1282: "Monty Hall"

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1282: "Monty Hall"

Postby Cousj001 » Fri Oct 25, 2013 4:47 am UTC

Image
"A few minutes later, the goat from behind door C drives away in the car."

Had to look online to find the what it was referring to. Once I understood the reference though, it did make me smile. I can think of plenty of people (me included) who would prefer a goat. A goat is self-sustaining, and doesn't require me to pay several thousand pounds a year in insurance, taxes etc..

EDIT: added alt text
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Re: 1282: "Monty Hall"

Postby rhomboidal » Fri Oct 25, 2013 4:50 am UTC

Or maybe the tiger eats the lady and the goat drives off in the Jaguar with -- wait, I might be getting confused, here...

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Re: 1282: "Monty Hall"

Postby Piogre » Fri Oct 25, 2013 5:11 am UTC

Cousj001 wrote:Once I understood the reference though, it did make me smile. I can think of plenty of people (me included) who would prefer a goat. A goat is self-sustaining, and doesn't require me to pay several thousand pounds a year in insurance, taxes etc..


The car may involve insurance and gas, but the goat requires you clean up poop.

Either, though, is preferable to the sisyphean task of trying to explain the Monty hall problem to non-math people who insist that you must be wrong.

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Re: 1282: "Monty Hall"

Postby Eebster the Great » Fri Oct 25, 2013 5:19 am UTC

I wish I could track down this vague story I remember about a contestant on Let's Make a Deal demanding she actually receive her "zonk" camel prize and making out with a cash offer much better than the $50 or whatever they normally give.

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Re: 1282: "Monty Hall"

Postby DBPZ » Fri Oct 25, 2013 5:20 am UTC

He could have won two goats and teach them T R I C K S, you know, some T R I C K S need two goats to perform.

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Re: 1282: "Monty Hall"

Postby burnum » Fri Oct 25, 2013 5:22 am UTC

I love the Let's Make a Deal logic problem. It always takes me a few moments to rework out why the probabilities are weighted. However, once things click, it's such a beautifully clean puzzle.

I can just imagine Beret Guy knowing the right move in the game, and ignoring it anyway in order to get the "undesirable" item. :)

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Re: 1282: "Monty Hall"

Postby ShadedKnight » Fri Oct 25, 2013 5:25 am UTC

From what I've heard goats are actually rather difficult to take care of though, lots of health problems.

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Re: 1282: "Monty Hall"

Postby DBPZ » Fri Oct 25, 2013 5:32 am UTC

And, the Predictor can "almost certainly" predict his choice, so what should he choose?

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Re: 1282: "Minty Hill"

Postby Eternal Density » Fri Oct 25, 2013 5:34 am UTC

rhomboidal wrote:Or maybe the tiger eats the lady and the goat drives off in the Jaguar with -- wait, I might be getting confused, here...

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Re: 1282: "Monty Hall"

Postby rick.s » Fri Oct 25, 2013 5:38 am UTC

Um, really the answer is goat BBQ.

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Re: 1282: "Monty Hall"

Postby Antior » Fri Oct 25, 2013 5:39 am UTC

Yeah since I first heard of this problem, I have been wondering why a goat constitutes a loss. Why not an empty room behind a door?

Piogre wrote:Either, though, is preferable to the sisyphean task of trying to explain the Monty hall problem to non-math people who insist that you must be wrong.


Let alone explaining it to math PhD's who insist that you must be wrong.

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Re: 1282: "Monty Hall"

Postby phlip » Fri Oct 25, 2013 5:52 am UTC

Antior wrote:Yeah since I first heard of this problem, I have been wondering why a goat constitutes a loss. Why not an empty room behind a door?

Well, it's a reference to some TV game show, which had a chance of giving a joke prize which was usually some kind of animal (usually the contestant would actually get some token amount of cash in lieu of actually getting the animal in question). This is the same reason why it's called the "Monty Hall problem" - Monty Hall was the host of that TV show.

