if you don't get this paradox you never will You are faced with a game involving three doors Behind one door is I know why you guys sent this to me by the way because we were talking about this on some other stream where you were telling me if I'm in the Price is Right and I choose door number one and they remove door number three I have to switch my door No the I don't Why do I have to switch my door Is a brand new car and behind the other two are goats The host Monty Hall asks you to choose a door You pick door one Next Monty opens door two revealing one of the goats He offers you the option to switch to door three or remain with your chosen door I'm locking in my god door I'm not changing doors Are you guys changing doors No I think he's trying to get me to switch doors because he's a con man and he wants me to loose So he's going to try and get me to not believe that my door is the right door cuz his ass knows what door the car's behind Should you do the vast majority of people choose to stay for purely psychological reasons Those who attempt a logical response conclude it doesn't matter It's a 50/50 choice After all there are exactly two doors and we have no information about which has a car behind it That's my logic but he's going to tell me I'm wrong for some reason They've removed door two Okay I had a one in three chance of me being right Now I have a one in two Yes it's a new decision to be made because they've removed one of the options but that doesn't mean that my option is less likely the than the other because it's still 50/50 It doesn't become two out of three chance that I win if I switch That's just stupid Or do we In fact the optimal strategy is to switch doubling your odds of winning This is it doesn't double your odds The Monty Hall paradox Despite being a solved problem its solution widely accepted and mathematically proven No it's not How is it mathematically How is it mathematically proven I No I literally can't understand it I literally can't understand it I Dude it's No chat Seriously No shut up Shut up for a second and let me explain There's three door bro I'm about to do this with cups I'm about to do this with cups I'm about to get three [ __ ] cups I'll put a coin under one of them and I can [ __ ] remove one cup And your dumbass switching doesn't [ __ ] make it more likely that now you're picking the coin under the cup Do it Hold up I'm going to shut off my camera and move the [ __ ] cups around I'm going to poll chat Pick a cup Okay And then I'll remove one of the other cups and you can choose Okay Ready One two three Pick a cup Pick a cup What cup do you think the tooth floss is under Whatever chat chooses that'll lock in I'll remove a cup and then I'll give you the option of switching It's so even Most people are choosing the middle cup You believe that I did not move the floss That's the logic that most of you are are having because you saw me put it under the second one and you went "He did it He didn't move it." Okay end the end the poll End the poll 40% chose middle 32 right 32 left You guys locked in middle cup Now pull if you switch Do you switch left or right You originally had the right cup Do you want to switch It's 5545 God [ __ ] damn it It's not Okay Yes Okay This is This is [ __ ] This is dumb as hell This is dumb as hell This is dumb as hell Okay Why does that Why does that No Chad listen No Chad listen Okay you guys switched Okay Yes it worked I Okay maybe it worked Okay No now I'm getting it because I had to remove because you chose one of the wrong answers Oh my god I get it I get it I get it now Because if you had chosen the right cup you didn't right If you had chosen the left cup and I had pulled one away Oh my god I get it Okay Wait wait let me explain Let me explain When you pick what door you want there's a twothirds chance you're going to pick the wrong cup And if you pick you're more likely to pick the wrong cup than the right cup And so if you pick the wrong cup they still have to move one of the wrong answers out of the board And because you were statistically more likely to pick the wrong cup that means they got rid of the other wrong cup which means the right cup is the one that you didn't pick I get it remains a source of confusion disbelief and even outrage The typical explanations tend to only confuse the skeptic further In this video I'm going to explain why that is History The Monty Hall paradox gets its name from Monty Hall the host of the 1960s game show Let's Make a Deal contest where you would win a $100 as the [ __ ] grand prize would choose one of three doors knowing a big prize was behind one while the other two hid smaller prizes or sometimes goats The original game wasn't set in stone Monty would occasionally offer cash instead of the option to switch or his decisions might be influenced by what made money safe bro There's a dollar in there for better TV Fast forward to 1990 when Marilyn Voss Savant introduced a simplified version of the scenario in her Ask Marilyn column In her version Monty always reveals a goat and always gives the player the chance to switch The surprising result switching doubles your odds of winning boosting them from 1/3 to 2/3 Get me on the prices right now and I'll switch And then and then watch I'll lose And then that's where I rush the host That's where I go but I tried it with I tried it with tooths That's when the real controversy started Professors mathematicians and skeptics flooded Voss Savant with letters insisting she was wrong Some refused to believe it even when the math clearly showed otherwise At its heart the Monty Hall problem is a clash between intuition and logic When we first hear the setup it's easy to get caught up in the story wondering things like "Is Monty trying to trick me?" or "Can I really trust him?" I would want to take that into account though But you're supposed to look at it in a computer mindset These are natural thoughts but they miss the mark The math behind the problem doesn't care about Monty's intentions or