[ASMR] The Monty Hall Problem

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  • @ThatOneGuy-999-
    @ThatOneGuy-999- Год назад +20

    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
    @onesim6662 Год назад +84

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

    • @ASMRMaths
      @ASMRMaths  Год назад +6

      Thanks so much! Love this puzzle

  • @Phill.__.
    @Phill.__. Год назад +47

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

    • @ASMRMaths
      @ASMRMaths  Год назад +2

      Thank you! Glad you liked them

  • @tvincentmkh1976
    @tvincentmkh1976 Год назад +42

    guarantee yourself a smile when @DidoASMR uploads🙂

    • @ASMRMaths
      @ASMRMaths  Год назад +12

      Guarantee myself a smile when I see comments like this 😊

    • @hampt3r
      @hampt3r Год назад +3

      wrong channel

    • @Scott_McKin
      @Scott_McKin Год назад +3

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

  • @ryan4121
    @ryan4121 Год назад +132

    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
      @krazzed3243 Год назад +3

      What would it take to convince you?

    • @submaryne3518
      @submaryne3518 Год назад +27

      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
      @Wopedomer Год назад +9

      @@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
      @fahrenheit2101 Год назад +22

      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
      @ryan4121 Год назад

      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
    @TheVipeerr Год назад +9

    So relaxing. A camera perspective video from the past.

  • @Kaarija1
    @Kaarija1 Год назад +19

    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
      @dgmarie Год назад +5

      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
      @rhysscale912 Год назад

      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.

  • @158-i6z
    @158-i6z Год назад +7

    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.

  • @vuyokazindaleni4624
    @vuyokazindaleni4624 Год назад +10

    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

  • @spicyramennoodles9202
    @spicyramennoodles9202 Год назад +7

    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
      @rileystevens9714 Год назад

      Exactly my thinking as well

    • @FedeDragon_
      @FedeDragon_ Год назад

      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

  • @Hollygrrr32
    @Hollygrrr32 Год назад +9

    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

  • @itsprinklesasmr
    @itsprinklesasmr Год назад +12

    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
      @thechamp-vp4jj Год назад

      😂 😂 Wasupp sprinkles, what u doing

    • @ASMRMaths
      @ASMRMaths  Год назад +3

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

    • @itsprinklesasmr
      @itsprinklesasmr Год назад

      @@thechamp-vp4jj hiii 👋

    • @itsprinklesasmr
      @itsprinklesasmr Год назад +1

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

  • @tsu177
    @tsu177 Год назад +1

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

  • @mobo5845
    @mobo5845 Год назад +7

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

    • @Jetstream_Sam
      @Jetstream_Sam Год назад +1

      I read that name very wrong

    • @LiamLeao-e2e
      @LiamLeao-e2e 3 дня назад

      Because they are the same person just a different channel

  • @chongwong8202
    @chongwong8202 10 месяцев назад +2

    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.

  • @Victeur
    @Victeur Год назад +1

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

    • @Victeur
      @Victeur Год назад

      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 RUclips comment it would be too long I’ll just keep watching the vid and tell if I was right

    • @Victeur
      @Victeur Год назад

      Cool i was right

  • @George_vv
    @George_vv Год назад +3

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

  • @IsaacPerez-k2s
    @IsaacPerez-k2s Год назад

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

  • @countseelore
    @countseelore Год назад +4

    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

  • @thearith724
    @thearith724 Год назад +1

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

  • @I_do_Random_Stuffs
    @I_do_Random_Stuffs Год назад +3

    Best car ever but I would just take the goats

  • @herotbe
    @herotbe Год назад +5

    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
      @ASMRMaths  Год назад +3

      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
      @ASMRMaths  Год назад +2

      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

  • @conmor_
    @conmor_ Год назад +7

    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
      @fahrenheit2101 Год назад

      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.

  • @masonz9213
    @masonz9213 Год назад

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

  • @DomenicoPezzullo-ib9bg
    @DomenicoPezzullo-ib9bg 2 месяца назад

    what's the app you've done this on

  • @SheckQT
    @SheckQT Год назад

    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
      @klaus7443 Год назад

      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
      @annavalle9409 Год назад

      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.

