## The Monty Hall Problem

The Monty Hall Problem is a famous (or rather infamous) probability puzzle. Ron Clarke takes you through the puzzle and explains the counter-intuitive answer.

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### Comments

25 comments posted so far. Login to add a comment.

35

#### 3. bonzenbrunzer commented 10 years ago

I'd rather win a lottery ticket...

anyone got some tips???

anyone got some tips???

25

#### 4. equilibrium2x commented 10 years ago

wasn't this here a while ago? i mean i usually see the noteworthy clips on this site. except for that frisbee one. that one sucked, misleading title too.

52

#### 5. Natan_el_Tigre commented 10 years ago

Awe... The voice reminded me of Maurice Moss from the IT Crowd.

40

#### 11. librabooks commented 10 years ago

Shoot! I thought it was the Monty Python problem. Dealing with the hamster and elderberry issue.

64

#### 12. Sizzlik (admin) commented 10 years ago

#10 Duh..then you simply dont switch...you got a 66.6666.......% chance of winning a goat ..better question is..what to do when the prizes are all different? Like one door a goat, other a car and the last a house..then the chances change =) And today the hosts interupt you by saying "Ok..you switched doors..i give you xxx for the door you switched to" ..*montyception*

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#### 13. seldomseen77 commented 10 years ago

#3 Actually there IS a mathematical tip I can give you for the lottery.

It doesn't increase your chances of winning (only buying more tickets can do that), but it increases the average money that you win, when you win.

The tip is to use totally random numbers. If you pick meaningful numbers, like the date on which you played, you drastically increase the chances of someone else having the same numbers, and so you will have to split what you gain. If you choose perfectly random numbers, you'll almost always be the only guy that wins, when you win.

It doesn't increase your chances of winning (only buying more tickets can do that), but it increases the average money that you win, when you win.

The tip is to use totally random numbers. If you pick meaningful numbers, like the date on which you played, you drastically increase the chances of someone else having the same numbers, and so you will have to split what you gain. If you choose perfectly random numbers, you'll almost always be the only guy that wins, when you win.

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#### 14. archis commented 10 years ago

13#

It remainds me of guy who won the lottery, he chosse random numbers by trowing darts on lottery ticket.

Back to topic. Imagine you have thousand doors and you pick one. Imagine host opens another 998 doors. So which one will have the car? your door or the door that host didnt open? In other words there are 2 groups. On group is your door with chance of succes 0.001 and other group with 999 doors with chance of succes of 0.999.

It remainds me of guy who won the lottery, he chosse random numbers by trowing darts on lottery ticket.

Back to topic. Imagine you have thousand doors and you pick one. Imagine host opens another 998 doors. So which one will have the car? your door or the door that host didnt open? In other words there are 2 groups. On group is your door with chance of succes 0.001 and other group with 999 doors with chance of succes of 0.999.

41

#### 15. Dae commented 10 years ago

That is actually the puzzle that is the movie las vegas 21.

http://en.wikipedia.org/wiki/21_%282008_film%29

I think that this whole theory is very weird. Both answers (50% chance and 66% chance) are correct, it's just a way of thinking. It's actually proof that probabilities are bullshit.

IMHO.

http://en.wikipedia.org/wiki/21_%282008_film%29

I think that this whole theory is very weird. Both answers (50% chance and 66% chance) are correct, it's just a way of thinking. It's actually proof that probabilities are bullshit.

IMHO.

37

#### 16. Tarc commented 10 years ago

#14

The 50% chance is not an (correct) answer, but an assumption or intuition. It does SEEM odd though, but only because it's our intuition.

Plus it's not even a "theory", it's proven.

Another way of thinking is that at first you have 2x the chance of picking a goat, so most likely you really PICKED the goat, and you better swap it.

The 50% chance is not an (correct) answer, but an assumption or intuition. It does SEEM odd though, but only because it's our intuition.

Plus it's not even a "theory", it's proven.

Another way of thinking is that at first you have 2x the chance of picking a goat, so most likely you really PICKED the goat, and you better swap it.

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#### 19. Sizzlik (admin) commented 10 years ago

#17 did you watch AND understand the vid? Sure 2 doors are a 50/50 chance...but you started with 66% taking a goat at first place..so there is only a 33% chance you lose if you swap..anyways..even if there is a 50/50 chance you still have to choose..swap or not swap..

Its called Probability theory also..go wiki it..

Its called Probability theory also..go wiki it..

54

#### 21. loadrunner commented 10 years ago

If you make a comment, you have 50% chance a person reading it gives you thumbs up.

#20

It is all about the very first pick.

Now if there are 10 doors, 9 goats and 1 ferrari. you have a 90% chance to pick a goat in the first try

now the gameshow guy opens 8 goat doors. There is a very big chance you picked the goat. And a very small chance you already were on the car. So do you swap to the other door??

or to make it very clear. there are 1000 boxes, 999 containing 1 dollar one of them contains 10 million dollar. after you pick one, the gameshowguy takes away 998 wrong boxes, worth one dollar. Did you pick the millions on the first try? or is it a bigger chance you picked a dollar the first try.

there are two boxes left now. the one you picked the first try and the other box.

#20

It is all about the very first pick.

Now if there are 10 doors, 9 goats and 1 ferrari. you have a 90% chance to pick a goat in the first try

now the gameshow guy opens 8 goat doors. There is a very big chance you picked the goat. And a very small chance you already were on the car. So do you swap to the other door??

or to make it very clear. there are 1000 boxes, 999 containing 1 dollar one of them contains 10 million dollar. after you pick one, the gameshowguy takes away 998 wrong boxes, worth one dollar. Did you pick the millions on the first try? or is it a bigger chance you picked a dollar the first try.

there are two boxes left now. the one you picked the first try and the other box.

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#### 24. samxgx commented 10 years ago

well... the problem with this theory is that it depends on an "if" based condition: IF your first pick was... right / wrong

when you know the results of your first pick: a goat, then yes. 66% chance its the other door.

But if the result was a car on first pick, then there's only 33% chance that the car is behind the other door...

so this theory is right only IF your first pick was wrong and you would know about it... when you are unaware of the result of your first pick, your second pick is a 50% chance situation

when you know the results of your first pick: a goat, then yes. 66% chance its the other door.

But if the result was a car on first pick, then there's only 33% chance that the car is behind the other door...

so this theory is right only IF your first pick was wrong and you would know about it... when you are unaware of the result of your first pick, your second pick is a 50% chance situation

39

#### 25. juzzur commented 6 years ago

Sozzer....3 years later I can see that you were right.

http://priceonomics.com/the-time-everyone-corrected-the-worlds-smartest/

My brain still hurts

http://priceonomics.com/the-time-everyone-corrected-the-worlds-smartest/

My brain still hurts

## +27 1. cameramaster commented 10 years ago