1282: "Monty Hall"

This forum is for the individual discussion thread that goes with each new comic.

Moderators: Moderators General, Prelates, Magistrates

User avatar
Klear
Posts: 1965
Joined: Sun Jun 13, 2010 8:43 am UTC
Location: Prague

Re: 1282: "Monty Hall"

Postby Klear » Fri Oct 25, 2013 12:57 pm UTC

orthogon wrote:Some other variants:
The Monty Burns problem: Opening two of the doors will release the hounds!


The third one has, of course, a bottomless pit.

And then there's the infamous Full Monty variation...

dp2
Posts: 346
Joined: Wed Aug 18, 2010 3:06 pm UTC

Re: 1282: "Monty Hall"

Postby dp2 » Fri Oct 25, 2013 1:01 pm UTC

The problem boils down to this: If you don't switch, you're saying you guessed right in the first place, when you had only a 1/3 chance.

User avatar
Monika
Welcoming Aarvark
Posts: 3673
Joined: Mon Aug 18, 2008 8:03 am UTC
Location: Germany, near Heidelberg
Contact:

Re: 1282: "Monty Hall"

Postby Monika » Fri Oct 25, 2013 1:01 pm UTC

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.

Oh yes, the pain, the pain.

However, explaining it to math people isn't that much better. In our 4th-semester Probability class, only taken by students of math&CS and to-be math teachers (not e.g. CS&business administration, technical CS, software engineering&internet technology or business math students, with whom we shared many other math classes), the prof asked whether we thought switch was better or whether it didn't matter. I don't remember exactly, I think around half got it wrong. But even after explaining it throughout the lecture, in the end of it still many were not convinced.


Indeed.

J L wrote:
Wikipædia wrote: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?"

That's a pretty neat explanation. With a million doors it becomes a lot more intuitively convincing than with 3.
Wikipædia wrote:She received thousands of letters from her readers; 92% of the general public, 65% of universities, and many with PhDs, were against her answer."
Or so I would have thought.

Pfhorrest wrote: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.

While I have problems following the rest of your explanation, this is pretty neat. Just ask the question like this: 1 door with prize, 2 doors empty (to avoid the problem that value is put on the goat, too). Pick one. Do you wish to stay or do you wish to open *the other two doors* (get to keep all the prizes behind all 2 doors, which may be a total of 0 or 1). Suddenly it becomes clearer that the chance is 2/3 when switching.

dp2 wrote:The problem boils down to this: If you don't switch, you're saying you guessed right in the first place, when you had only a 1/3 chance.

Absolutely. But people see it as again picking between two doors, which they intuitively consider to have the same likelyhood of the prize.
#xkcd-q on irc.foonetic.net - the LGBTIQQA support channel
Please donate to help these people

User avatar
cellocgw
Posts: 2067
Joined: Sat Jun 21, 2008 7:40 pm UTC

Re: 1282: "Monty Hall"

Postby cellocgw » Fri Oct 25, 2013 1:12 pm 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?

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.


For the other greybeards in the thread: "But I must warn you, behind the other 2 doors are narcs!" "Uhhhh... I'll take the reds, man."

ETA - Some new pseudoquiz show on ComedyCentral showed a CraigsList post (ostensibly real, I never tracked it down) from someone trying to give away 2 dozen goats.
Last edited by cellocgw on Fri Oct 25, 2013 1:17 pm UTC, edited 1 time in total.
resume
Former OTTer
Vote cellocgw for President 2020. #ScienceintheWhiteHouse http://cellocgw.wordpress.com
"The Planck length is 3.81779e-33 picas." -- keithl
" Earth weighs almost exactly π milliJupiters" -- what-if #146, note 7

User avatar
cellocgw
Posts: 2067
Joined: Sat Jun 21, 2008 7:40 pm UTC

Re: 1282: "Monty Hall"

Postby cellocgw » Fri Oct 25, 2013 1:15 pm UTC

Klear wrote:
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 goatC'e st la vie.


