other words, it’s not an independent probability. Clearest explanation I’ve ever seen. And the only one that actually makes sense.

@IAMTHEMUSK

Жыл бұрын

But how do you decide the door that has 2/3? It’s 50/50

@personthatisnotmehi

Жыл бұрын

But what if I wanted the goat

@blackdragon4664

Жыл бұрын

I still didn’t get it until I read your comment lmao

@advaysatardekar8537

Жыл бұрын

Tnx for explaining. I understood it tnx to u.

@advaysatardekar8537

Жыл бұрын

​@@IAMTHEMUSK I will explain it: *Choose one door. You will win the prize if you are right.* 🚪🚗 🚪🐐 🚪🐐 ⅓ ⅓ ⅓ Probability *You have higher chance of choosing - 🐐* 🚗 - ⅓ 🐐- ⅔ Host reveals one 🐐 🚪🚗 🚪🐐 🚪🐐 Host : This is🐐 *Host after revealing tells that you can switch or stay with the door.* *Should you switch or stay?* *Chances - 50/50?* *Wrong!!!* Solution: *As you can see, you are more likely to have a - 🐐* *So, switching would have more chances of you winning the car!!* *Switch - ⅔* *Stay - ⅓* *SIMPLE*

Guys, switching always gets the opposite result of what you originally chose. Choose bad door originally = End up with good door Choose good door originally = End up with bad door Since it's more likely that you chose the wrong door in the beginning (there are 2 wrong doors and only 1 good door) then switching is more likely to get you to the right door.

@evangelineodibo8014

Жыл бұрын

This is the best most comprehensible explanation I’ve found on this, thank you :)

@seignee

Жыл бұрын

@@evangelineodibo8014 no prob ^^ glad to help :) i found a lot of other explanations confused me so when i had this epiphany i had to post it XDD

@Trazyn_The_Finite

Жыл бұрын

Unfortunately, I know from personal experience that even this explanation sometimes does not work somehow

@seignee

Жыл бұрын

@@Trazyn_The_Finite thats alright. we all have different mental processes. its best to focus on finding that missing mental link, and try to really dig deep on it. for me my brain is kind of like a brute force thinker so i really need to go through the motions to get something to click lol. other people like doing it more efficiently though, but my brain just doesnt work that way

@rileysinclair5980

Жыл бұрын

I've been ruminating on this problem for awhile and even have a pretty strong background in math, but it was this comment that really helped explain it to me best. Thanks for writing it

Here’s how I finally understood it: It is more likely that you chose the wrong door than not. Switching then is more likely to have desired result.

@agapideligianni9691

2 жыл бұрын

thankss

@superyahoobrothers

2 жыл бұрын

No

@YouTubeallowedmynametobestolen

2 жыл бұрын

@@superyahoobrothers Why not?

@YouTubeallowedmynametobestolen

2 жыл бұрын

Holy Moly. I''ve been wracking my brain over this for half an hour, and had a really good argument against the explanations I saw in other videos. (I haven't watched this one yet.) And you come along and put it into such a simple, short explanation--that is so easy to understand and makes such perfect sense to me. Kudos!

@naramukuriht

2 жыл бұрын

yes thats correct. Thats the most intuitive way of thinking about it.

The confusing part of the Monty hall problem is that the "host" reveals a door he knows is not the prize. This is often mentioned only briefly in the setup, but it is key to understanding why this happens. If the "host" chose the revealed door at random, the whole game falls apart.

@bearman975

Жыл бұрын

This video finally explained it to me but they go over the solution so fast that I missed it 5 times. There are only 2 scenarios, But one happens twice as often.(1:45 in video) A. If first pick is correct, switching always lose. B. If first pick is wrong, switching always win. The odds that first pick is wrong is 2 out of 3, therefore that scenario will happen 2 out of 3 times, so switching will give you a 2/3 chance of winning the car.

@alcoyot

Жыл бұрын

@@bearman975 thank you. That was the simplest explanation. You’re extremely smart! I haven’t seen it explained so easily anywhere

@davidkelly2

Жыл бұрын

@@bearman975 I've read so many articles on this, seen so many charts, and nothing could paint the picture to me. You, humble KZread user, just nailed it for me so concisely. Bravo

@bigbluebuttonman1137

Жыл бұрын

@@bearman975 Yes, it basically inverts the odds when you switch doors due to the host revealing one of the incorrect doors. The game of chance is built on a lack of knowledge; and the host gave you some. It's much better to simply step through the problem again more slowly than the explanation that was given here.

@freshoxygen2176

Жыл бұрын

Agreed. Without “motive” then the odds don’t change? Right

here is another way to understand it: Since there is only one of the three doors you can pick at the start, say you pick the actual car door as the initial pick... *[CAR]* [GOAT] -[GOAT]- *stay = win* switch = lose you could also pick the middle goat box initially: [CAR] *[GOAT]* -[GOAT]- stay = lose *switch = win* you could also pick the third box initially: [CAR] -[GOAT]- *[GOAT]* stay = lose *switch = win* so it is clear from all the possibilities that switching lead to winning twice, while staying lead to win only once... Switching > Stay

@GHanBax

4 жыл бұрын

In the staying situation, if you choose the car, there are two goats to switch to, either goat a or goat b. So it means there are two possible scenarios that could happen in staying against switching on winning. Making switching and staying 2-2, so the probability will be 50/50.