The specific game as spelled out in the Monty Hall puzzle, with the three doors and the host opening a losing door and offering you to switch wasn't an actual game on Let's Make a Deal, as far as I know... that was just a boiled-down-to-basics maths puzzle that used the trappings of a variety of games that were along that vein, stylistically (revealing things you didn't choose as a tease, or trying to get you to switch your unknown prize for a different unknown prize, or worse, trading your known prize for whatever's behind door number 2).

Apparently the show is still running... I don't know how popular it was or is in the US, but it's virtually an unknown over here. And yet the puzzle, with its canonical goats, remains.

Code: Select all

enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};
void ┻━┻︵​╰(ಠ_ಠ ⚠) {exit((int)⚠);}
[he/him/his]

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Re: 1282: "Monty Hall"

Postby deltaplan » Fri Oct 25, 2013 5:54 am UTC

What about the wolf and the cabbage ?

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Re: 1282: "Monty Hall"

Postby BlitzGirl » Fri Oct 25, 2013 6:00 am UTC

deltaplan wrote:What about the wolf and the cabbage ?

Well, the wolf was left at the river.

The cabbage will remain a mystery.
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Re: 1282: "Monty Hall"

Postby Envelope Generator » Fri Oct 25, 2013 6:01 am UTC

deltaplan wrote:What about the wolf and the cabbage ?


The wolf has no use for grass and the cabbage won't learn tricks.
I'm going to step off the LEM now... here we are, Pismo Beach and all the clams we can eat

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Re: 1282: "Monty Hall"

Postby BlitzGirl » Fri Oct 25, 2013 6:03 am UTC

Envelope Generator wrote:
deltaplan wrote:What about the wolf and the cabbage ?

The wolf has no use for grass and the cabbage won't learn trickses.

I taught my cabbage to stay. It's doing quite well, actually.
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Re: 1282: "Monty Hall"

Postby AtG » Fri Oct 25, 2013 6:12 am UTC

The game show host knooows...

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Re: 1282: "Monty Hall"

Postby Arancaytar » Fri Oct 25, 2013 6:13 am UTC

Okay, so this explains the goat. Now where did he get the cabbage and wolf?
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Re: 1282: "Monty Hall"

Postby Envelope Generator » Fri Oct 25, 2013 6:15 am UTC

BlitzGirl wrote:
Envelope Generator wrote:
deltaplan wrote:What about the wolf and the cabbage ?

The wolf has no use for grass and the cabbage won't learn trickses.

I taught my cabbage to stay. It's doing quite well, actually.


I've found my cabbage leaves.
I'm going to step off the LEM now... here we are, Pismo Beach and all the clams we can eat

eSOANEM wrote:If Fonzie's on the order of 100 zeptokelvin, I think he has bigger problems than difracting through doors.

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Re: 1282: "Monty Hall"

Postby luckykaa » Fri Oct 25, 2013 6:34 am UTC

Arancaytar wrote:Okay, so this explains the goat. Now where did he get the cabbage and wolf?


He got the wolf from Ebay.

He actually ordered a bobcat but bought it from black hat.

Not sure about cabbages. Do these mythical objects really exist?

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Re: 1282: "Monty Hall"

Postby da Doctah » Fri Oct 25, 2013 7:17 am UTC

phlip wrote:The specific game as spelled out in the Monty Hall puzzle, with the three doors and the host opening a losing door and offering you to switch wasn't an actual game on Let's Make a Deal, as far as I know... that was just a boiled-down-to-basics maths puzzle that used the trappings of a variety of games that were along that vein


Uh, there's where you're wrong, for certain values of wrong. I grew up during the heyday of Let's Make a Deal and can run through the description. Earlier rounds would have people choosing between a box and an envelope, or a box and a bigger box, or a box and a curtain, sometimes receiving prizes of value, other times a worthless "zonk" (I don't remember any actual goats, but a donkey and cart was one such "you lost" prize).

In the final round, the contestant who had won the most valuable prize up to that time would be offered a chance for the "deal of the day", which was the only part of the show that used the three doors. (If the biggest winner elected to keep what she had already won, Monty would move on to the second-highest, and so on until someone agreed to play.) That contestant would be offered a choice of three doors. Monty would (always) open one of the doors not chosen, revealing a prize that was of some value but never the grand prize of the day, and then offer the contestant the choice to switch to the other as-yet-unopened door.