Obscenified that for ya :twisted:
resume
Former OTTer
Vote cellocgw for President 2020. #ScienceintheWhiteHouse http://cellocgw.wordpress.com
"The Planck length is 3.81779e-33 picas." -- keithl
" Earth weighs almost exactly π milliJupiters" -- what-if #146, note 7

dp2
Posts: 346
Joined: Wed Aug 18, 2010 3:06 pm UTC

Re: 1282: "Monty Hall"

Postby dp2 » Fri Oct 25, 2013 1:37 pm 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

After 5 games, always switching: 1 wins (20%)
After 10 games, always switching: 5 wins (50%)
After 20 games, always switching: 11 wins (55%)
After 50 games, always switching: 31 wins (62%)
After 100 games, always switching: 65 wins (65%), right about where we expect it.

That's the problem with probability. It's too easy to try once, lose, and think "See? I lost!" I only won 1 in 5 times at first -- that's not going to convince a non-believer.

User avatar
mathmannix
Posts: 1453
Joined: Fri Jul 06, 2012 2:12 pm UTC
Location: Washington, DC

Re: 1282: "Monty Hall"

Postby mathmannix » Fri Oct 25, 2013 1:38 pm UTC

Were I to be on the show, I would probably like the goat - especially if I had no need for the car! I mean, if the car is a little sports car, it wouldn't be that practical for me. Plus we already have two cars, and IIRC, when you win a car on a television game show, you still have to pay for taxes, tags, and to get it home from Hollywood Studios, CA to the other side of the country where you live.

Goats may be difficult to take care of, but worse case scenario, the goat dies and you eat it, nice family barbecue style. I've had goat, and it's good gravy. Not a bad worse-case scenario. If you can take care of it properly, you at least have a free lawnmower/fertilizer for your lawn, not that the HOA where I live would allow it, but my rural in-laws could definitely make use of it and all these other aspects if that happens, so it's a very nice present.

Also, there's the whole "goats eat anything" idea. OK, so while they might eat tin cans IRL (it's probably true; I know from personal experience that camels at a drive-through feeding park will take and eat your whole gallon-sized plastic bucket!) that doesn't mean that it's good for them, necessarily. So I might still have to put the cans out for the recycle man, but maybe the goat can help with the newspaper, or at the very least, help with the pounds of wasted food we throw out weekly - I am an American, after all!

Bonus: we can think of it as a pet, too - providing companionship just like an outdoor dog. (Although utilizing this aspect may very well decrease the eventual barbecue idea.)

So, overall, the goat at least should decrease my gas/effort/time spent mowing the lawn, decrease my need for Permalawn to fertilize the grass, and decrease my trash output. And, when it dies, be that a week or ten years after I win it, I get a few good barbecues out of it. Let's see a car do all that.
I hear velociraptor tastes like chicken.

User avatar
orthogon
Posts: 3102
Joined: Thu May 17, 2012 7:52 am UTC
Location: The Airy 1830 ellipsoid

Re: 1282: "Monty Hall"

Postby orthogon » Fri Oct 25, 2013 2:02 pm UTC

Klear wrote:
orthogon wrote:Some other variants:
The Monty Burns problem: Opening two of the doors will release the hounds!


The third one has, of course, a bottomless pit.

And then there's the infamous Full Monty variation...

:D The less said about that variation, the better. Some things really should be kept behind closed doors.
xtifr wrote:... and orthogon merely sounds undecided.

cct
Posts: 28
Joined: Wed Mar 14, 2012 1:55 pm UTC

Re: 1282: "Monty Hall"

Postby cct » Fri Oct 25, 2013 2:24 pm UTC

I was led to believe that goats don't like grass. Mind you, they do like the clover, the dandelions, the tulips, and any other plants on your lawn.

As for the Monty Hall Problem: the way I convinced myself was that, the host has information the contestant does not have, and provides some of the extra information to the contestant by opening the door; so, the contestant has no information for making his first choice, but has partial information for making his second choice.

wormspeaker
Posts: 9
Joined: Wed Aug 10, 2011 6:15 pm UTC

Re: 1282: "Monty Hall"

Postby wormspeaker » Fri Oct 25, 2013 2:29 pm UTC

Here is a simple illustration of the possibilities in a single game.

