"If you stick with your first choice, you will end up with the Caddy if and only if you initially picked the door concealing the car. If you switch, you will win that beautiful automobile if and only if you initially picked one of the two doors with goats behind them."

so - because you're twice as likely to have made a mistake first time (compared with switching), you're twice as likely to be correct by switching?

if you open a door with a goat, it's still only a 1/3 chance you picked the car in the first place (2/3 you did not) so switching swings the odds in your favour

It's not really a maths problem, it's a logic one.

so odds are 1/3 that you'll get the car, and 2/3 that you've got the goat.

Monty opens a door and shows a goat

If you picked the car and switch, you'll get a goat. The odds of this (as above) are 1/3.
If you picked a goat, Monty must have revealed the other goat, so the remaining door must have the car behind it. Again the odds of this are 2/3.

Therefore, logically speaking, you maximise your chances by switching as you've no way of knowing whether you picked a goat or the car up front.

Imagine it was a 1 in 100 choice. You pick number one, then he rules out all the other wrong boxes apart from number 48. The odds are clearly in your favour to switch to box 48, unless you magically chose the right box on your first pick. The only reason it is hard to get our heads round is because it is only 1 in 3, so it only very slightly nudge it in your favour by switching. And you would feel a right twat if you smugly changed your mind and then turned out to be wrong. I think Mr Logic did this in a Viz strip actually, went on Deal or No Deal and left with 1p.

The rules are still the same. Behind one of the 1000 doors is car and behind the other 999 doors are chickens. The contestant has to pick one door at random. Then the host has to open 998 doors out of the 999 not chosen by the contestant. The host offers the contestant the choice of sticking with their door or switching to the host's single unopened door. The aim is to win the car.

Now let's look at The rules for the host choosing which doors to open
1) If the contestant has chosen the door with the car, then the host can open any 998 doors leaving a single door with a chicken
2) If the contestant has chosen a door with a chicken, then the host MUST open 998 doors with the chicken leaving the door with the car closed.

So, should the contestant stick or switch?

Well, the probability of the contestant choosing the winning door is 1/1000. Not good odds. The probability of the host having the winning door is 999/1000. However, the host has made it easier for the contestant by opening all his doors except for the one with the car. That single door represents all the other doors and there is a 999/1000 chance of a car behind the host's door.

Therefore, the contestant should switch as the probability of winning the car goes from 1/1000 to 999/1000. That is, the contestant is 999 times more likely to win with switching than sticking. (999/1000 is 999 times bigger than 1/1000)

Let's redo the thought experiment, but with 100 doors. The probability of the contestant choosing the winning door is 1/100. The probability of the host having the winning door is 99/100. If the contestant switches, the probability of winning the car goes from 1/100 to 99/100. That is, the contestant is 99 times more likely to win with switching than sticking. (99/100 is 99 times bigger than 1/100)

Again, but with 10 doors. The probability of the contestant choosing the winning door is 1/10. The probability of the host having the winning door is 9/10. If the contestant switches, the probability of winning the car goes from 1/10 to 9/10. That is, the contestant is 9 times more likely to win with switching than sticking. (9/10 is 9 times bigger than 1/10)

Finally, 3 doors......The probability of the contestant choosing the winning door is 1/3. The probability of the host having the winning door is 2/3. If the contestant switches, the probability of winning the car goes from 1/3 to 2/3. That is, the contestant doubles their chances to win with switching than sticking. (2/3 is twice as large as 1/3).

I don't like Monty Hall problem because it is a simple and exact maths problem deliberately obfuscated by the fuzziness of language. It's only purpose to catch you out because the problem has not been fully explained and you use the ambiguity of language to fill in the gaps and make personal assumptions. The person posing the problem can then show off. The Stephen Fry of maths problems.

a real feature from a gameshow where people are allowed to stick or switch and the idea is to work out which option gives you the highest EV. where is the fuziness of language?

there is room for 'good' decision making in deal or no deal though. but all you do whenever offered something is add up the totals in the remaining boxes, divide it by the number of boxes left and compare it to the offer. depending on the situation people might give up some EV for the chance for a bigger prize (which is how i justify occasionally playing the lottery) but there's not any more to it than that. the last switch decision is just 50/50

## this seems pretty clear to me

## oh i think i get it

"If you stick with your first choice, you will end up with the Caddy if and only if you initially picked the door concealing the car. If you switch, you will win that beautiful automobile if and only if you initially picked one of the two doors with goats behind them."

so - because you're twice as likely to have made a mistake first time (compared with switching), you're twice as likely to be correct by switching?