@muhammadreyvannatechnoury9767

4 жыл бұрын

@@GHanBax so its 50/50 then...

@max-ty6ph

4 жыл бұрын

@@GHanBax No this is actually not correct. Because you're assuming all "scenarios" occur at the same probability. You as a player has three roads to go down, picking Goat A, Goat B or picking the car. You as a player decide (unknowingly of course) which road you will go down which will all have an EQUAL chance of 1/3, because there are only three options available to you and your choice is random. In the case that you actually chose the car (1/3) there is a 50/50 chance of which door the host will open because he has to choose one randomly let's say. That is why there is an option added for the host in the case you pick the car door because he does not have a forced move, but can rather choose between two alternatives (opening Goat A or Goat B). But this does not alter the original odds for you to choose the car-door so even those two scenarios have to sum up to 1/3 because they can only happen when you choose the car, which is one third of the time. So there are 4 scenarios that can occur in total: 1) Goat A opened given you chose Goat B = 1/3 * 1 (because Goat A will ALWAYS be opened when you choose Goat B) = 1/3 2) Goat B opened given you chose Goat A = 1/3 * 1 (because Goat B will ALWAYS be opened when you choose Goat A) = 1/3 3) Goat A opened given you chose car = 1/3 * 1/2 (because 50% of the time the host will open Goat A and 50% he will open Goat B) = 1/6 4) Goat B opened given you chose car = 1/3 * 1/2 (because 50% of the time the host will open Goat A and 50% he will open Goat B) = 1/6 So this still means that 1/3 of the time you will land in scenario 3 or 4 and switching would lose you the game while scenario 1 and 2 wins you the game, which happens 2/3 of the time.

@rudygirish364

3 жыл бұрын

THAT'S A MUCH SIMPLER WAY OF EXPLAINING!

@rudygirish364

3 жыл бұрын

THAT'S A MUCH SIMPLER WAY OF EXPLAINING!

If you open the door and get the goat, Do you get to keep the goat?

@jamez6398

9 жыл бұрын

Yes.

@Annadog40

9 жыл бұрын

Forget the car I'm a get the goat!

@MrLemonGrahb

9 жыл бұрын

Hannah Pil Nah you have to feed the beast!

@carultch

9 жыл бұрын

Annadog40 If Bart Simpson were the contestant, it would be an elephant.

@lnvlogs2136

8 жыл бұрын

+Annadog40 I've always wanted a pygmy goat for a pet.

EASY EXPLANATION Option 1: you pick goat a, Monty picks goat b, you swap and win the car. Option 2: you pick goat b, Monty picks goat a, you swap and win the car. Option 3: you pick the car, Monty picks goat a/b, you swap and pick the remaining goat. SO! 2/3 you win the car when you swap. See? Easy.

@eamoncobb3754

8 жыл бұрын

There are 4 options

@eamoncobb3754

8 жыл бұрын

Option 4: You pick the car, Monty picks b you swap and get the goat a

@marcusooi1510

7 жыл бұрын

WRONG! Option 1: you pick goat a, Monty picks goat b, you swap and win the car. Option 2: you pick goat b, Monty picks goat a, you swap and win the car. Option 3: you pick the car, Monty picks goat a, you swap and pick the remaining goat. Option 4: you pick the car, Monty picks goat b, you swap and pick the remaining goat. SO! 1/2 you win the car when you swap. See?

@IntensePeppers

7 жыл бұрын

Marcus Ooi - Options 3 and 4 are the same. Which brings it back to 2/3

@cediv715

7 жыл бұрын

I love how you say WRONG! and yet you're wrong yourself

i have no clue of what just happened...

@jameswest8280

Ай бұрын

Hop on the bus, we're both headed for the same place.

@Puppetter_

5 күн бұрын

The ace senerio helps you better understand it, pick randomly = 1/52 because one of the cards is the ace. Reveal all the cards except one and you see there isn’t the ace in it means that either you pick the 1/52 ace which is very unlikely OR you switched so your presentage is 51/52 (The reasons it’s 51/52 and not 50/50 is because the one you picked randomly at the start is 1/52)

Who's here because of Brooklyn 99 If yes: BOOONNNNEEEE?!!

@apa6502

5 жыл бұрын

Don't EVER speak to me like that again!

@jaybond9864

5 жыл бұрын

@@apa6502 how DARE you, I am your SUPERIOR OFFICER!

@micah4029

5 жыл бұрын

*BONE!?*

@jaz8342

5 жыл бұрын

Hahaha yes

@sakonan4883

4 жыл бұрын

you're fired

I can't drive… give me the goat.

@gwenythjackaway3770

10 жыл бұрын

Your icon is cute.

@alannar.5520

10 жыл бұрын

Thanks!

@Unbiasrobloxxer

10 жыл бұрын

Alanna R. Your icon is cute.

@thomassargent2236

10 жыл бұрын

I want to get on that game show. I have a better chance of the goat. ILL SELL MILK AND. BUY STUFF.

@kevinmendoza6386

4 жыл бұрын

Five years later and nothing.

Hopefully this explanation helps: If you pick one door, you have a 1/3 chance of getting it right. Logically, the other two options would be 2/3 since its 2 options out of 3. Now, assume there are two sides. Your 1/3 side for your pick and the 2/3 side for the two other options. The host reveals a goat from the 2/3 side, this reduces the options from the 2/3 side to one option. So now you are left with your 1/3 side one option vs 2/3 side with one option. Its better to switch.