Code: Select all

-----A-------   -----B-------   -----C-------
Car    Cntst   Car    -----   Car    -----
Goat   Monty   Goat   Cntst   Goat   Monty
Goat   -----   Goat   Monty   Goat   Cntst

-----D-------   -----E-------   -----F-------
Car    Cntst   Car    -----   Car    -----
Goat   -----   Goat   Cntst   Goat   Monty
Goat   Monty   Goat   Monty   Goat   Cntst


Result of Switching
A: Lose
B: Win
C: Win
D: Lose
E: Win
F: Win

Result of Not-Switching
A: Win
B: Lose
C: Lose
D: Win
E: Lose
F: Lose

As we can see Switching results in 4 to 2 in favor of winning. Not-Switching results in a 4 to 2 in favor of losing.

rmsgrey
Posts: 3655
Joined: Wed Nov 16, 2011 6:35 pm UTC

Re: 1282: "Monty Hall"

Postby rmsgrey » Fri Oct 25, 2013 2:35 pm UTC

My preferred way of convincing non true-believers is to use an ordinary pack of playing cards. First I explain the procedure: I'll ask them to, without looking at the faces of the cards, pick out the ace of spades. Without them looking at their card, I'll then look through the deck and pick out the ace of spades (or a card at random) and reveal the other 50 cards. then I'll give them the chance to switch cards with me, and whoever ends up with the ace of spades is the winner. Having explained the procedure, I'll then go through it with them a few times. It's fairly obvious that I've got a much better chance of picking the winning card than they do since the only way I won't pick it is if they already have...

With the classic version, I think one of the problems people have is that they've been told the answer when Monty doesn't know which door the car's behind - in that version, it doesn't make a difference whether you switch or not when you happen to be in a case where he didn't reveal the car. Being in a world where Monty could have revealed the car but didn't looks a lot like being in a world where Monty couldn't have revealed the car, but the difference in how you get there makes a difference in the chances of you having picked the car - when you don't pick the car and Monty picks blindly, then you only have a goat revealed half the time, which cancels out it being twice as likely that you missed the car in the first place.

It's profoundly weird that the difference between the two scenarios is in the thing that never actually happens in either so it's understandable that people have trouble with it.

project2051
Posts: 178
Joined: Fri Jan 29, 2010 2:20 pm UTC

Re: 1282: "Monty Hall"

Postby project2051 » Fri Oct 25, 2013 2:37 pm UTC

cellocgw wrote:
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?

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.


For the other greybeards in the thread: "But I must warn you, behind the other 2 doors are narcs!" "Uhhhh... I'll take the reds, man."

ETA - Some new pseudoquiz show on ComedyCentral showed a CraigsList post (ostensibly real, I never tracked it down) from someone trying to give away 2 dozen goats.



The solution is to go with door number 4... and the cleaver.

R3sistance
Posts: 37
Joined: Mon Aug 02, 2010 1:37 pm UTC

Re: 1282: "Monty Hall"

Postby R3sistance » Fri Oct 25, 2013 2:47 pm UTC

dp2 wrote:
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

After 5 games, always switching: 1 wins (20%)
After 10 games, always switching: 5 wins (50%)
After 20 games, always switching: 11 wins (55%)
After 50 games, always switching: 31 wins (62%)
After 100 games, always switching: 65 wins (65%), right about where we expect it.

That's the problem with probability. It's too easy to try once, lose, and think "See? I lost!" I only won 1 in 5 times at first -- that's not going to convince a non-believer.


I never wrote it to convert people :), I wrote it to further understand it. But anyway the page has the facility to simulate runs. The biggest problem with my page is the interface isn't very intuitive, perhaps someday I'll go back and fix that...

Anyway there are three fields, Rounds, Delay (MS) and Switch (%). You can use that to simulate if people were actually playing to get a large sample size and this all works off of javascript so people can verify the fact it works in an unbiased method :P. "Rounds" is essentially the sample size so you can get it to run say 100,000 simulated games.

but to go back to what you are talking about; this would be called a "Hasty Generalization" which is a type of informal fallacy.