  • @lotteroelandt
    @lotteroelandt Год назад +5

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

    • @ASMRMaths
      @ASMRMaths  Год назад +5

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

  • @massmarsilii
    @massmarsilii Год назад +4

    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
      @ASMRMaths  Год назад +2

      Well… puzzle debunked!

  • @supernevs0766
    @supernevs0766 Год назад

    Nice movie reference at the beginning.

  • @HannahWhite_4
    @HannahWhite_4 Год назад

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

  • @courtneymichelle5746
    @courtneymichelle5746 Год назад +1

    I PICKED DOOR 1 TO START :D

  • @merabooo
    @merabooo Год назад

    i love probability so this was very entertaining and relaxing

  • @Gor4ngi
    @Gor4ngi 11 месяцев назад

    Could you cover the birthday paradox?

  • @philipgallo8779
    @philipgallo8779 Год назад

    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

  • @fahrenheit2101
    @fahrenheit2101 Год назад

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

  • @thexspirix
    @thexspirix Год назад

    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 😅

  • @stick3908
    @stick3908 Год назад +6

    What if I’d prefer the goat?

    • @lotteroelandt
      @lotteroelandt Год назад +1

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

    • @ASMRMaths
      @ASMRMaths  Год назад +2

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

  • @SC4RCR0W
    @SC4RCR0W Год назад

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

  • @cadynwurm4601
    @cadynwurm4601 9 месяцев назад

    I got it after you modeled 100 doors

  • @alanalouisepennell
    @alanalouisepennell Год назад +1

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

  • @insignificantfool8592
    @insignificantfool8592 3 месяца назад

    "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.

  • @ItsYaGirlNix
    @ItsYaGirlNix Год назад

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

  • @AlexanderFischer-k1p
    @AlexanderFischer-k1p Год назад +3

    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
      @klaus7443 Год назад

      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.

  • @aardvarklettuce
    @aardvarklettuce Год назад

    My uncle taught me this once it is mad

  • @FedeDragon_
    @FedeDragon_ Год назад

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

  • @lucent6894
    @lucent6894 Год назад +4

    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
      @klaus7443 Год назад +1

      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
    @appeleper4436 5 месяцев назад

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

  • @YS-rk1ck
    @YS-rk1ck Год назад

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

  • @nikeprojock
    @nikeprojock Год назад

    sounds like witchcraft to me

  • @Marlin-ez
    @Marlin-ez Год назад

    I mean, goat is cool as well...

  • @selina9260
    @selina9260 Год назад

    Just found your channel! Love these kind of videos!

  • @Mikhail715
    @Mikhail715 Год назад

    Can you do a video on sine waves?

  • @UpNextBeatz
    @UpNextBeatz Год назад

    annnd now to you WAYNE BRADY haha

  • @Mason13245
    @Mason13245 Год назад +1

    I'll take the goat please

  • @sharnamraj8712
    @sharnamraj8712 Год назад +1

    BOOONNNNEEE (please tell me your guys got the reference)

    • @stuartcarlyle2185
      @stuartcarlyle2185 Год назад +1

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

  • @thechamp-vp4jj
    @thechamp-vp4jj Год назад

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

  • @Ineverexisted38
    @Ineverexisted38 Год назад

    Im to tried to sleep

  • @voidscollide7009
    @voidscollide7009 Год назад

    id rather have the goat

  • @freshzoother7533
    @freshzoother7533 Год назад

    what if i just want the goat?

  • @ЛилияЯмилевна
    @ЛилияЯмилевна Год назад

    //999 flashback//

  • @NotEpimethean
    @NotEpimethean Год назад

    can i sell the car to buy a goat?

  • @daffodilyellow2430
    @daffodilyellow2430 Год назад +1

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

    • @fahrenheit2101
      @fahrenheit2101 Год назад

      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.

  • @firebreath5587
    @firebreath5587 Год назад

    Bro stole the first scene from 21

  • @periculumpluviae
    @periculumpluviae Год назад

    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
      @RonaldABG Год назад +1

      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.

  • @jimmytipsTV
    @jimmytipsTV Год назад +1

    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
      @klaus7443 Год назад +1

      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
      @fahrenheit2101 Год назад +2

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

    • @jacobbridges9075
      @jacobbridges9075 Год назад

      @@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
      @fahrenheit2101 Год назад +3

      @@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.

  • @purpleunicorn87
    @purpleunicorn87 Год назад

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