@TheGoldenPostcard

3 ай бұрын

By far the best explanation I've ever read.

@jasonavina8135

Ай бұрын

Yeah this is the best explanation i think

SO SIMPLE. The big question is, do you want a brand new car or a goat?

@raw_oyster

4 жыл бұрын

I'll take one goat, please. 🐐 😎 (His name is Kevin 😏)

@iisaperson9914

3 жыл бұрын

i want goat boi

@gettingshotsomeonesgonnapa8635

3 жыл бұрын

Lol

@branwen-ho3wh

3 жыл бұрын

Goat

About 4 years later, I know how the math works but my brain still doesn’t see why it makes sense but at the same time it does

@ShivamSharma-5622

Жыл бұрын

Ikr if you run simulations, it's very clear that we should switch. But this problem simply doesn't 'click'.

@justinjun3896

Жыл бұрын

Perfectly said

@seignee

Жыл бұрын

Guys, switching always gets the opposite result of what you originally chose. Choose bad door originally = End up with good door Choose good door originally = End up with bad door Since it's more likely that you chose the wrong door in the beginning (there are 2 wrong doors and only 1 good door) then switching is more likely to get you to the right door.

That card explanation and visual was so much more useful than any verbal explanation I've heard

I think I get it, You have a 2/3 chance of picking the goat before the host reveals a goat. The car has a 1/3 chance. Chances are likely that you picked the goat before the host revealed a door. So if you swap, it would bring you to the car likely since your original choice was more likely to be the goat.

@yomoma7871

5 жыл бұрын

Nope. U have 2/3 chance but when you choose one it is 1/3 and 1/3 of the goats will be revealed anyway so its 1/3. Pretend you have 2 cards u pick one reveals the goat then ud know which one is the car but if u pick goat he tells u the goat which is the one u pick and u still know.

@leowiding8792

5 жыл бұрын

Yo Moma I hope you realize his comment was made 5 years ago, in 2013...

@SamoIsKing

5 жыл бұрын

It makes alot more sense when there are more options, like the deck of cards he used.

@joeparker511

5 жыл бұрын

Yo Moma you’re wrong

@shashu8205

5 жыл бұрын

You explained it better then any other person has ever had.

I FINALLY GET THIS! I honestly have broken my brain with this problem so many times. It still feels super weird of course, and I always believed the calculations but assumed the answer of why that is true would allude me. Using the cards really helped me to grasp it, thank you!

The way I personally understand this problem is that there is always 3 doors involved, so it doesn't change to 50/50 at any point - the probability is "locked in" from the start. When you first choose a door it's "unlikely" you have selected the correct door (because you only have a 1 in 3 chance of selecting the correct door). It's more "likely" that you have selected an incorrect door - because there's a 2 in 3 chance of that happening. So it's actually "twice as likely" that you've selected a wrong door than the right door (2 out of 3 chance versus 1 out of 3 chance). Therefore you should already be thinking of switching doors, right? But which other door to choose? At this point the host does you a huge favour by revealing a door he already knows has a goat behind it. He's essentially saying: "Here, let me show which of the doors you should switch to." The door you're currently sitting on (the first door you picked) STILL has a 1 in 3 chance of being the correct door. Probability-wise nothing has changed in that regard. But since it's already been established that you've likely picked the wrong door - and you now know which door to switch to - you should switch. Here's the kicker though. Making the switch won't always be the right decision. 2 out of 3 times it will be the right decision, and 1 out of 3 times it will be the wrong decision. But which odds do you prefer?

@jonah.donohue

8 ай бұрын

Thank you

@jakejones5736

4 ай бұрын

An even SIMPLER explanation is by switching, the contestant is effectively trading one door for TWO! How so? Because the host is essentially saying "if the car is behind EITHER of the two doors that you did not chose, you WIN!"

This is a much better explanation than the others that I've watched. A great source of science as always, AsapSCIENCE.

The scenario with the cards only works if the dealer knows where the Ace is. If I picked a card off the top and you flipped over 50 other cards randomly and none was the ace, both cards left would have the same probability of being the ace. The knowledge of the dealer or game show host is the only reason this works.

@max5250

2 ай бұрын

Correct.

@jakejones5736

Ай бұрын

@@max5250 I used to believe the opposite until "somebody" suggested I run an actual trial. This indeed made me a believer! There is no shame in conceding. The shame comes from stubbornly refusing to learn.

@max5250

Ай бұрын

@@jakejones5736 I don't care what do you believe, as long as you read with understanding, and that doesn't go well as we can see.

Excellent Explanation. Thanks!

I've seen this like 10 times, a lot of variations and every time it has been explained, but only now I actually get it. THANKS!!

Short answer: You have a higher chance of picking the wrong door. Theres a 1/3 chance that you'll pick the car and a 2/3 change that you'll pick a goat. If you pick a goat (which you most likely will) and another goat is revealed behind another door, if you swap, you get the car.

@nicolesong6199

10 жыл бұрын

The question is, WHY?????? WHY DO THEY HAVE THAT CHANCE OF PICKING IT???????????????????

@cstill

10 жыл бұрын

Nicole Song You're being too vague for me to help you.

@nicolesong6199

10 жыл бұрын

Like for example, in the deck of cards, why is the remaining unflipped card from the deck 51/52? Nobody really explained that, except the maths equation which I 1. have not learnt 2. don't really understand.