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

wolfticket
Posts: 40
Joined: Mon Sep 08, 2008 6:32 pm UTC

Re: 1282: "Monty Hall"

Postby wolfticket » Fri Oct 25, 2013 2:50 pm UTC

Do you know if the host was always going to offer you the switch?
Because if the host knows where the prize is then he could only offer you the switch if the host knows you are already on the prize, in the knowledge that a smart player will always switch.

Other than that, this has been seriously helpful to my brain:
dp2 wrote:The problem boils down to this: If you don't switch, you're saying you guessed right in the first place, when you had only a 1/3 chance.

Thank you :)

User avatar
Klear
Posts: 1965
Joined: Sun Jun 13, 2010 8:43 am UTC
Location: Prague

Re: 1282: "Monty Hall"

Postby Klear » Fri Oct 25, 2013 3:07 pm UTC

dp2 wrote:That's the problem with probability. It's too easy to try once, lose, and think "See? I lost!" I only won 1 in 5 times at first -- that's not going to convince a non-believer.


It should be enough to convince you to stay away from gambling, though =)

User avatar
mojacardave
Posts: 346
Joined: Mon Jul 04, 2011 1:01 pm UTC

Re: 1282: "Monty Hall"

Postby mojacardave » Fri Oct 25, 2013 3:30 pm UTC

Anybody else think this comic was a thinly disguised troll by Randall to get us all bogged down discussing the Monty Hall problem?

User avatar
orthogon
Posts: 3102
Joined: Thu May 17, 2012 7:52 am UTC
Location: The Airy 1830 ellipsoid

Re: 1282: "Monty Hall"

Postby orthogon » Fri Oct 25, 2013 3:43 pm UTC

wolfticket wrote:Do you know if the host was always going to offer you the switch?
Because if the host knows where the prize is then he could only offer you the switch if the host knows you are already on the prize, in the knowledge that a smart player will always switch.

Good point.
wolfticket wrote:Other than that, this has been seriously helpful to my brain:
dp2 wrote:The problem boils down to this: If you don't switch, you're saying you guessed right in the first place, when you had only a 1/3 chance.

Thank you :)

Well, yes, but that's also true in the case where Monty chooses blindly, and in that case there's no advantage to switching.
xtifr wrote:... and orthogon merely sounds undecided.

User avatar
keithl
Posts: 662
Joined: Mon Aug 01, 2011 3:46 pm UTC

Re: 1282: "Monty Hall"

Postby keithl » Fri Oct 25, 2013 3:48 pm UTC

Dammit, Monte, I wanted the door itself! Have you priced game show sets lately?

And we should discuss the goat that drove away with the car. It will not have to pay tags and taxes. A goat able to drive would be incredibly valuable. Perhaps it is friendly with white beret's goat, and will visit frequently, giving its friends fun rides.

Our neighbors just down our suburban street bought a goat. When our new apple trees get tall enough to survive nibbling, perhaps we will buy one, too. We can buy our new goat a car. It can drive it, or eat it.

User avatar
Klear
Posts: 1965
Joined: Sun Jun 13, 2010 8:43 am UTC
Location: Prague

Re: 1282: "Monty Hall"

Postby Klear » Fri Oct 25, 2013 4:01 pm UTC

mojacardave wrote:Anybody else think this comic was a thinly disguised troll by Randall to get us all bogged down discussing the Monty Hall problem?


If so, I believe he's failed so far, to a degree; I don't think anybody who disagrees with the 1:3 thing showed up yet. They'll probably come sooner or later.

User avatar
mojacardave
Posts: 346
Joined: Mon Jul 04, 2011 1:01 pm UTC

Re: 1282: "Monty Hall"

Postby mojacardave » Fri Oct 25, 2013 4:09 pm UTC

Klear wrote:
mojacardave wrote:Anybody else think this comic was a thinly disguised troll by Randall to get us all bogged down discussing the Monty Hall problem?


If so, I believe he's failed so far, to a degree; I don't think anybody who disagrees with the 1:3 thing showed up yet. They'll probably come sooner or later.


