The Monty Hall Problem (paging Math nerds!)

[gincognito]

So I'm reading this novel ("The Curious Incident of the Dog in the Nighttime" or some such thing) and it mentions the Monty Hall Problem. Seeing as I have a very superficial surface interest in math this struck me as, well, interesting. I'm sure many of you are aware of it, but I'll put it forth in skiing terms:

You are on a game show. You are presented with three doors. Behind one door there is a pair of PM Gear Bro Models. Behind the other two are snowblades. You pick a door. To drag out the suspense, the host opens one of the doors you did not pick and reveals a set of snowblades. He then asks you if you want to stick with your choice or to switch to the other still-closed door. Assuming you want the Bro Models, what should you do?

Sick and ashamed and happy (and sorry if this is boring or old news),
d.

[Crinkle]

go with original instinct. don't change the door!!!!!

[bad_roo]

Snowblades rule and represent tried and tested technology. Bag 'em.

[Big E]

Mathematically speaking, you should switch doors. I remember working this out back in Probability class. I should go back through it as a good refresher and present my work here, but I'm at work already and am not really in the mood.

[The AD]

I think you should switch because you know Monty isn't going to open the door that has the Bro Models. So, you started with a 1:3 chance of picking the door with the skis. Monty opening one snowlerblade doesn't affect your probability if you keep your original pick, but does change your probability if you change your pick.

[Will]

http://en.wikipedia.org/math/51d4831...0d3e019c19.png

As the above is gibberish to me I should point out that I suck at math, but I am a fucking genius when it comes to using google.

edit - but I can't spell.

[Tippster]

See, I totally disagree w/all the smart people on this. Yo9u picked a door when you had a 1/3 chance. Now it's 1/2. There is a 50/50 chance you're still right...

[Viva]

Bend Monty over, yank down his pants, and bugger him in front of a live studio audience.

Note, although this isn't what I would do, I'd gladly tune in to watch you do it.

[Beaver]

You start with a 1/3 chance but as soon as he reveals te snowlerblades the odds drop to 50/50. The explanation given in the book is bullshit. It would only be correct if no doors were revealed.

[Yossarian]

Heh. The correct answer is to switch.

I used to use this example when I taugh high school math and intro Engineering stats to college undergrads. All you 50-50 people are quite wrong, which is why this is a fun one - it doesn't jibe with our sense of how things should be.

It's actually an example of conditional probability, and a nice teaser into the general subject of probability and statistics. It can also motivate a discussion of the Bayesian/Non-Bayesian approach for more advanced math geeking.

But basically, the short explanation is as follows:

Getting more information doesn't change the underlying probability structure, it only modifies your information set. The Bro's haven't moved unless Monty is fucking around with you, in which case he deserves bukkake death from above.

You had a 1/3 chance of being right at first, and therefore a 2/3 chance of being wrong. Stay, and you'll still be right 1/3 of the time. Switch, and when you were wrong to begin with, you'll now be right. Thus, 2/3s.

That's the easiest laymans explanation anyway. I could spell it out further, but it's not worth it. Go write out the possibilities on paper, and you'll see it.

[Big E]

Basically, Yoss put Will's equation into words. Forgot that it was that straightforward (amazing how even the simplest things recede into those distant reaches when you're not using them regularly).

[bad_roo]

Given that the original odds of picking the goat were 2/3, by switching you ensure that you'll win if you originally picked a goat.

If you want to see if it really works and isn't just a bunch of maths geeks wanking themselves off, go here and try it. http://people.hofstra.edu/staff/stev...tyHallSim.html

[iceman]

What if you wanted a goat in the first place, smart guys?

[gincognito]

What if you wanted a goat in the first place, smart guys?

That's why I changed the goats to snowblades. Cause no one in their right mind* wants snowblades.

Sick and ashamed and happy (and threw in a * in order to exempt bad_roo and his burly British possee who obviously do not fit the criteria),
d.

[edg]

I found that book unbelievably irritating... but maybe that's just me. I just found the style of it really pedantic and frustrating (Yes, yes; I understand that it's meant to be written in that sort of style, but puh-lease...)

edg

[Ireallyliketoski2]

By switching, the player is ensuring that he will win if he originally picked the snowerblades. The probability of picking a snowerblades was 2/3, so the player should switch.

Check out my latest work in number theory

Theorem:
Every number is interesting.

Proof:
We will empirically start trying to prove every number is interesting.
1 is interesting because there is one world, one sun, one earth, etc.
2 is interesting because there are male and female pairs of most species.
3 is interesting because of the holy trinity.
4 is interesting because of the four points of the compass.
so forth and so on.
5 is interseting because there are the 5 points of a star.
so forth and so on...

It becomes clear that the empirical approach is tiresome and tedious, so let us try to prove this theorem by contradiction. Assume that there exists a number that is not interesting, the fact that this number is not be interesting makes it an interesting number, so every number must be interesting.
QED

[AntiSoCalSkier]

By switching, the player is ensuring that he will win if he originally picked the snowerblades. The probability of picking a snowerblades was 2/3, so the player should switch.

Check out my latest work in number theory

Theorem:
Every number is interesting.

Proof:
We will empirically start trying to prove every number is interesting.
1 is interesting because there is one world, one sun, one earth, etc.
2 is interesting because there are male and female pairs of most species.
3 is interesting because of the holy trinity.
4 is interesting because of the four points of the compass.
so forth and so on.
5 is interseting because there are the 5 points of a star.
so forth and so on...

It becomes clear that the empirical approach is tiresome and tedious, so let us try to prove this theorem by contradiction. Assume that there exists a number that is not interesting, the fact that this number is not be interesting makes it an interesting number, so every number must be interesting.
QED

But what if there are lots of numbers that are not interesting? In that case, none of them would be interesting due to the fact that they're not interesting.

[watersnowdirt]

this makes my head hurt.

I'm going back to the Maggot picture thread.

[Out_to_lunch]

I'm usually wrong when I second guess myself, so I would stick, with the first choice. Usually i'm pretty good with math, but never taken stat, and I still have no clue how to prove this.

[Ireallyliketoski2]

But what if there are lots of numbers that are not interesting? In that case, none of them would be interesting due to the fact that they're not interesting.

That's interesting.

[Alkasquawlik]

I think a true skier would stick with the original choice, find out that he got snowblades, grab the fruit boot sticks and beat the living crap out of the host with said fruit boots in a fit of snowblade induced rage and then open up all the doors to finally retrieve the all precious goat. (or BroModels, whichever one floats your boat)

Gin- Don't you think the ending is crazy. That the autistic kid in a fit of rage actually killed his mother, and that his father in order to hide from the police and suspicion of neighbors told his son that he had a bad dream and that mommy "moved away". That was a shocker ending.










Just kidding.... or am I?

[gincognito]

I must've missed that part...or was that what the triangle proof was referring to?

[Out_to_lunch]

The real question is what if you were on The Price is Right, and made it to the showcase, and the first was 50 million pairs of snow blades. Would you take that or go for the second? The second could be 50 million pairs of bro's OR a new dinet set.

[The AD]

The real question is what if you were on The Price is Right, and made it to the showcase, and the first was 50 million pairs of snow blades. Would you take that or go for the second? The second could be 50 million pairs of bro's OR a new dinet set.

Not possible since I couldn't even make it to the contestants row. From years of watching I've determined 99.9% of the contestants fit into one of the following categories:

1. Frat/Sorority member
2. Fat black woman
3. Clueless old person
4. Military personnel in uniform