## *(compared with having got it right first time)

## Basically, yes.

## i understand it as

you have a 1/3 chance of having picked the car

2/3 chance you did not

if you open a door with a goat, it's still only a 1/3 chance you picked the car in the first place (2/3 you did not) so switching swings the odds in your favour

## if you open the door with the goat, that's it, game over

you'd keep the goat.

## Goat's well tasty. Cadillacs guzzle fuel like 55-year-old divorcees do whisky on a Friday night.

I'll stick with the goat.

## goat: LOSES

## picture it with 100 doors and it becomes a lot clearer

## i can win 100 doors?

## the best of the doors on double cassette

http://drownedinsound.com/community/boards/social/4298409#r6167917

## It's great they can start working on the other stuff on the list now that cancer is cured

## Do you specialise on saying silly things?

## No

## ...maths lecturer Dr John Moriarty.

## the usual way to explain that is that you imagine the exact same thing except he doesn't open a door

you win the same stuff, except one of them isn't a prize, you just switch from 1 door to two doors and it gives you a better chance

## now this one

http://en.wikipedia.org/wiki/Birthday_problem

## to summarise

if you have 30 random people, there is a 70% chance that two of them will have the same birthday

## That's not a problem, it's just a calculation

## i'm glad you think i'm capable but i didn't name it

## if you have 30 random people, there is a 70% chance that two of them will have help with over 50% of the average 15% deposit on their first mortgage.

## I remember explaining this problem to a friend once

and she said "yeah, but if you switched and lost you'd be fucking raging"

:D

## ^wise

## :D

## also, good to see more voyager leaving the solar system news

## It's gonna take me 300,000+ years to walk that far apparently.

Best get to it.

## did you read about the blobfish?

## Guys guys guys

You're all missing the main headline news http://www.bbc.co.uk/news/uk-england-lincolnshire-24047706

## Well done to them, annoyed at their midget mate who does fuck all though

## Poor wee bastard

## i just looked at the picture before, but I've read it now

thanks to evolution it'll probably retain that title for a few years to come

## this is pretty unfair really

no one has filmed it (or even seen it perhaps) in its natural habitat, so we don't really know what it looks like.

## can someone do the maths then?

in the first instance you're 33.3% of being right. then what?

## then nothing changes

## unless you're a goat

in which case you've got a 70% chance of having the same birthday as Monty Hall

## *if it's a leap year

## ^if it's not a leap year, the goat is replaced by a cadillac

and Monty Hall is replaced by Nicholas Parsons

## You pick a door at random

It's not really a maths problem, it's a logic one.

so odds are 1/3 that you'll get the car, and 2/3 that you've got the goat.

Monty opens a door and shows a goat

If you picked the car and switch, you'll get a goat. The odds of this (as above) are 1/3.

If you picked a goat, Monty must have revealed the other goat, so the remaining door must have the car behind it. Again the odds of this are 2/3.

Therefore, logically speaking, you maximise your chances by switching as you've no way of knowing whether you picked a goat or the car up front.

## "It's not really a maths problem, it's a logic one."

"so odds are 1/3 that you'll get the car, and 2/3 that you've got the goat."

## :)

## logic is a branch of maths

http://drownedinsound.com/community/boards/social/4436331#r7710376

## That said, I suppose logic is a branch of decision maths.

I take that back. It is about maths.