To be fair, that may well be to do with the fact that there's a dedicated thread for that argument. I believe it's in the Mathematics subfora. I haven't visited in a while: makes me want to bang my head against a wall.

Edit to add appropriate link.

Endovior
Posts: 12
Joined: Fri Dec 14, 2012 4:10 pm UTC

Re: 1282: "Monty Hall"

Postby Endovior » Fri Oct 25, 2013 4:13 pm UTC

wolfticket wrote:Do you know if the host was always going to offer you the switch?
Because if the host knows where the prize is then he could only offer you the switch if the host knows you are already on the prize, in the knowledge that a smart player will always switch.

Other than that, this has been seriously helpful to my brain:
dp2 wrote:The problem boils down to this: If you don't switch, you're saying you guessed right in the first place, when you had only a 1/3 chance.

Thank you :)


In the classical formulation of the problem, the host is assumed to be required to offer the switch, though this may or may not be explicitly stated. In an interview, Monty Hall himself pointed out that he was in no way required to do so; that's something he'd do to mess with people. (the forum won't let me post a direct link to the article, for whatever reason, but the name of the article is "Behind Monty Hall's Doors: Puzzle, Debate and Answer?"; Google can get you there)

Naturally, in versions of the problem where this is not explicitly stated, the objection of 'this is not a well-formed problem' is entirely valid, as are less-technical objections regarding potential duplicity of the host. Regardless, if the offer isn't explicitly written into the rules, it's not a safe bet in the way the perfect math problem version is.

User avatar
Sprocket
Seymour
Posts: 5951
Joined: Mon Mar 26, 2007 6:04 pm UTC
Location: impaled on Beck's boney hips.
Contact:

Re: 1282: "Monty Hall"

Postby Sprocket » Fri Oct 25, 2013 4:30 pm UTC

<3
I'm happy baret guy is back.
:D
"She’s a free spirit, a wind-rider, she’s at one with nature, and walks with the kodama eidolons”
Image
Image
Image
Image
Image
Zohar wrote: Down with the hipster binary! It's a SPECTRUM!

User avatar
Klear
Posts: 1965
Joined: Sun Jun 13, 2010 8:43 am UTC
Location: Prague

Re: 1282: "Monty Hall"

Postby Klear » Fri Oct 25, 2013 5:25 pm UTC

Endovior wrote:(the forum won't let me post a direct link to the article, for whatever reason, but the name of the article is "Behind Monty Hall's Doors: Puzzle, Debate and Answer?"; Google can get you there)


You'll be able to once you have five posts under your belt. Welcome to the forums, BTW!

User avatar
Wnderer
Posts: 640
Joined: Wed Feb 03, 2010 9:10 pm UTC

Re: 1282: "Monty Hall"

Postby Wnderer » Fri Oct 25, 2013 5:29 pm UTC

How about this form of the game.

1. The object is to pick the Ace of Spades out of a standard deck of 52 cards.
2. You pick a card from the deck but don't look at it.
3. The dealer then throws out 50 cards that are not the Ace of Spades, so the dealer has one card and you have one card.
4. Then you get to choose whether to keep your card ( without looking at it )or switch cards with the dealer.

Should you switch cards?

User avatar
Klear
Posts: 1965
Joined: Sun Jun 13, 2010 8:43 am UTC
Location: Prague

Re: 1282: "Monty Hall"

Postby Klear » Fri Oct 25, 2013 6:06 pm UTC

Wnderer wrote:How about this form of the game.

1. The object is to pick the Ace of Spades out of a standard deck of 52 cards.
2. You pick a card from the deck but don't look at it.
3. The dealer then throws out 50 cards that are not the Ace of Spades, so the dealer has one card and you have one card.
4. Then you get to choose whether to keep your card ( without looking at it )or switch cards with the dealer.

Should you switch cards?


I would switch dealer. This is a boring game.