@mattwoods3057

10 жыл бұрын

Nicole Song Alright first I'll address your problem with JeffIsAPrettyCoolGuy. The chance of you choosing the car is 1/3. If you switch, then you will get a goat, as that would be the only open door left after the host opens the other goat door. So that is a fail. However, the chance of you choosing a goat on your first pick is 2/3. Switching would give you the car, since the car door would be the only available door after the host reveals the other goat door. So 2/3 of the time (because 2/3 of the time you choose a goat) switching helps. Now for your problem with the deck of cards. Math is not a living being. It doesn't think "oh look, 50 cards of the 51 pile got turned over and none of them were the ace of spades. Better adjust probability!" It doesn't work like that. Math stays still and doesn't account for the change. However, you can still choose that card from the 51 pile that wasn't turned over. And since the turned over 50 cards are invalid, that card "inherits" all of its probability. Remember, before I flipped any of the 51 over, the chance of it having the ace of spades was 51/52 and math doesn't adjust. So now, the probability in that one card is 51/52, giving it a way higher advantage over the first card you chose, which only has a 1/52 chance.

@RealBagels

10 жыл бұрын

Nicole Song becouse when you picked the first one it was a 51/52 chance that its the wrong one so when they flip the other ones its more likely you picked the wrong one the first time so switching improves your chances!

brilliant explanation. Especially the analogy with the playing cards. Keep up the good work, guys!

But if I want the goat?

@maniacpwnageking

10 жыл бұрын

Don't switch.

@kazenohitori7032

10 жыл бұрын

HAHA

@juancruzcastiglione5991

6 жыл бұрын

ChrisCucinell then stay

This surely only works if the door that was opened, was intentionally selected, rather than being randomly selected.

@Hank254

21 күн бұрын

Correct, if the host opens a door randomly then don't bother switching.

Still don't get it...

My mom grew up with 2 goats in Asia.

Switching doors reverses the odds. Your chance of selecting the winning door at the start is 1 out of 3. If you keep that door, then the odds of you having chosen the correct door at the start are still 1 out of 3. Revealing a losing door does nothing to the odds if you stick. If you switch though, you reverse the odds: If you originally picked a losing door (and there's a 2 out of 3 chance that you did) then you now win. If you originally picked the winning door (which you only had a 1 out of 3 chance of doing) then you now lose. Switch doors, people.

@AlastairjCarruthers

Ай бұрын

@@NDAsDontCoverIllegalActs True, but 33.3% (the probability of you picking the car at the start and then losing by switching) is still less than 66.6% (the probability of you picking an empty door at the start but then winning by switching). If you pick a door then switch, there's a 2 in 3 chance that you'll win. If you pick a door and don't switch, then there's only a 1 in 3 chance that you'll win.

At the end by revealing the space of every possible outcome you cleared it all out.Good work.The best explanation there is.

those are multiple amazing explanations that made me understand the monty hall problem much better. great, concise video

I've seen this explained so may times and it is still mind boggling, great explanation though :)

You should solve this problem with the probability of the host. When you first pick door A which has the car (lucky, 1/3 chance happening), then host can choose to open randomly Door B or Door C (1/3 chance happening) When you first pick Door A (which has no car, 2/3 chance happening), then the host has to open the Door B and avoid Door C (assuming that Door C has the car). That make Door C has 2/3 chance has the car. And you should switch to have 2/3 chance to win.

Think of it like this. You had 1/3 chance of choosing the car at the beginning, meaning there was a greater chance (2/3 chance) it was somewhere else. When the host opened the door with a goat behind there it that 2/3 chance still exists but it’s now behind just one door. That’s why you should always switch. It’s not a guarantee you’ll win but 2/3 of the time you will, so your odds are better

This problem has been consuming me for a while thank you for explaining

first time you watch it...wtf second time to watch it....OOOOH

Here's another way to think about it which I found interesting: you pick door number 1, and the host offers you a chance to keep with door number 1 and open it, or to switch to both doors numbers 2 and 3 and open BOTH. Now, obviously you will switch to open both and will have a two thirds chance of winning. Now in our case, the same principal applies. You choose door number 1, giving the probability of the prize being behind doors number 2 or 3 to be 2/3. Monty then opens one of the doors 2 or 3, which contains a goat. Now how can eliminating a door to choose from ( an option ), decrease the probability from 2/3 to 1/2? By removing an outcome in which we lose, how could that negatively effect the probability of us winning? Hence the probability of winning by choosing the non originally picked, non opened door concentrates to 2/3.

@ShermanHempler

Жыл бұрын

Ok… this is incredibly underrated. This is an absolutely genius way to help wrap the mind around this.

@kirilhoholko8970

Жыл бұрын

This explanation is better than the video, so underrated

@itadoriyuuji752

Жыл бұрын

Seriously explained it to me better than the video. Kudos to you bud.

YOOO THE LITTLE CHART THING AT THE END HELPED SO MUCH.

I want a sad little goat I would take it home Make it a happy little goat Bgf

@Vikasslytherine

8 жыл бұрын

+Matilde Neto Arabs had been doing this for centuries.

@digitalmonster6049

7 жыл бұрын

+Vikas Dhyani 😂😂😂😂😂

@deinemuddamithut

7 жыл бұрын

just the right height, no bucket required

For any number of doors n, the player’s chosen door has odds of 1/n, and Monty’s door represents the BEST of the other (n-1) doors. So Monty’s door has odds (n-1)/n. The greater the number n, the longer the player’s odds, and the better Monty’s odds.