## Too late, sucker

## But the post times match!!!

(To be honest, shouldn't have tried to explain something while tired)

## kinda disappointed with cat_race's contribution to this thread

## yeah, i was playing starcraft

and i'm pretty sure it's been done on here before anyway

## you could have stirred such monstrosity :(

## just can't do it about these sorts of probability/EV things

unless it's on a poker forum

## I'd say I'm pretty good at maths, but I've never understood this.

## think of the revealing of the goat

as the elimination of balance

## don't try to picture the goat. instead, only try to realize the truth

there is no goat

## depends which door you pick tbf

## :D

## Which thread do you pick?

http://drownedinsound.com/community/boards/social/4172551

or do you want to change to this one?

http://drownedinsound.com/community/boards/social/4202336

## Derren Brown explained it quite well

Imagine it was a 1 in 100 choice. You pick number one, then he rules out all the other wrong boxes apart from number 48. The odds are clearly in your favour to switch to box 48, unless you magically chose the right box on your first pick. The only reason it is hard to get our heads round is because it is only 1 in 3, so it only very slightly nudge it in your favour by switching. And you would feel a right twat if you smugly changed your mind and then turned out to be wrong. I think Mr Logic did this in a Viz strip actually, went on Deal or No Deal and left with 1p.

## Let's have a thought experiment and imagine the Monty Hall problem with a 1000 doors

The rules are still the same. Behind one of the 1000 doors is car and behind the other 999 doors are chickens. The contestant has to pick one door at random. Then the host has to open 998 doors out of the 999 not chosen by the contestant. The host offers the contestant the choice of sticking with their door or switching to the host's single unopened door. The aim is to win the car.

Now let's look at The rules for the host choosing which doors to open

1) If the contestant has chosen the door with the car, then the host can open any 998 doors leaving a single door with a chicken

2) If the contestant has chosen a door with a chicken, then the host MUST open 998 doors with the chicken leaving the door with the car closed.

So, should the contestant stick or switch?

Well, the probability of the contestant choosing the winning door is 1/1000. Not good odds. The probability of the host having the winning door is 999/1000. However, the host has made it easier for the contestant by opening all his doors except for the one with the car. That single door represents all the other doors and there is a 999/1000 chance of a car behind the host's door.

Therefore, the contestant should switch as the probability of winning the car goes from 1/1000 to 999/1000. That is, the contestant is 999 times more likely to win with switching than sticking. (999/1000 is 999 times bigger than 1/1000)

Let's redo the thought experiment, but with 100 doors. The probability of the contestant choosing the winning door is 1/100. The probability of the host having the winning door is 99/100. If the contestant switches, the probability of winning the car goes from 1/100 to 99/100. That is, the contestant is 99 times more likely to win with switching than sticking. (99/100 is 99 times bigger than 1/100)

Again, but with 10 doors. The probability of the contestant choosing the winning door is 1/10. The probability of the host having the winning door is 9/10. If the contestant switches, the probability of winning the car goes from 1/10 to 9/10. That is, the contestant is 9 times more likely to win with switching than sticking. (9/10 is 9 times bigger than 1/10)

Finally, 3 doors......The probability of the contestant choosing the winning door is 1/3. The probability of the host having the winning door is 2/3. If the contestant switches, the probability of winning the car goes from 1/3 to 2/3. That is, the contestant doubles their chances to win with switching than sticking. (2/3 is twice as large as 1/3).

I don't like Monty Hall problem because it is a simple and exact maths problem deliberately obfuscated by the fuzziness of language. It's only purpose to catch you out because the problem has not been fully explained and you use the ambiguity of language to fill in the gaps and make personal assumptions. The person posing the problem can then show off. The Stephen Fry of maths problems.

tl;dr

## load of rubbish innit

## I agree, it's a maths problem designed to catch people out with the fuzziness of language

## lol, no it's not

a real feature from a gameshow where people are allowed to stick or switch and the idea is to work out which option gives you the highest EV. where is the fuziness of language?

## What's the best door to choose

If want to win a goat?

## So, on Deal or No Deal, it makes no difference if you switch or not,

because without the agency of the host knowing what is in the other box, it is not really a Monty Hall problem, right?

## correct.

there is room for 'good' decision making in deal or no deal though. but all you do whenever offered something is add up the totals in the remaining boxes, divide it by the number of boxes left and compare it to the offer. depending on the situation people might give up some EV for the chance for a bigger prize (which is how i justify occasionally playing the lottery) but there's not any more to it than that. the last switch decision is just 50/50