User avatar
Moose Anus
Posts: 443
Joined: Fri Oct 14, 2011 10:12 pm UTC

Re: 1282: "Monty Hall"

Postby Moose Anus » Fri Oct 25, 2013 6:08 pm UTC

The best way to understand the solution is to imagine 100 doors instead of just 3 doors. You choose a door, he opens 98 non-winners. Now you can choose the 1 door he didn't open or your original door.
Lemonade? ...Aww, ok.

cnaw
Posts: 3
Joined: Mon Apr 30, 2007 7:41 pm UTC

Re: 1282: "Monty Hall"

Postby cnaw » Fri Oct 25, 2013 6:12 pm 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...


You're not confused. You just forgot one little detail: Velociraptors can open doors as well.

Endovior
Posts: 12
Joined: Fri Dec 14, 2012 4:10 pm UTC

Re: 1282: "Monty Hall"

Postby Endovior » Fri Oct 25, 2013 6:15 pm UTC

Klear wrote:
Endovior wrote:(the forum won't let me post a direct link to the article, for whatever reason, but the name of the article is "Behind Monty Hall's Doors: Puzzle, Debate and Answer?"; Google can get you there)


You'll be able to once you have five posts under your belt. Welcome to the forums, BTW!


Ah, figures it'd be something like that. I've actually had an account for quite a while, but I mostly just lurk; posted here in particular because I actually did some research into the topic a month or so back (not quite a GOOMHR moment, but close enough that I felt compelled to point people towards the article in question).

User avatar
Username4242
Posts: 168
Joined: Fri May 01, 2009 9:03 pm UTC
Location: (Previously) Montana State University--Bozeman, Montana.

Re: 1282: "Monty Hall"

Postby Username4242 » Fri Oct 25, 2013 6:20 pm UTC

Piogre wrote:
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.


The easiest explanation I've heard is to extend the problem to 100 doors. Nobody will say that a 1 in 2 chance is similar to a 1 in 100 chance. It's only when three doors are involved that people form a mental block.

EDIT: Oops, was beaten to it.

User avatar
Rorgg
Posts: 78
Joined: Fri Dec 29, 2006 6:06 pm UTC

Re: 1282: "Monty Hall"

Postby Rorgg » Fri Oct 25, 2013 6:22 pm UTC

However, explaining it to math people isn't that much better. In our 4th-semester Probability class, only taken by students of math&CS and to-be math teachers (not e.g. CS&business administration, technical CS, software engineering&internet technology or business math students, with whom we shared many other math classes), the prof asked whether we thought switch was better or whether it didn't matter. I don't remember exactly, I think around half got it wrong. But even after explaining it throughout the lecture, in the end of it still many were not convinced.


I remember trying to explain this to my former brother-in-law, a high school earth science teacher. The logic didn't do it. Analogies didn't do it. Reductio ad absurdum: no. Charts? Nuh-uh. Finally, we just played cup-and-ball style 50 times with him not switching and 50 times with him switching. The practical results were close enough to the predicted to where he SAID he finally believed my assertion -- but still didn't act convinced.

JimsMaher
Posts: 145
Joined: Wed Mar 14, 2012 5:14 pm UTC

Re: 1282: "Monty Hall"

Postby JimsMaher » Fri Oct 25, 2013 8:16 pm UTC

Code: Select all

Car      Goat      Duck      Result
Plyr      Mnty      Stay      WIN!
Plyr      Mnty      Swap      lose
Plyr      Stay      Mnty      WIN!
Plyr      Swap      Mnty      lose
Mnty      Plyr      Stay      ****
Mnty      Plyr      Swap      ****
Stay      Plyr      Mnty      lose
Swap      Plyr      Mnty      WIN!
Mnty      Stay      Plyr      ****
Mnty      Swap      Plyr      ****
Stay      Mnty      Plyr      lose
Swap      Mnty      Plyr      WIN!