Thank you so much for explaining this! This is the best video I have found on the monty hall problem!! Thanks so much!!

Basically the reason this is such a popular "gotcha", is because most people don't think about or realize they key factor - that the host knows where the prize is. If there's no host, just three doors, and you pick one, and then open a second door at random (which turns out to not have the prize) - then it would be true 50/50 because both are just as likely to contain the prize.

@miaryaigne6379

Жыл бұрын

This isn't accurate - the puzzle works just fine even if the host has no idea where the car is, because it's only analyzing your chances of success when a goat is revealed. Any hypothetical scenario where the host opened a door and the car was behind it would be thrown out because it's not part of what we're looking at. If you pick one of the doors, then the host randomly opens another and reveals a goat, there's still a 66% chance that the third door has the car behind it.

@RonaldABG

Жыл бұрын

@@miaryaigne6379 That is not correct. You are probably thinking something like the scenarios in which the host reveals the car are additional to the original 66% in which the player starts picking wrong and then wins by switching. But they are not additional, those cases are took from those 66%, so when you eliminate them you reduce the total games that you will be able to win by switching. This is better seen in the long run. If you played 900 times, you expect to start picking about 300 times the car and 600 times a goat. Now, if the host makes a random revelation, then the possible cases are: 1) In all the 300 games that you have the car in your door he will reveal a goat, as his two available doors have two goats. You win by staying. 2) In 300 of the games that you have a goat in your door he will manage to reveal the other goat. You win by switching. 3) In 300 of the games that you have a goat in your door he will accidentally reveal the car and so the game will end. So, if he happens to reveal a goat, you could only be in case 1) or in case 2), that constitute a subset of 600 games, from which you win by each strategy in 300 of them (1/2). This is different to the host always revealing a goat and offering the switch, allowing you to win by switching in all the 600 games that you started picking a goat. And if there are still doubts, take it to the extreme: imagine another condition in which he knows the locations but only reveals a goat when the player has picked the car, because his intention is that the player switches and so he loses. In all the other situations he forces the game to end inmediately. So, if we only look the cases when a goat is revealed, it is obvious that the car is 100% likely to be behind your door; it is impossible to win by switching in that game.

the deck of cards is the best explanation ever

I can't drive yet, can I have BOTH goats? I guess I could sell the car too...

@Bleacher22

10 жыл бұрын

Or you can ride on both goats. :)

@candybar379

10 жыл бұрын

Domantas Grazulevicius That.Is.GENUIS!

@Mark_Grand

10 жыл бұрын

Lol

This took me a while to wrap my head around it but it finally makes sense now.

BRO IVE WATCHED LIKE 10 VIDEOS EXPLAINING THIS AND I FINALLY GET IT

I would still love to see someone who, after door Nr.2 has been opened to show a goat, says: "I'll change my choice to door Nr.2!"

Short answer is that your first choice is more likely to be wrong. Which makes your second chance twice as likely to be right

Best 3 ways of explaining Monty Hall I've seen. The Ace in the deck of cards is a great way logically understanding it The A/B scenarios where staying makes you win 1/3 and switching makes you win 2/3 is also a good way of re-wording the problem to understand the probability And finally the expansion of each scenario showing that switching is 6/9 is clear as water Nice video!

Okay that deck of cards explanation made it so much clearer

what if I want a goat?

@TedManney

8 жыл бұрын

+Teresa Zhang Stick with your original pick, of course. There's a 2/3 chance that it was a goat and nothing happens during the course of the game to change that.

@XaxtonRevolution2

8 жыл бұрын

+Teresa Zhang Then you should still switch because you have to pay taxes on -the prize that you win,- and if you win the car, you can sell it and pay the taxes on it, and then you'll have enough money to buy a goat, and you get to choose whatever goat you want out of way more than 2.

@teresazhang6915

8 жыл бұрын

+Xaxton Revolution that didn't make much sense but ok 🐐

@shadow110

8 жыл бұрын

Sell the car and buy more goats.

@XaxtonRevolution2

8 жыл бұрын

OwlVision Exactly

The host never picks a winning door, so your odds of winning change in the second round, and aren’t random. You’ll only lose 1/3 of the time if always switching, whereas you lose 2/3 of the time if you never switch. The math changes in round 2 because the host doesn’t choose at random; if they did choose at random, it wouldn’t matter whether or not you switched in round 2. The intuitive math ignores the host’s knowledge (and cheat) of outcomes.

@jakejones5736

4 ай бұрын

"if they did choose at random, it wouldn’t matter whether or not you switched in round 2." Not so. Doesn't matte HOW the goat is selected. Only that it is selected.

@sdubgaming

4 ай бұрын

@@jakejones5736 Fair point!

@max5250

4 ай бұрын

@@jakejones5736 "Not so. Doesn't matte HOW the goat is selected. Only that it is selected." Wrong. The only way of goat being selected (and car not being revealed) is if choice is not random.

@jakejones5736

4 ай бұрын

@@max5250 When the contestant's door contains the car, please explain how (as you have proclaimed) a goat will NOT be randomly revealed.