whether you're suspicious of him It's all about simplifying One more Oh my god I can't I want to watch the video the scenario to focus purely on probabilities Stripping away the human element lets us see the numbers for what they are and find a clear answer In real life it might make sense to ask those psychological questions But with this paradox solving the abstract problem gives you the solution You just have to trust the map To do that you need to understand the game strict rules One there are three doors One hides a car and the other two hide goats Two you pick a door Three Monty opens a different door revealing a goat Four you're given the option to switch to the remaining closed door In this version Monty is essentially a robot To make it even clearer we could add a rule 3.1 If Monty can choose between two goats he Wait why am I not getting it [Laughter] again Wait why am I not getting it again Oh my god No it's actually starting to not make sense to me again I'm watching this and I'm like wait no it's still 50/50 Okay no I got to repeat this to myself When you choose the right answer it will always answer somehow the right answer He always picks the lower numbered door or flips a coin Holy [ __ ] It doesn't affect the probabilities It just removes any uncertainty about his actions In the example we started with rule three wasn't spelled out explicitly But the critical piece is that Monty knows where the car is and always opens a door with a goat that isn't yours That's the key to why switching is the better move You Yeah If he opened a random door then it wouldn't matter cuz sometimes he would just reveal the car You'd have to accept these rules to fully understand why the math works 100 doors 99 goats Get the [ __ ] out of here now That's too much Oh is he going to go into different random hypotheticals Talk about Marilyn Vos Savant's 100 doors 99 goats exp All right hold up chat Let me go get 99 red solo cups It's a clever way to make the Monty Hall problem easier to understand by exaggerating the setup By scaling up the scenario the logic behind switching becomes more obvious Or at least that's the idea Here's how it works Imagine you're faced with 100 doors Behind one of them is a brand new car and behind the other 99 are goats Monty Hall asks you to pick a door and you go with door one Door 97 Now Monty begins opening the other doors one by one revealing goats You know it's also another fun fact If you tell somebody to pick a random number they're more bound to pick a prime number that is not divisible because it seems more random behind each He starts with door two and continues all the way to door 100 except for one curious exception He skips over door 29 So now there are two unopened door Door one your original pick and door 29 the one Monty intentionally left closed Monty offers you the chance to switch to door 29 What should you do In that scenario I wouldn't want to switch At this point most people lean towards switching leaving one specific door out of the 99 he opens seem deliberate And intuitively it feels like door 29 must be the better choice And they'd be right Switching is the better move because the odds of winning shift dramatically in your favor Oh that's true It's the same It's the same logic I look at it in the sense of like if I was the host I would try and [ __ ] you over with that mindset But why When you picked door one there was only a one in 100 chance that you chose the car and a 99 out of 100 chance that the car was behind Yeah Either way he has to remove 98 ghosts One of the other doors Monty's actions don't change those initial odds They just redistribute the 99 out of 100 probability across the remaining unopened doors By the time Monty reveals goats behind all but one of those doors all of that probability condenses onto the single unopened door door 29 Switching gives you a 99% chance of winning the car 99% chance of winning the car compared to just 1% if you stick with your original choice But there's a big catch This explanation while powerful isn't perfect It relies on abstract thinking and the ability to generalize insights from one scenario to another Scaling up to 100 doors makes the average of switching feel obvious in this Wait So then in the in the classic game show with Howie Mandel deal or no deal When they when you pick a case in the beginning and you have $1 and a million dollars left you're supposed to switch It's context But then if I did switch and I got a dollar I think I would burn the set to the ground But it requires a mental leap to apply the same logic back to the original three door problem Here's why In the 100 door example the scale is so exaggerated that it's easy to focus on the specific numbers and the unusual setup You're looking at 99 doors being eliminated which makes door 29 stand out as the obvious choice But the principle that's actually at play how probabilities redistribute after Monty reveals the goats applies just as much to the three door version The challenge is helping people see that the math doesn't change no matter how many doors you start with Without making this connection clear the 100 doors 99 goats explanation can feel disconnected or even confusing People might see it as an entirely different problem No it's because they're unable to remove the right door That's all it is They're unable to remove the door that has the prize under it And so if you had a million doors and you chose one number and I removed 999,998 doors you're going to go "Well maybe I was lucky." But in reality I just removed all of the other unlikely doors and left you with the one that it probably is Problem rather than an exaggerated version of the same one To fully understand the Monty Hall paradox it's important to focus not on the size of the setup but on how Monty's actions shift the odds in both scenarios That's the key to why switching works Another way to explain the Monty Hall problem is by breaking it down step by step through all possible scenarios This method called exhaustive