The biggest difference from the internet version is that there were no overt "zonk" prizes in this round. The contestant was assured of getting something nice, with the tension revolving around whether it was the biggest prize of all. No goats here.

The show's "prize pointers", by the way, flourishing the various boxes and curtains and revealing the prizes hidden inside or behind other prizes, were Jay Stewart (also the show's announcer) and Carol Merrill. Merrill is the aunt of actress Carla Gugino.

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Re: 1282: "Monty Hall"

Postby orthogon » Fri Oct 25, 2013 8:09 am UTC

To be fair to the people who have trouble getting it, the most common problem is not realising that Monty would never open a curtain that contained the car. That's not obvious if you haven't seen the show; the show format would be potentially just as gripping if there was a chance of his revealing the car the first time he opened a curtain. Partly the issue is that it's difficult to formulate the problem so as to make this clear without making it less counter-intuitive.

Anyway, a few variants on the Mony Hall problem:

The Monty Schrodinger problem (for quantum physicists): Each curtain conceals a superposition of a car and a goat. If you lose you have to take home a dead cat.
The Monty Lenin problem (for soviet-style communists): Each curtain conceals a single potato.
The Monty Green problem (for environmentalists): Same setup as Monty Hall, but the car is the booby prize that nobody would want
The Monty Trader problem (for fat-cat city traders): Same setup as Monty Hall, but if you choose wrongly you get the car anyway.
The Monty Thatcher problem (for Thatcherite-Blairites): Same set-up as Monty Hall, but one curtain conceals adequate and urgently needed hospital treatment and the other two contain MRSA-ridden fleapits.
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Re: 1282: "Monty Hall"

Postby J L » Fri Oct 25, 2013 8:10 am UTC

In any case, it seems that problem made a lot of people very angry, and very confused:

"Vos Savant wrote in her first column on the Monty Hall problem that the player should switch since the first door has a 1/3 chance of winning, so the second door has a 2/3 chance as the host always opens a losing door on purpose. (vos Savant 1990a) She went on to explain her answer by asking the reader to visualize the player selecting #1 amongst a million doors. Following the constraints, the host opens all remaining doors except door #777,777. Her conclusion: "You’d switch to that door pretty fast, wouldn’t you?"

She received thousands of letters from her readers; 92% of the general public, 65% of universities, and many with PhDs, were against her answer."

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

(Warning: Following those other paradox/problem links is a serious time sink.)

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Re: 1282: "Monty Hall"

Postby alexh » Fri Oct 25, 2013 8:16 am UTC

Wouldn't there be two doors open if he'd won a goat? The door Monty opened to reveal a goat and the door Beret Guy picked? Unless he's being especially subversive and changing his pick to the open door...

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Re: 1282: "Monty Hall"

Postby Pfhorrest » Fri Oct 25, 2013 8:16 am UTC

Antior wrote:Yeah since I first heard of this problem, I have been wondering why a goat constitutes a loss. Why not an empty room behind a door?

Actually, making that change makes the solution to the problem much more intuitive.

There's a prize behind one of these three doors. You can either have whatever prize may or may not be behind one door of your choosing, or whatever prize may or may not be behind either of the other doors. If you take the first option, your chosen door opens and you see whether it has a prize behind it. If you take the second option, one of the other two doors which doesn't have a prize opens first (cause at least one of those two is guaranteed to have nothing), and then the other door opens and you see whether it has a prize behind it. In effect, if you take the first option ("stay") you get to open one of the doors, and if you take the second option ("switch") you get to open two of the doors.