@max5250

4 ай бұрын

@@jakejones5736 Only when the contestant’s door holds a car, host can randomly reveal one of two goats, but that happen with only 33.3% chance. Most of the time, player will pick one of two goats, and the host will have only one door with a goat to open, and if he did open one of two closed doors randomly, he would reveal a goat with 50% chance, that is, he would reveal the door with a goat with total of 33.3% chance (the other two 33.3% chances relate to situations where a car is behind the other closed door, and where a car is behind the door player picked, respectively).

i like the way you explain the result and way you got there in a few ways brings you a bigger audience :)

omg this is the best explanation for the monty hall problem i have come across yet, THANKS :D

If I chose goat do I get to keep it?

@bryan4490

9 жыл бұрын

Aaaaah :(

@LillianRZP

9 жыл бұрын

***** I thought that you could, but no one takes it xD

@elyasheve

4 жыл бұрын

Yea.

This is how I understand it: it is more likely that you pick the wrong door the first time, because 2/3 of the doors are wrong. So, if they show you the other wrong door it is still *more likely* that the first door you picked is a wrong door therefor the third door is *more likely* to be the right door.

Thank you bro, this was actually really helpful.

This is a great video, the Monty Hall problem is really hard to wrap your head around, so I had to watch it a few times before I got it.

This just blew my mind

holy shit! that equation @ 2:07 looks like it came from a alien mothership!!!

@LuisPereira-bn8jq

10 жыл бұрын

The equation is nothing but an absurdly trivial instance of what simpletons like calling Bayes' "theorem". C, H and S denote, respectively, the "door with the car", "door guessed at first" and "door that was shown" random variables. But hey, then again maybe I am an alien, because I do indeed feel embarrassed to belong to a species that so readily parades it's mathematical ignorance as a badge of honor.

@PANTYEATR1

10 жыл бұрын

Luis Pereira I used to be great at math until I ran into one bad teacher, that's when I earned my mathematical ignorance badge. don't judge me lol.

@giemelregis00

10 жыл бұрын

Luis Pereira Alieeens :3

@charliekew1757

10 жыл бұрын

Luis Pereira Lol wut?

This was so insightful

The best explanation of the Monty Hall Problem on the internet!

The best way to visualize this math problem is by raising 3 fingers, imagine 1 is correct and 2 are wrong, if you choose one of the wrong fingers you would always end up on the winning finger and if you choose the winning finger you end up with the losing one, so the probability is 2/3 to win the car.

@seignee

Жыл бұрын

holy shit i get it. lets assume you always switch doors at the end. if your original choice was wrong, youll always end up with the right door. if your original choice was right, you'll always end up on the wrong door. in the beginning, its more likely that you picked wrong, because there are 2 wrong choices and only 1 right choice. meaning, since its more likely you picked wrong choice then its more likely you'll get the correct door at the end, because switching always gets the opposite result of what you originally chose.

I think I'm finally convinced. If you do the card experiment 100 times, and if the last two cards really had the same probability (a 50-50 chance) of being the Ace of Spades, then you would would have chosen the right card to begin with about 50 times. The illogic of choosing the right card out of 52 cards half the time is obvious to me.

@max5250

2 жыл бұрын

Don't try to convince yourself, try to understand. Host always have twice the players door, do his odds are twice as better.

@YouTubeallowedmynametobestolen

2 жыл бұрын

@@max5250 In trying to understand it, I became convinced. Also, sometimes trying to convince yourself of both sides of an issue--first one, then the other--is the best way to understand it. Also the best way to approach it with an open mind; also the best way to come to the correct conclusion.

@klaus7443

2 жыл бұрын

@@KZreadallowedmynametobestolen What is it that you are convinced of?

@YouTubeallowedmynametobestolen

2 жыл бұрын

@@klaus7443 That there is an advantage to changing the door you want.

@klaus7443

2 жыл бұрын

@@KZreadallowedmynametobestolen ...okay...I was the confused cat!

+Kevin "Your card would actually have a 50/52 chance since there are still two cards facing downward" but only one of them can be the Ace of Spades; the other makes up one of the other 51. Hence 1/52 plus 51/52 = 1 (the total sum of probabilities in a sample space always being 1).

That deck of cards analogy really helped me understand

I love that paradoxon ^^

@whiteninjaplus5

10 жыл бұрын

This sentence is false.

@Tomatenmark13579

10 жыл бұрын

*Head explodes*

I can't lie, I'm still confused.

@kulebrero

Жыл бұрын

When you first pick a door, you have only a 1 in 3 chance of being right. The host opens a door on purpose that is wrong. So your best chance is to assume you were wrong to begin with and now the host has shown you the other wrong door, so the unopened door is likely to be the winning door. Put another way, 33% of the time you’ll be right, 66% you’ll be wrong. One chance you guessed the right door and two chances that you guessed the wrong door. You have no way of knowing if your first guess is right or wrong. All you know is that statistically you have a bigger chance of being wrong than of being right the first time. Therefore, your best chance to win is to pick one door and expect it was the wrong door. Let the host show you the other wrong door, and switch your answer to the third door.

Finally a Answer too that question i have been waiting years to find the answer by seaching and reading but this video was i needed :3

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.

I tried understanding this but I just can't do it lol

@nosirrahx

9 жыл бұрын

Here is another way to look at it. Lets play a different game. In this one you can pick a door and stick with it or you can pick the other 2 doors instead. In this case switching to the other 2 doors if the obvious choice because you are doubling your odds. Now for why this matter. Why would it matter if when you switch I open one of the doors for you? It obviously doesn't. This is why switching is always the right choice. You get to have 2 open doors, the host just opens one of them for you.

