: Monty Hall paradox: Why do only Only 0.00001% understand it?
Intro Have you ever noticed how some things that seem
simple are actually quite perplexing? Take, for example, the common warning to never pour water on
a grease fire. It's a fact that most of us have learned through trial and error, but it's not
exactly the most intuitive response. In the heat of the moment, when panic sets in, our instincts
tell us to douse the flames with water. But little do we know, that's exactly what we shouldn't do!
Science is riddled with counterintuitive concepts that make us question our understanding of the
world. Consider Einstein's twin paradox, where one twin travels through space at high speed,
only to return and find that the twin who stayed on Earth has aged more.
How can this be? It defies logic, yet with a touch of mathematical genius, it turns out to be true.
The laws of the universe sometimes play tricks on our minds, challenging our preconceived notions.
And let's not forget the unpredictable dynamics of human relationships.
Have you ever tried doing something cute for your partner while they are fuming with anger?
Surprisingly, rather than melting their icy demeanor, it often exacerbates their anger.
In this video, I invite you on a journey through the perplexing Monty Hall paradox.
Prepare to abandon any notion of understanding it on your own, because when I reveal the solution,
you'll find yourself questioning everything you thought you knew. It's a mind-bending puzzle that
will make you question your very existence. Are you ready to have your world turned upside down?
--- Michael Jordan Can’t Sleep
Picture yourself in a fancy-schmancy five-star hotel. You're all cozied up in bed, ready for some
sweet dreams. Just as you start to drift off, you hear the sound of thundering footsteps coming from
the hallway. You peer through the peephole, only to see a colossal shadow making its way toward
your room. Who could it be, you wonder? You gather the courage to open the door,
and lo and behold, standing right in front of you is none other than Michael freakin' Jordan.
Yeah, you heard that right! The basketball legend himself is standing in your hotel corridor,
looking all epic. You invite him in, curious as to why he's gracing you with his presence.
Maybe he needs some advice on how to keep his sneakers fresh or something.
As he plops himself down on your bed, Michael starts pouring his heart out to you. It turns out
that since retiring, he's had a lot of time on his hands. So what does he do with all that free time,
you ask? Well, he's been hitting the books and writing on his blog, SneakerSlamDunk.org.
You listen intently, hoping that this unexpected visit won't take up too much
of your precious sleep time. But then he drops a bombshell. Among all the
things he's learned and discovered, there's one nagging question that keeps him awake at night.
Naturally, you can't just leave the man hanging. You ask him what's on his mind, and
he spills the beans. Turns out, he came across a mind-boggling question while studying statistics.
Try as he might, he just couldn't crack it. The worst part? The answer he thought was right was
actually wrong according to some snooty book. Here's the problem: Imagine you're faced with
three doors. Behind one door, there's a sick ride, like a shiny new car. Behind the other two doors,
there are goats. Don't ask me why goats, but they're there. So, you choose a door,
let's say Door No. 1. Then, the host, who knows what's behind each door, opens another door,
Door No. 3, revealing a silly goat. And then he's like, "Hey, wanna switch to Door No. 2?"
No wonder this question kept MJ awake at night. This problem is a brain teaser, in the form of
a probability puzzle, loosely based on the American television game show Let's Make a
Deal and named after its original host, Monty Hall. Why don't you
take a second to answer the question? What would you do? Would you switch the door?
--- Intuitive Explanation
Most people come to the conclusion that switching does not matter because there
are two unopened doors and one car and that it is a 50/50 choice. This would be true if the
host opens a door randomly, but that is not the case, because the host’s choice in turn depends
on the choice we make initially. I know it’s hard to believe, but the wisest thing to do
in order to find the car is to accept the switch. In any case. Indeed, a player who stays with the
initial choice wins in only one out of three of these equally likely possibilities, while
a player who switches wins in two out of three. Hard to believe? Let’s see if I can convince you.
Let's suppose you initially pick a goat. If this is the case,
the contestant will win the car by switching because the other goat can no longer be picked,
since the host had to reveal its location. On the other hand, let's suppose you initially
pick the car. In this case, switching won't help, and you could only win the car if you
decided to stick with it. Using the switching strategy, winning or losing thus only depends
on whether the contestant has initially chosen a goat, which is more likely, since two out of
three cards are goats, or the car, for which there’s only one chance out of 3 to be picked.
I know what you’re thinking: this is completely counterintuitive! Well,
don’t be surprised. I’ve been telling you since the beginning: this video will puzzle your mind.
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--- A More Formal Explanation
The best way to truly believe that the solution to the Monty Hall problem is
true is to try the simulation for yourself. But if you want to understand why it works
mathematically, let's break it down. Imagine there are 3 doors. Since the
cards are three and you can only pick one, your original choice has a 1/3 chance of winning,
while the other two doors combined have a 2/3 chance because the total
probability of the system must add up to one. When the host provides information about the 2
unchosen doors - revealing that one of them does not have the car behind it- the 2/3 chance of the
car being behind one of the unchosen doors rests on the unchosen and unrevealed door,
as opposed to the 1/3 chance of the car being behind the door you chose initially.
Still not convinced? Let's imagine there are 300 doors instead of just 3. You choose door 1, giving
you a 1/300 chance of winning. Monty then opens 298 out of the remaining doors, leaving you with
the option of door 1 or door 201. Now, even though your 1/300 odds remain the same for door 1, Monty
has actually increased your chances by giving you the best door out of the remaining 298 doors.
The Monty Hall paradox has been proven time and time again with
countless mathematical simulations. And if you're still skeptical, don't worry, even
mathematicians have scratched their heads over this one. One genius mathematician, Paul Erdős,
didn't believe the answer was right until he saw simulations of the winning "switch" strategy.
So, the next time you come across this problem, remember that trying it out for yourself is the
best way to believe in the solution. And no matter how many doors there are, always go for the best
option to increase your chances of winning. ---
--- A valuable lesson
This paradox holds valuable lessons for us on two fronts. Firstly, it prompts us to reflect upon the
notion that knowledge empowers us to make better decisions. This principle extends beyond basic
applications and can also be observed when we calculate probabilities. The more we understand
about a given topic, the more accurately we can predict outcomes and make informed choices.
Secondly, this paradox sheds light on the workings of science itself.
It doesn’t matter how long people spend under a Facebook post fighting for who’s right and
who’s wrong about the Monty Halla paradox. The correct answer is only one, and you can verify
it by simply repeating the experiment a bunch of times. This emphasizes the ultimate authority of
experimentation in scientific inquiry. No matter how sophisticated our theories or calculations
may be, it is the experiment that has the final say. This serves as a reminder of the tremendous
value of the scientific method in helping us comprehend the intricacies of reality.
We owe a debt of gratitude to Sir Francis Bacon for his contributions in this regard.
Now you know how to keep up a conversation with Michael Jordan if you’ll ever find him asking for
help in a luxury hotel room. You’re very welcome. ---
The Monty Hall paradox gained attention after a reader named Craig F. Whitaker
asked about it in a letter to Marilyn Vos Savant's column in Parade magazine. Savant,
who has the highest IQ recorded in the Guinness Book of Records, wrote in her column that the
player should switch doors. This answer was met with disagreement from many readers,
including those with PhDs. Despite some confusion from readers who didn't realize the host always
reveals a goat, most of Savant's correspondents understood the problem's assumptions. However,
they still initially believed Savant's answer was incorrect. This led to three more columns being
dedicated to the paradox. ---
Hey! This video ends here! Thanks for watching everyone! Do you think you understood the Monty
Hall paradox, or do you need some more time to think about it? Let us know in the comments below!
I'll see you next time on the channel. ---