- Today we're talking about trusting your gut.
A lot of times your gut's a pretty reliable source.
If I'm walking through the woods and I see
a pack of wolves, my gut's gonna be like,
"Hey, run," and I would do that.
But should you always stick with your gut instinct?
- No!
- What?
(funky music)
To illustrate this point, we're going to look at
the Monty Hall Problem.
Here's how it works.
You're on a game show. You've got three doors.
Behind one, a great prize.
Let's say it's a car, like a really cool car.
Behind the other two, sheep.
Oh what, you're gonna be one of
those people who's all like,
"Oh, a sheep's a good prize, anyway!"
Well, fine, then it's a dead sheep.
Oh God, that's upsetting.
Fine, it's a live sheep. Undo!
So you've gotta pick one out of the three doors.
And we hit the streets with a tiny game show to
present the people with that exact choice.
- Tiny Tiny Game Show!
- Tiny Tiny Game Show.
- It's so tiny.
- Whoa!
- Behind one of these wonderful doors is a brand new car!
- Whoa!
- Whoo!
- What kind of car is it?
- Well, you're gonna find out, aren't you?
- Okay, okay.
Behind two of the doors...
is a sheep!
- What am I gonna do with a sheep?
- I dunno.
- I mean, in the right market,
that could be worth the same thing, though.
- Yeah, well, you know.
- You don't want a sheep.
- You don't want a sheep!
- These sheep are sick.
- So what I need you to do is just pick a door.
- I highly recommend door number one.
Don't you dare!
But also door number two's great.
- I'm gonna go with door number one.
- Number three.
- Number one.
- I think we're gonna go with number two.
- Three.
- You just gave us the "no, don't pick three" look.
- What are you talking about?
- Three.
- I'm gonna pick door number two.
- Number three.
- So let's look at the odds of you winning.
No matter which door you choose from the start,
you have a one in three chance of winning
and a two in three chance of losing.
Each door on its own offers the same probability.
So, you've picked your door and crossed your fingers
when suddenly, the game show host opens up
one of the doors you haven't picked
to reveal that one of the sheep is behind it.
And he gives you the option to switch your choice.
I'm gonna reveal to you...
- Oh my gosh.
- That behind door number three...
- That's a sheep.
- [Man] Sheep. - [Host] ...is a sheep.
- There's a dead sheep.
- He fainted.
- Oh!
- That's what I'm talking about.
- So knowing that, do you wanna stick with door number three
or switch to door number two?
Should you switch?
Even if it feels like you're betraying your gut instinct?
Yeah! You should switch.
Why?
Well, what's important to note is that if you combine
the probability of two doors, you'd have
a two in three chance of winning
and a one in three chance of losing.
So because the probabilities have stayed the same,
that door you picked initially had a one in three chance
of harboring a sweet new ride, while the other two
combined had a two in three chance.
But now that one of those two unpicked doors
has been eliminated, that remaining door
still has that same two in three chance.
So by switching, you're twice as likely to win.
Does that make sense?
Here, watch how better off people fare when they switch.
- I wanna pick number two.
- You're switching to door number two?
- I'm switching to door number two.
- See what happens.
You're gonna switch to two?
- You won the brand new car!
- Whoa!
- It's a car!
- Whoa!
- Brand new!
You won the brand new car!
- A brand new car!
- Is it the same sheep?
- No, it's a different sheep.
- [Host] And here's a supercut
of all the losers who didn't switch.
Let's delight in their misery.
- I think I'm gonna stick to two.
(sad music)
- You're gonna go with your gut?
- You're sticking with door number three?
(sheep bleat)
- Aww, it's a sheep!
- Aww, it's a sheep.
- Son of a biscuit!
- Aww!
- Oh no!
- Aww, you got a sheep!
(sheep bleat)
- Aww!
- You got a sheep!
- When you first choose, it's only one third of a chance.
So you actually have a better chance
when you select a new door.
- See, that lady gets it.
Now if it still doesn't make sense to you,
let's blow the whole thing up and say
that you were presented with 50 doors.
You pick one.
The host then opens 48 doors and
gives you the chance to switch.
Are you gonna stick with that one random door you picked
or switch to the one door that the host didn't open?
Makes a little more sense? Kinda, yeah?
So, the next time you find yourself
in one of those classic three-door scenarios, breathe easy.
You've got this.
And that's some cool science for ya.
- It's cool. It's math, but I think--
- Ah, you're right. Well...
- It's fine.
- It's still a subject in school.
(both make random noises)