[ASMR] The Monty Hall Problem

[@ThatOneGuy-999-]

18:19 was my moment of realisation… good explanation. Before the video I had no idea how the scenario worked, although I had heard of it before

[@onesim6662]

A really cool trick and really well explained. Love these little mathmatical puzzles

[@ASMRMaths]

Thanks so much! Love this puzzle

[@Phill.__.]

Loved the very visual explanations, it gives a different level of understanding

[@ASMRMaths]

Thank you! Glad you liked them

[@tvincentmkh1976]

guarantee yourself a smile when @DidoASMR uploads🙂

[@ASMRMaths]

Guarantee myself a smile when I see comments like this 😊

[@hampt3r]

wrong channel

[@Scott_McKin]

@@hampt3rit’s the same person why does it matter so much

[@158-i6z]

The easiest way to understand this is to realize that you have a 66% chance of picking a goat door in the first place, and when you remove the remaining goat door, there's still a 66% that you picked a goat door, but now there's only two doors left. So it's 66% chance that the door you're on is a goat door, so you should switch. The whole reason this is confusing is because we're used to a random elimination process. I.e. if the host removes a random door without telling us that it was a goat door that he removed. If that was the case, then it would make no difference to switch or stay.

[@ryan4121]

Maybe this is one is just over my head, but I still wasn't convinced the chances were anything other than 50/50 after one option is eliminated haha. But either way, excellent video per usual!

[@krazzed3243]

What would it take to convince you?

[@submaryne3518]

I made a program in java, to replicate this scenario 100,000 times, 50,000 times where i swap doors, and the other 50,000 times where i dont swap doors. It's true. swapping doors does increase the chance of you getting the prize. program did it in under 2 seconds btw

[@Wopedomer]

@@submaryne3518but why? Shouldn’t it be an equal chance of randomly picking it the first time vs picking the other door they give you?

[@fahrenheit2101]

I cant blame you - it feels very counterintuitive. However, the 2 possible scenarios, while equivalent in terms of the remaining 2 items, are different in their probability of arising. You're twice as likely to have messed up your first guess, so after the goat reveal, you're twice as likely to be currently at a goat door than a car door. Yes, no matter what, there is a car behind one door, and a goat behind the other, but you're just more likely to be on the goat after the first guess.

[@ryan4121]

These are good responses. I feel like I should convinced. Here, fix this thinking. I feel like it’s equivalent to just having two doors. If you know it’s not behind Door C, it’s only behind Door A or B assuming the question is posed to you every time you are giving the three door selection and make a choic, either right or wrong initially. So you have door A, or door B. One is right. One is wrong. That’s 50/50?

[@TheVipeerr]

So relaxing. A camera perspective video from the past.

[@Hollygrrr32]

Monty hall deniers have an issue of not knowing the difference between possibility and probability, yes it’s possible that I could walk home and find a million dollars on my bed and it’s possible I might not, just because there’s two choices it doesn’t mean it’s a 50/50

[@UpNextBeatz]

annnd now to you WAYNE BRADY haha

[@Kaarija1]

Love the video, but I noticed one problem. Deal or No Deal is not an example of the Monty Hall Problem. This is because the whole point of the problem is relying on the fact that the host knows they won’t reveal a car. In Deal or No Deal, however, you are the one choosing, and therefore it is just by luck that you made it to the last two boxes without seeing the 250k. In that case it is just 50/50. If I made a mistake (I’m 13 so I probably did lol) , I would love to know where I went wrong as I am starting to learn more about probability. Good night everybody 💤

[@dgmarie]

Don't doubt yourself too much because of your age, theres a lot of really smart 13 year olds out there. I think you are completely right here, the logic behind the problem depends on the fact that the door opened will always have a goat behind it, which means that there is a 2/3 chance the other door has a car and a 1/3 chance the door you picked is the car. Ive never seen deal or no deal so im not completely sure, but assuming the boxes are opened at random you are definitely right

[@rhysscale912]

If I had to guess I would say that the £250,000 starts as the car and if it stays in the game until the final two boxes then great. However, if the £250,000 is revealed and therefore removed from the game I'd imagine the next highest amount (£100,000 I think) would replace it and become the new car. I might be wrong but that makes sense to me as I don't think the car has to only be the jackpot but it can be whatever you decide is the best prize to win, of course in deal or no deal this would just be the largest amount of money still left in the game.