@SillyGoose2024

8 жыл бұрын

+nosirrahx this made absolutely no sense whatsoever, and further confusing . Sorry,

@nosirrahx

8 жыл бұрын

uannoyme74 It all comes down to avoiding your first choice which always wins 1/3 times. If 1 door has a 1/3 chance of winning then 2 doors have a 2/3 chance of winning. When the host opens a door for you and that door by the rules of the game always is a loosing door then the final door has a 2/3 chance of winning because it makes no difference that the host opens one of those 2 doors for you, you still got to see behind 2 doors.

@SillyGoose2024

8 жыл бұрын

nosirrahx yes, i understand that but when the host offers the contestant the opportunity to stay with his original selection or change to the remaining door, he is offering him a binary option.....one or the other. that's the *NEW PUZZLE* , and this new puzzle is *only* introduced AFTER the host has acknowledged two things: a) the second door doesnt have the prize b) the first door, which is the contestant's original selection, may or may not have the prize.

@nosirrahx

8 жыл бұрын

uannoyme74 Think of this with 1 million doors. You pick 1 door. You then have the option to stick with that 1 door or let the host open 999,998 doors that are not the winner, do you really think that your door magically becomes right 50% of the time? There is no new puzzle. Your first choice is correct 1/3 times and that never changes, unless you change doors. 1-1/3 is 2/3 and there is no way to avoid this math. You can try this out yourself BTW. Switching always results in winning 2/3 of the time.

No, it's impossible. No matter what door you choose it will always be a goat because some selfish person decided that you'll just "think" you have a chance at winning.

@thenuclearscientist4959

9 жыл бұрын

TRDOAndyRocks Lol. You're saying maybe all the doors have goats? Even if 1 had a car, what kind of game show is this?

How it clicked for me is that it all hinges on the host removing a wrong answer. He doesn’t randomly remove a door, he removes one of the wrong ones. He’s not allowed to remove your door no matter what you selected.

I’ve know about this paradox for a while, I still don’t understand it, but I can finally accept it as fact after watching this video

"What door?"

Aww... u didnt win the car u won a goat, YES :D

This the first video to make it make sense! Thank you

I couldn't understand this problem when my teacher explained it to the class a few years back. But this actually makes a lot more sense now.

I haven't taken statistics in a while, but shouldn't you just multiply the 2 probabilities together? P1 = 1/3 P2 = 1/2 P = 1/6 The chance of you choosing correctly, regardless of whether you switch or not, should be 17% (or 1 in 6 times).

@howardbaxter2514

9 жыл бұрын

No. You are assuming they are independent of one another. They are dependent of one another.

@ravekid23

9 жыл бұрын

That shouldn't matter. For example the odds of pulling a spade on the first card would be 13/52. The odds of pulling another spade would be 12/52. Multiplying them together the chance of pulling 2 in a row would be about 6%.

@HumptyDumptyOakland

9 жыл бұрын

終わり Perhaps you should redo some of your probability classes, the answer isn't 1/6 as the video explained.

@LXNC8

9 жыл бұрын

終わり the odds of choosing the second card will be 12/51 if you are not considering replacement.

@LXNC8

9 жыл бұрын

終わり and these two events are independent of one another coz you have taken into account non replacement thus you have excluded those terms which were in the intersection.

Guys. The EASIEST way to understand this is as follows: The removed door is ONLY a bad door. In the 'problem' ONLY a BAD door is removed. ONLY if it was a RANDOM door removed would you be left with a 50/50 chance. To take it to the extremes as an example: You have to choose 1 out of 1,000,000 doors to win. You pick a door. Your odds of winning is 1/1,000,000. Now, I remove 999,998 BAD doors, leaving only 2 remaining. As he said in the video, the odds that your door is correct is still 1/1,000,000 but the odds that the remaining door is correct is 999,999/1,000,000. What are the odds that you picked the one of a million doors correctly and not that I removed every wrong door leaving the only correct one? What I don't understand is how this is so difficult for other people to figure out.

@elmotareal

10 жыл бұрын

yup, that's the key, everything else is rubbish

@HeateDMaGic

10 жыл бұрын

But since they remove 1 goat, leaving only 2 doors left (1 car and 1 goat) then allowing you to switch, it always comes down to a 50/50 decision. The 1st choice doesn't even matter. It's just there to make you get nervous when you have to make your "REAL" choice.

@elmotareal

10 жыл бұрын

HeateDMaGicGaming the trick is that they know which is the right choice, thus their actions affect probabilities

@LuisPereira-bn8jq

10 жыл бұрын

HeateDMaGicGaming This is simply incorrect. You are falling into precisely the error that the problem is supposed to explain.

@marlan__

10 жыл бұрын

Scenario A) X in Y doors will contain the car. You have a X/Y chance. Scenario B) You choose a door and all other incorrect doors are removed. Probability is (Y/Y - X/Y)

I get the table at the end, but could you explain why your card at 1:13 has a 51/52 chance of being the Ace of Spades, instead of a 1/52 chance like the one I chose?

In a nutshell, choosing a goat door garuntees that you will win if you switch, since the other goat will be eliminated. And you have a 2/3 chance of choosing a goat door in the beginning. Therefore, 2/3 chance of switching being.the correct choice

er why did that second card have a 51/52 chance of being the ace of spades?