Another analogous scenario: there are two glass boxes, one of them 1ftx1ftx1ft and the other 2ftx1ftx1ft, obscured behind a wall. There are three holes in the backs of those boxes, one per square foot; so one hole in the middle of the back of the short box, and two holes in in the back of the tall box. Three tubes, red green and blue, one of which has a prize in it, attach to those holes, and you get to pick which tube attaches to the short box, which is called "your" box. (This is analogous to picking which door you want). The tubes feed their contents into the boxes, and the boxes are then raised from behind the wall, and at the point where the top half of the tall box is exposed, you are asked: which box would you like to claim the contents of, "your" box or the bigger one? (This is analogous to Monty opening a "goat" door and asking if you want to switch). One way or another, the top half of the tall box is always going to be empty thanks to gravity (i.e. thanks to Monty always picking an empty door), and one way or another there's a 2/3 chance of the tall box having the prize, because it has two prize holes while the short one only has one. So the odds are always in your favor to pick the tall box instead of "your" box.

Now think of the classic Monty Hall problem again, but in your imagination put the door you picked into a small box and the other two doors together into a bigger box. When Monty asks you to stay or switch, realize he's asking you which box you want to claim the contents of. Obviously, the bigger one's a better bet. You know that at least one of the doors in that box is worthless since there's only one prize, so Monty showing you that tells you nothing. But there's 2/3 odds that one of the doors in that box has the prize, and only 1/3 odds that the one door in the smaller box has the prize.
Last edited by Pfhorrest on Fri Oct 25, 2013 8:19 am UTC, edited 1 time in total.
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Re: 1282: "Monty Hall"

Postby Klear » Fri Oct 25, 2013 8:18 am UTC

burnum wrote:I can just imagine Beret Guy knowing the right move in the game, and ignoring it anyway in order to get the "undesirable" item. :)


I like the fact that only one door is open. That means he chose the goat door that was opened for him and didn't even have to risk getting a car on accident!

Edit:



At least the professors were right about math education being abysmal =)

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Re: 1282: "Monty Hall"

Postby MichaelKarnerfors » Fri Oct 25, 2013 8:47 am UTC

I finally managed to make sense of the Monty Hall Problem this way:

  1. In 2 out of 3 cases, you picked the wrong door. You need to switch to win. But which of the two remaining doors is it? One is the prize, one is a non-winner.
  2. The gameshow host steps in: he eliminates the non-winning door for you.
  3. Now you know which door is the winner since there is only one left, switching is a guaranteed win.
So... in 1/3 of the cases, switching is a 100% chance of loss.
But in 2/3 of the cases, switching is a 100% chance of win, because in those cases you can't pick the wrong door if you switch.

...unless you wanted the goat... in which case you must always switch... to the door the game show host opened. :D

/MK

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Re: 1282: "Monty Hall"

Postby TG333 » Fri Oct 25, 2013 9:09 am UTC

I still cant make sense of the MHP with a goat, a donkey and baby ducks behind the doors.
I don't wanna hear your excuses! The building has to be at least... three times bigger than this!

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Re: 1282: "Monty Hall"

Postby peewee_RotA » Fri Oct 25, 2013 10:55 am UTC

I won a goat, you've got to be kidding me!
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Re: 1282: "Monty Hall"

Postby Klear » Fri Oct 25, 2013 11:20 am UTC

peewee_RotA wrote:I won a goat, you've got to be kidding me!


Goatcha!

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Re: 1282: "Monty Hall"

Postby R3sistance » Fri Oct 25, 2013 11:24 am UTC

Monty Hall... that brings back memories... to get my head fully around it I built a simulator for it. Even if some already existed that were better; actually writing the code that simulated this situation did help me further understand what was going on!

And just to show I really did write a simulator... http://www.r3sistance.com/montyhall.php

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Re: 1282: "Monty Hall"

Postby Klear » Fri Oct 25, 2013 11:35 am UTC

R3sistance wrote:Monty Hall... that brings back memories... to get my head fully around it I built a simulator for it. Even if some already existed that were better; actually writing the code that simulated this situation did help me further understand what was going on!

And just to show I really did write a simulator... http://www.r3sistance.com/montyhall.php


Tried it once, switched, got goat. C'est la vie.

