The Easiest Problem Everyone Gets Wrong

We know how difficult the Monty Hall Problem is for so many people even after they’re shown all the math behind the best possible strategy. It’s basic probability, but it’s deceptive -- and it all started with the Bertrand’s Box Paradox.

In this video, I go back to the origins of a probability problem that continues to plague humanity. And it all started in 1889 when French mathematician Joseph Bertrand published his “Calcul des probabilités,” which included a simple scenario involving gold and silver coins.

70 years later, recreational math columnist Martin Gardner unveiled The Three Prisoners Problem involving the pardoning of one of three prisoners scheduled to be executed. The mathematical concept was the same as Bertrand’s Box, but The Three Prisoners continued to be a probability paradox that haunted everyone from the readers of Scientific American to professional mathematicians.

But the Monty Hall Problem is really what made this mathematical illusion explode. By the 1990s, there was an all-out argument about whether all of these problems -- Bertrand’s Box, Three Prisoners, and Monty Hall -- were paradoxes or simple 50/50 coin flips. It’s time to go back to the beginning… and show why there’s something even more important than solving this math problem.

*** SOURCES ***

*** LINKS ***

Vsauce2:

Hosted and Produced by Kevin Lieber

Research And Writing by Matthew Tabor

Editing by John Swan

Huge Thanks To Paula Lieber

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[rcurl]

"I'm about to stretch my winkey until it snaps."

Well I'm scared.

[darkviking]

It really feels like Kevin is training us for when he eventually takes over the world, and the only way to survive is through paradoxical games he set up.

[willfreese]

I once wrote a program that ran a long series of Monty Hall examples. I was sure it would prove the contestant who did not switch would win just as often as the one who did. When I ran the program, the contestant who switched won twice as often. It was fun having my own code tell me how wrong I was.

[ahlpym]

My favourite way to explain the Monty Hall problem:

Imagine you're going into the game with the plan to switch. In that case, you want your first guess to be a losing door, so that the other losing door will be revealed and you get to switch to the winning door.
And since there 2 losing doors, you have a 2/3 chance of successfully doing this. So always switching gives you a 2/3 chance of ending up with the winning door.

[Bigfoot_With_Internet_Access]

Everybody gangsta till Kevin starts stretching his winky until it snaps

[soumyasharma]

Kevin: Right?
Me: nods head
Kevin: *wRoNg*

*_Cries in corner_

[christianboi]

This didn’t make sense to me as a child when I heard it, but now that I’m older it makes complete sense. There’s a 1 in 3 chance that whatever your picking is the right choice. That means that there is a 2 in 3 chance that one of the other two is the right choice. If you eliminate a wrong option then there is still a 2 in 3 chance. If someone explained it like that to me when I was younger I would’ve gotten it easily.

[NEBREUELPHFTARRRR]

For the Monty hall a way to make it more intuitive IS imagining 1000 Doors you pick one door the présentator opens 998 Doors only the one you have picked and an other one Can be the right door, you know it's probably the other door still closed.

[Psicough]

I swear Internet Historian sounds like he's about to laugh the whole time

[shaunab]

"You're watching this video because you're a smart, curious person"
Me: Nodding my head pretending I understand

[decemberist]

I’m sorry sir, but that is pink, not purple

[codnewbgamer]

This is the most intuitive version of the Monty Hall problem I’ve ever seen

[itmightbe]

Me watching this alone: probability and such

Me when my mom walks in: I AM ABOUT TO STRETCH MY WINKY UNTIL IT SNAPS

[harikishanrakhade]

Whenever Michael(Vsauce1) seems to arrive at a conclusion, he says, "Or is it?"
And when Kevin seem to arrive at it, he says, "WRONG!"

[justintime]

I've watched many Monty hall paradox problems. About half of them have successfully made me understand. But Everytime I encounter it again I have to learn it all over again. It's a really counterintuitive problem.

[saityusufbulur]

The biggest mistake of people who don't understand the Monty Hall Problem is that they accidentally see 2 empty boxes as one box. So when they choose a box, they think there are only TWO different scenarios in front of them: The chosen box is empty, or the box has prize in it. It's WRONG.

In fact, there are THREE different scenarios about chosen box: The prize box, the 1st empty box and the 2nd empty box. Remember, there are 2 empty boxes in the game, not one.

[Ice]

I always had a feeling that Internet Historian was a little stretchy orange man.

[greenat]

Kevin: Right?
Me: Yea-
Kevin: WRONG!
——————————
Kevin: Right?
Me: N-
Kevin: Yes!

[TryniaMerin]

I'm laughing extremely hard. This is a thoroughly amusing way to learn about math paradoxes!

[tremkl]

When I heard the Monty Hall version of the statement, it definitely seemed like it should be 50/50, but I think I found the coin version much clearer. Sure, 50% of the remaining possibilities are a gold coin, but if you had selected the gold/silver option, there would have been a 50% chance you drew the silver coin first.