[@itsprinklesasmr]

This is so interesting! I've seen this used in game shows but could never fully wrap my head around it. Thank you Dido 😊

[@thechamp-vp4jj]

😂 😂 Wasupp sprinkles, what u doing

[@ASMRMaths]

Thank you so much for stopping by sprinkles! Hope you liked the explanations 😊

[@itsprinklesasmr]

@@thechamp-vp4jj hiii 👋

[@itsprinklesasmr]

@@ASMRMaths explained perfectly! keep up the math videos 😋🤯

[@vuyokazindaleni4624]

Hey Dido ! may you please cover more linear algebra topics ❤ I've been binge watching your videos almost every night since I found your channel (it's that good!!) ... all the love from south africa

[@chongwong8202]

SIMPLE TERMS: You have a 1/3 chance of choosing the correct door. That means you have a 2/3 chance you DID NOT choose the correct door. Because of this, there is a 2/3 chance that one of the other two doors has the car. When one is proven to be a goat, the probability remains the same (there is still a 1/3 chance you chose the correct door originally and a 2/3 chance you didn’t). If you switch doors, you are virtually picking two doors, as you are choosing the 2/3 chance rather than the 1/3 chance.

[@tsu177]

the way i understand it is that changing doors is effectively the same as being able to choose 2 doors from the start

[@Victeur]

Im so proud of me!!! I found the solution by my own when you explained the rules

[@Victeur]

Well I guess that’s it, I’ll continue to watch the video but here’s what I guess it is : he always show a door with a goat in it basically you had 1/3 chance to have the car inside ur door, so now that you know that there is a door you didn’t choses with the goat, then there were 2/3 chance of picking the wrong door and yes I realized I can’t explain it in a KZbin comment it would be too long I’ll just keep watching the vid and tell if I was right

[@Victeur]

Cool i was right

[@spicyramennoodles9202]

Question: In DOND, you aren't guaranteed that the 250k will end up as part of the two boxes at the end -- rarely does it ever. Therefore, doesn't this mean that the principle of Monty Hall is only dependent on situations in which there is 100% chance of getting to that situation? (i.e. if the producer always guarantees the car/jackpot within the last two unopened boxes?)

[@rileystevens9714]

Exactly my thinking as well

[@FedeDragon_]

yes I also think in DOND it doesn't work, since when you eliminate the boxes you can actually eliminate the 250k, whilst Monti Hall deliberately chooses a door where there's a Goat . So I believe it's 50% in DOND

[@mobo5845]

yo this asmr maths guy looks and sounds so much like dido asmr 🤔 hope the two legends will collab one day 🙏

[@Jetstream_Sam]

I read that name very wrong

[@LiamLeao-e2e]

Because they are the same person just a different channel

[@JohnoFromNZ]

@@LiamLeao-e2e Nuh uh

[@IsaacPerez-k2s]

21 black Jack film had a scene where they explained this problem. Its so interesting. Thank you Dido!

[@George_vv]

I'm glad I chose 3 at the beginning I really wanted a goat.

[@countseelore]

I was thinking about the deal or no deal example before you mentioned it but it doesn't really follow the Monty Hall Problem. With the original example, the host actively knew which doors had what behind it, and will actively remove the goat & you actively know the likelihood of picking a goat is double that of picking the car so it's logical to bet against it When it comes to the deal or no deal example, you have equal likelihood of picking either the £250,000 or 1p. Whilst the likelihood of not picking the £250,000 would be 23/24, it would be the same probability as not picking the 1p so there's no difference in betting in favour of your original pick or betting against it

[@HannahWhite_4]

No way at first I actually guessed out the 100 cars that that one had the car

[@thearith724]

I think you should try doing some trigonometry exercise next and love ya videos dude

[@I_do_Random_Stuffs]

Best car ever but I would just take the goats

[@ASMRMaths]

😂

[@fahrenheit2101]

Haha I feel like you've probably offered a nice explanation but I keep falling asleep before I can hear it...

[@merabooo]

i love probability so this was very entertaining and relaxing

[@massmarsilii]

i used to always watch let’s make a deal and always say when there was 3 doors i had a 50/50 chance since they show me one

[@ASMRMaths]

Well… puzzle debunked!

[@SheckQT]

People always forget that in probability the most important thing is the time line so the probability of u winning will switch from 1/3 for all to 1/2 for both

[@klaus7443]

People like you forget that the most important thing is that it can't be 1/2 for both unless the host revealed a goat when that door had a 1/3 chance of having the car behind it....which it didn't.