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Re: 1282: "Monty Hall"

Postby phlip » Fri Oct 25, 2013 11:54 am UTC

da Doctah wrote:
phlip wrote:The specific game as spelled out in the Monty Hall puzzle, with the three doors and the host opening a losing door and offering you to switch wasn't an actual game on Let's Make a Deal, as far as I know... that was just a boiled-down-to-basics maths puzzle that used the trappings of a variety of games that were along that vein


Uh, there's where you're wrong, for certain values of wrong. I grew up during the heyday of Let's Make a Deal and can run through the description. Earlier rounds would have people choosing between a box and an envelope, or a box and a bigger box, or a box and a curtain, sometimes receiving prizes of value, other times a worthless "zonk" (I don't remember any actual goats, but a donkey and cart was one such "you lost" prize).

In the final round, the contestant who had won the most valuable prize up to that time would be offered a chance for the "deal of the day", which was the only part of the show that used the three doors. (If the biggest winner elected to keep what she had already won, Monty would move on to the second-highest, and so on until someone agreed to play.) That contestant would be offered a choice of three doors. Monty would (always) open one of the doors not chosen, revealing a prize that was of some value but never the grand prize of the day, and then offer the contestant the choice to switch to the other as-yet-unopened door.

The biggest difference from the internet version is that there were no overt "zonk" prizes in this round. The contestant was assured of getting something nice, with the tension revolving around whether it was the biggest prize of all. No goats here.

The show's "prize pointers", by the way, flourishing the various boxes and curtains and revealing the prizes hidden inside or behind other prizes, were Jay Stewart (also the show's announcer) and Carol Merrill. Merrill is the aunt of actress Carla Gugino.

Neat! Good to know, I'll file this away for the next time the discussion comes up. Like I said, the show is essentially an unknown here, I've never actually seen it... everything I know about it is from Wikipedia and half-remembered conversations like this one... I obviously remembered this bit wrong.

Code: Select all

enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};
void ┻━┻︵​╰(ಠ_ಠ ⚠) {exit((int)⚠);}
[he/him/his]

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Re: 1282: "Monty Hall"

Postby ymr049c » Fri Oct 25, 2013 12:00 pm UTC

I first viewed this one on my phone, which cropped the image down to Monty standing in front of the empty closet. No hint of the beret guy happily getting his goat.

That was confusing.

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Re: 1282: "Monty Hall"

Postby Bastor » Fri Oct 25, 2013 12:23 pm UTC

I never understood the problem.

I mean I understand it but....who would want a sports car when you can have a GOAT!

Goats are awesome. I bet we'd drink beer together and have fun and stuff...

There should be 2 cars and a goat. That way the problem would make sense.

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Re: 1282: "Monty Hall"

Postby RogueCynic » Fri Oct 25, 2013 12:25 pm UTC

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Re: 1282: "Monty Hall"

Postby BlitzGirl » Fri Oct 25, 2013 12:29 pm UTC

RogueCynic wrote:its been done before.http://en.wikipedia.org/wiki/Bart_Gets_an_Elephant

So...you're saying the Simpsons did it?
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Re: 1282: "Monty Hall"

Postby Platypodes » Fri Oct 25, 2013 12:36 pm UTC

I love how this comic takes a classic scene of "failure" and turns it into happiness.

Can't we all relate at some level to the poor dude who, through an unlucky guess, missed his chance at something awesome and walked away with crap instead?

It's great to see that dude walk away smiling!
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Re: 1282: "Monty Hall"

Postby Klear » Fri Oct 25, 2013 12:41 pm UTC

BlitzGirl wrote:
RogueCynic wrote:its been done before.http://en.wikipedia.org/wiki/Bart_Gets_an_Elephant

So...you're saying the Simpsons did it?


South Park did that!

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Re: 1282: "Monty Hall"

Postby orthogon » Fri Oct 25, 2013 12:41 pm UTC

Some other variants:

The Monty Don problem: One of the doors conceals a shrubbery
The Monty Python problem: same as the Monty Don problem
The Monty Burns problem: Opening two of the doors will release the hounds!
xtifr wrote:... and orthogon merely sounds undecided.


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