@number1w00t

10 жыл бұрын

When you picked the first card, you had a 1/52 chance of it being the winning card (ace of spades). That means you had a 51/52 chance of picking any of the losing cards. So as cards are removed, your original chance of being wrong (51/52) still holds constant. So when there are only two cards left, your pick and the one left in the deck, you still kept that original chance of 1/52 for being correct. That still means you had a 51/52 chance of picking wrong, and since there is only one card left for which to hold that chance, the single remaining card holds that 51/52 chance of being the winning card. Basically your starting odds don't change even as options are removed. A 1/3 chance of winning at the start remains as such.

@TomH999111

10 жыл бұрын

But surely as you remove cards the chance of picking the ace of spades doesn't remain constant?? 1/52 then 1/51 then 1/50 etc..?

@number1w00t

10 жыл бұрын

The cards that are removed aren't random. The game host knows which card is the ace, so will choose to remove cards that they know aren't the ace. The two numbers that remain constant are the 1/52 chance that you picked the ace of spades, and 51/52 chance that you did not pick it.

@douglaspantz

6 жыл бұрын

Let's test that. You ask a man to pick a card from the deck You say, "I'll show you where the ace of spades is." You do this by instead of flipping over the ace, you flip over every other card, leaving the ace being the unflipped over card.

With my luck I'd get a goat

@morgankovac3632

3 жыл бұрын

wow your luck must be great then according to how many people in the comments want a goat

Thanks man! I learned this in grade 6 through the numberphile video and it made no sense. You explained it perfectly!

It's funny how at the end they drew the 2 goats taking little poops on the option to "Stay". :P

About the card thing, if you flip the rest over after choosing the first one, don't the odds go from 1/52 to 50/52 after you choose your own card? Because, there's only 2 cards left, and you know none of the flipped up 50 are the ace of spades. If you purposely leave the ace turned down as the last card, probability has no effect, as it would be 100% certain, since you chose it. Am I incorrect? or both the cards now have a 1/2 chance of being the ace of spades

@HumptyDumptyOakland

9 жыл бұрын

You are incorrect. The remaining card not turned over has a 51/52 chance of being the Ace, your 1st pick still has a 1/52 chance. Get a pack of cards and try it yourself,

@JMan360

9 жыл бұрын

Why don't you try it out for yourself

@Fearcely

9 жыл бұрын

HumptyDumptyOakland but if the cards are turned over, and none but 2 are shown to be the ace, don't the odds change because only 1/2 which are left can possibly be the ace.

@HumptyDumptyOakland

9 жыл бұрын

Jesse Lopez Get a pack of cards and try it yourself. See how often the Ace is the card you picked initially and how often it's the card left over after you've discarded 50 of the remaining 51 cards.

@Fearcely

9 жыл бұрын

HumptyDumptyOakland ok dad

Heres a question, why do humans get "annoyed"? I understand when something hurts or is uncomfortable we dont like it but why do we get annoyed for no reason or for something someone else always does that isnt necessarily offensive?!?!?

@ethanjohnston8194

6 жыл бұрын

Dustin DeBolt we like to be right or think we are right

Thank you for explaining it with a deck of cards. By increasing the scale, this made a lot more sense.

So Kevin was right...

@pinkparrot8

13 күн бұрын

Who's Kevin....

Survivor 41 brought me here, I had to check the odds

This is so intriguing

I literally watched this 5 times and I still don't understand it

@amaluralure7205

7 жыл бұрын

cos you are dannaGOAT obviosly!

@DannaGoat

7 жыл бұрын

+Amalur Alure I don't get it

@DannaGoat

7 жыл бұрын

+DannaGoat I get the initial idea but I don't get the end

@DannaGoat

7 жыл бұрын

+Amalur Alure I just re watched it and I get it now, I don't know why it took so long lmfao

@tamicawiley2022

7 жыл бұрын

You'll understand soon keep trying and never give up

i'd rather have the goat...

This doesn't seem like a paradox to me when you understand the proposition that the host picks the second door knowing that a car isn't behind it. So basically it's just a word play puzzle or something....not a paradox.

I saw an explanation in an other vid that was quite easy to understand: The door you initially pick has a 1/3 chance to have the price, the remaining 2 doors have a combined chance of 2/3. The host eliminates one of them, so the 2/3 chance concentrates on one door.

I completely understand this. But it still seems strange that the chances are not 50/50 =P

My simple explanation for the monty hall problem is that well, lets say on the first round, you pick a door, one that has a goat (2/3 chance). If you swap, assuming that you have a goat, you automatically win. Its impossible to pick a goat instead of a car if you pick the goat the first round, then swap. Since there is a 2/3 chance of picking a goat the first round, swapping automatically keeps that 2/3 chance. It may sound complex in text, and I can relate to this. It took me a while to understand, but I realized that this explanation was true. Swapping gives you a 2/3 chance to win a car in the end. Try drawing out a picture of 3 doors, label 2 doors goat, and 1 door a car. Pick a goat door, then reveal the other goat door. Then, swap to the car, and since picking a goat first is 2/3 chance and you win a car everytime if you swap after picking a goat, you will see that you will always get redirected to the car. Now, pick the car, reveal 1 goat door, then swap. Since choosing a car in the first round gives you a 1/3 chance, that gives you a 1/3 chance to win a goat when swapping. Like I said, all of what I said here may seem complex at first, and hard to explain, but once you get it, you will understand. x)

*I have 1/2 a brain cell. It takes at least 1 brain cell to understand this video. I am short 2/3 of a brain cell*