[@annavalle9409]

When you pick the fisrt choice (one door), you know that at least one of the other two is a "Loose". Am I right? Nevertheless, if you were asked to change your door (one) with the other two (both) I think you would accept. Am I right? It doesn't matter if the host shows you that one of the two doors is a "Loose", you already knew it. The opened "Loose" door can make you think the final choice is between two doors (50% - 50%). The real final choice is between one door (out of three) and two doors (out of three), one of which is opened.

[@herotbe]

Hey dido ! got a queston 10:10 how do you know if you switch from a goat you will 100% receive a car ? isnt there 2 options once u picked one door so its just a 50/50 regardless ?

[@ASMRMaths]

So this perspective on the right hand side of the comparison table is looking at if you were to switch every time you’re asked the question “stick or switch?”. Therefore, if you originally pick a goat, when the other goat is revealed, switching will win you a car 100% of the time. Whereas if you originally pick the car and I reveal a goat, switching will lose. So 2/3 times, switching will win you the car. Hope this makes sense!

[@ASMRMaths]

I should clarify, the reason you win 2/3 times when switching is because there are 2 goats. So if you KNEW you picked a goat, I reveal a goat, switching wins 100% of the time

[@supernevs0766]

Nice movie reference at the beginning.

[@masonz9213]

Te first one was basically the thing in seasons 41 and 42 of survivor

[@ItsYaGirlNix]

I mean a goat ain’t a bad prize.. is it a baby goat? I mean.. goat milk.. now I’ve got a business 🤔

[@Meat_Scepter]

I got it after you modeled 100 doors

[@Gor4ngi]

Could you cover the birthday paradox?

[@thexspirix]

My friends at school told me about this problem and I did not understand it at all. In my mind it would always be 1/2 chance after a door has been revealed. I know realise how I was terribly wrong 😅

[@conmor_]

So, you stick. Win the goat. Milk the goat, sell the milk. Make enough money to buy another goat. Breed goats. Milk goats. Have a lot of goats, sell a lot of goat products. Become multi-millionare CEO of massive goat company. Get car and have money for like. Yw.

[@fahrenheit2101]

Well, theres still a 1/3 chance that sticking gives you the car... Which would be alright, but not as great as your lofty goals.

[@SC4RCR0W]

I guessed the correct door initially for the 100 door scenario 1% probability😮

[@alana-bananaa]

Why would I try so hard to get a door with a goat behind it? 😭

[@courtneymichelle5746]

I PICKED DOOR 1 TO START :D

[@philipgallo8779]

When you first picked you had a 33.3% chance of being right. He eliminates a door he knows is wrong so it leaves you with 2 options the door you picked with that 33% possibility or switching and now knowing that 66.6% lies is one of the two remaining doors he eliminates one so chances now of that 66.6% go to the one remaining door. Your brain sees two doors left and thinks 50/50 but when you originally picked your door your odds were 33.3% those odds for ur first door remain the same after he eliminated the wrong door but increased that 66.6% from the two doors to the only other one remaining. Don’t look at the 2 doors as a new separate problem where your odds changed to 50/50 cause it never changed the fact you originally picked with 33.3 % odds

[@lotteroelandt]

Important question: If I end up winning a goat, do I get to keep it? Because goats are cool ❤🐐

[@ASMRMaths]

Win win regardless then for you! You can keep the goat 🐐

[@AlexanderFischer-k1p]

i finally got it, even before the explanation. there is only 1/3 chance that u chose a car in the first choice and a 2/3 chance u picked a goat. damn its not thaaat hard

[@klaus7443]

That is not the reason switching doubles the chances of winning. You would have a 2/3 chance of picking a goat even if the host didn't know where everything is but no advantage in switching if he revealed a goat.

[@insignificantfool8592]

"I as the host know what is behind three doors, SO..." Why "so"? Does the revealing of the goat door follow from what is said before? No. So, the assumption that the host will always offer the switch is wrong. So, switching does not increase odds.

[@selina9260]

Just found your channel! Love these kind of videos!

[@aardvarklettuce]

My uncle taught me this once it is mad

[@DomenicoPezzullo-ib9bg]

what's the app you've done this on

[@stick3908]

What if I’d prefer the goat?

[@lotteroelandt]

That's what I'm saying! This is a win-win situation either way

[@ASMRMaths]

Then be sure you stick when asked “stick or switch!”