search lays out every possible outcome to make the solution crystal clear When you chart out all the possibilities a clear pattern emerges Switch lose win lose win lose versus win lose lose lose win lose lose lose win Wow So you lose way more in one of three of the scenarios How many people do you think on that show switched versus stayed I would assume the majority of people that didn't know this paradox would probably stay because at surface value you're just like "All right well my door's probably locked." Staying w I'm probably the right [ __ ] door which happens when you correctly picked the car on your first try In two out of three of the scenarios switching wins because the car is behind one of the doors you didn't initially choose This table is about as straightforward as it gets It leaves no room for debate Switching is the better option Yet even with all the possibilities laid out like this some people remain unconvinced Here's why While the table proves that switching works it doesn't address the lingering intuition that once Monty reveals a goat the odds should split evenly 50/50 between the two remaining doors People get I think the reason people refuse to switch is because he's a human If you were playing in a computer reveal the door you would probably go "Okay I understand my odds." But a person doing it you think they're conning you Stuck on the idea that Monty's reveal somehow resets the game even though the math says otherwise The exhaustive search shows the outcome but doesn't dig into why this counterintuitive result happens That is to think of it as a choice between your first pick and all the other options combined This perspective emphasizes that switching effectively gives you access to combining probability of the unchosen doors Okay I get that partitions is the basian approach with Wait why are there so many approaches to try and explain this to someone Do any of you guys still not get this I feel like after we did the cup [ __ ] I immediately understood it Like why is there a Beijian approach to [ __ ] explain to me why they literally just show me the cups run it three times I go "Okay yeah I get it." Which meticulously accounts for every detail To follow this reasoning you need to understand or at least accept the probabilities must be updated based on new information And the correct way to do this is by applying Bazy's rule The right hand side of Bazy's rule represents the probability of A given B In simpler terms oh hell no You're going to try and explain to someone that goes "Uh the odds are 5050 like I just did in the beginning of the [ __ ] video and they still don't get it after you show it to them." And so your next logical way of trying to make them understand the door paradox is showing them a complicated looking mathematical problem He is something we already know or just learn to be true Example let's say we picked door one and Monty revealed a goat behind door three Now we want to calculate the probability Oh Jesus Christ I get it I get it I get the basian reasoning dude The difficulty with the Monty Hall paradox isn't in understanding the math It's in confronting how we naturally think It forces us to question and override deeply rooted intuitions about fairness randomness and probability When Monty reveals a goat most people instinctively believe the remaining two options must be equally likely This feels fair because it aligns with our sense of symmetry Two doors left one car So it's a 50/50 chance But the paradox challenges this intuition Yeah you have to look at it at a whole problem by revealing a deeper truth Probabilities aren't static They can change based on new information even when the physical setup remains unchanged What makes this even harder to accept All right bro But I already explained that chosen doories Yet this act of revealing a goat redistributes the probabilities concentrating the chances of the car That visual just makes you understand it Are being behind the unchosen door This subtle shift is deeply unintuitive because it's not how we naturally process randomness or fairness We want to believe the remaining options are equal because that's what seems simple and fair For those who can trust the abstraction and focus solely on the math the solution becomes clear Switching gives you a two in three chance of winning while staying I think it's easiest to understand when you're running it Cuz when I was doing it for you guys and I wanted you to lose to prove that I was right you were always right because I want you to pick the right one But the o the only way my original thought process of it being 50/50 is right is if you immediately get it Leaves you with only one in three The math doesn't lie and it provides an undeniable answer But wow I could really scam people with out of money using this I hate that my mind goes to that Yo you could con the [ __ ] out of so many people doing this You could literally be like "Dude give me a dollar and I'll put five under a cup." And you like mix them around You go "Pick one." He picks one You move the other one Do you want to switch He's gonna go "No man Open that [ __ ] up." You would have to do the math to where statistically you're going to win more money But for those who remain tied to the narrative where Monty's reveal feels like a random event that resets the game the solution feels wrong no matter how it's explained They focus on the story instead of the probabilities And as a result the logic never quite clicks But this paradox is about more than just a game It's a reflection of how we approach complex problems in everyday life When faced with uncertainty we tend to rely on our instincts which are shaped by experience and intuition However in scenarios like this those instincts can be misleading The Monty Hall paradox teaches us that the tools of abstraction simplification and mathematical reasoning are essential for making sense of situations that aren't immediately intuitive At its core I get it I get it That was a very fun video