[@lucent6894]

The probability of finding the price is itself dependent on two probabilities/conditions.. 1:- probability of switching 2:-choice of Monty Since both probabilities are independent on each other ...thus there is equally likely event to happen .. which means probability of finding the price is 50% not 66%

[@klaus7443]

Your math is wrong. It's 50% if the host was opening a door that has a 1/3 chance of having the car behind it but it revealed a goat instead.

[@appeleper4436]

Technically yes, but in theory everything in life is 50/50 either you have the goat or you don't. :)

[@Mikhail715]

Can you do a video on sine waves?

[@FedeDragon_]

not sure it'll work in asmr but you should totally watch animation vs maths by Alan Becker

[@YS-rk1ck]

We can think it easier by imagning 100doors !!Oh!

[@thechamp-vp4jj]

Dido Thank very much for this videos, but Can you please do a collab with Jojo asmr😵😵

[@nikeprojock]

sounds like witchcraft to me

[@Marlin-ez]

I mean, goat is cool as well...

[@Mason13245]

I'll take the goat please

[@sharnamraj8712]

BOOONNNNEEE (please tell me your guys got the reference)

[@stuartcarlyle2185]

Detective Diaz how dare you i am your commanding officer, BONE, BONNEEE gotta love 99

[@Ineverexisted38]

Im to tried to sleep

[@freshzoother7533]

what if i just want the goat?

[@voidscollide7009]

id rather have the goat

[@ЛилияЯмилевна]

//999 flashback//

[@purpleunicorn87]

Literally just smell them. Smell the air coming from the other side. I promise you'll know which is which.

[@periculumpluviae]

After being shown the goat, you’ll have a 1/2 chance to get the car by staying, and you’ll have a 1/2 chance to get the car by switching, because you can’t stick with the door that has been eliminated

[@RonaldABG]

That does not make each remaining door equally likely to have the car. Remember that the host does not act randomly, but instead he already knows the location of the car and is not allowed to reveal it, so he does not fail in leaving it hidden in the other door that keeps closed in case the player has not managed to pick it at first. But as the player only starts picking the car door 1 out of 3 times on average, the host is who, using his knowledge, deliberately leaves it in the other door that avoids to open the remaining 2 out of 3 times.

[@daffodilyellow2430]

I couldn't follow this at all. You should be able to explain it simpler than this??

[@fahrenheit2101]

I think it was fine. The deal or no deal bit was a misunderstanding of the rules, but the rest was ok. In short, you probably picked a goat, so best to switch. He just illustrated that in a few ways.

[@NotEpimethean]

can i sell the car to buy a goat?

[@jimmytipsTV]

So no matter what happens it’s always down to a 50/50! You pick any door and you will always be told which one it’s not 😂 100 doors you get told which 98 are empty so your down to 50/50 lol makes no sense

[@klaus7443]

Wrong. No matter what happens you can always stay with the prize you originally picked or switch to a door with the opposite prize. So the host didn't have to open a door to reveal a goat at all, he could have simply asked if you want to switch to the opposite prize when you first picked a door.

[@fahrenheit2101]

My 1 sentence explanation of MH is "You probably fucked up the first guess" If you can accept that, the rest follows naturally.

[@jacobbridges9075]

@@fahrenheit2101why is it likely I fucked up the first guess? I had a 1/3 chance the first time and the second time my odds are 50% with either of the remaining

[@fahrenheit2101]

@@jacobbridges9075 lets go back to that first sentence Your odds were 1/3 of picking the car. You were *less likely* to pick the car. Therefore, *after* picking a door, it's *twice* as likely that door was a goat. If you agree with all that, the rest really should be obvious. If you keep disagreeing, do note that this is very easy to experimentally prove, i.e. you're demonstrably incorrect - all I'm doing is making an effort to help you see why I suppose I should debunk your logic directly too, to be safe Yes, there are always 2 doors at the end, and one is always the goat, and the other is always a car. That gives you 2 situations. Either you're on the goat, or the car. You don't realise that you've actually assumed these situations are equally likely to arise, and indeed if they were, it would be 50/50 odds. Yes, in isolation, that final choice is a 50/50, but the added context of the first round makes this no longer the case, as you've received information - specifically, you know as a prior that your current door is probably a goat. Thats all i can be bothered to say.

[@firebreath5587]

Bro stole the first scene from 21