**** Monty cannot remove the car.

Plyr = Initial pick
Mnty = what gets removed
Stay = stay with the initial pick
Swap = swap from initial pick to the remaining choice



Swap WIN! ... 2
Swap lose ... 2
Stay WIN! ... 2
Stay lose ... 2

The wise decision is to always swap, to avoid getting yelled at.

project2051
Posts: 178
Joined: Fri Jan 29, 2010 2:20 pm UTC

Re: 1282: "Monty Hall"

Postby project2051 » Fri Oct 25, 2013 8:26 pm UTC

JimsMaher wrote:

Code: Select all

Car      Goat      Duck      Result
Plyr      Mnty      Stay      WIN!
Plyr      Mnty      Swap      lose
Plyr      Stay      Mnty      WIN!
Plyr      Swap      Mnty      lose
Mnty      Plyr      Stay      ****
Mnty      Plyr      Swap      ****
Stay      Plyr      Mnty      lose
Swap      Plyr      Mnty      WIN!
Mnty      Stay      Plyr      ****
Mnty      Swap      Plyr      ****
Stay      Mnty      Plyr      lose
Swap      Mnty      Plyr      WIN!

**** Monty cannot remove the car.

Plyr = Initial pick
Mnty = what gets removed
Stay = stay with the initial pick
Swap = swap from initial pick to the remaining choice



Swap WIN! ... 2
Swap lose ... 2
Stay WIN! ... 2
Stay lose ... 2

The wise decision is to always swap, to avoid getting yelled at.


A strange game. The only winning move is not to play. How about a nice game of chess?

Pi is exactly three
Posts: 44
Joined: Fri Apr 17, 2009 9:33 pm UTC
Location: London, United Kingdom

Re: 1282: "Monty Hall"

Postby Pi is exactly three » Fri Oct 25, 2013 8:38 pm UTC

Username4242 wrote:It's only when three doors are involved that people form a mental block.

The way I make sense of the three-door version is: you pick a door at random, so the probability of the prize being behind it is 1/3. There's a probability of 0 that the prize is behind the door that Monty opens. Since the probabilities must sum to 1, the chance of the prize being behind the remaining door is 1-1/3-0 = 2/3.
"We are the weirdos, Mister!"
--Fairuza Balk, The Craft

I have travelled from 1955 to be a member of the unofficial board Council of Elders. Phear M3

Fritzed
Posts: 15
Joined: Fri Oct 02, 2009 4:58 pm UTC

Re: 1282: "Monty Hall"

Postby Fritzed » Fri Oct 25, 2013 8:38 pm UTC

Piogre wrote:
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.


This youtube video is actually a very well done explanation. Suitable even for those who are not mathematically inclined.

JimsMaher
Posts: 145
Joined: Wed Mar 14, 2012 5:14 pm UTC

Re: 1282: "Monty Hall"

Postby JimsMaher » Fri Oct 25, 2013 8:41 pm UTC

project2051 wrote:
JimsMaher wrote:The wise decision is to always swap, to avoid getting yelled at.


A strange game. The only winning move is not to play. How about a nice game of chess?


http://www.youtube.com/watch?v=NHWjlCaIrQo&t=3m52s

dp2
Posts: 346
Joined: Wed Aug 18, 2010 3:06 pm UTC

Re: 1282: "Monty Hall"

Postby dp2 » Fri Oct 25, 2013 8:52 pm 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...

The lady said to the tiger, as they stood behind some doors,
"I'm sick of this job. I don't know what we're waiting here fors.
I'm turning off life support. I'm putting an end to this joke."
The tiger thought about this, and then the tiger spoke.

"Starving the beast, at the very least, will just increase its hunger.
Go right ahead and starve me dead. It will only make me stronger."

The lady said, "I'm bustin' out of this prison.
I got laser vision, and I'm burning a hole in the wall."
The tiger said "Wait, you'll start a fire,
destroy the entire lady and the tiger hall.

"Felines and dames in flames will hardly serve your aims.
Do you surmise it's wise to have laser beams emitting from your eyes?"

"Point taken, cat. I can well see that our lives are worth protecting,
but I submit it's time we quit this hoping and expecting.

"Felines and dames in flames will hardly serve my aims,
but in my dreams, it seems that my eyes are always shooting laser beams."

The hall remains, it still contains a pair of doors, a choice.
Behind one door, a muffled roar, behind the other, a voice.

http://www.youtube.com/watch?v=ni0Ss-i2b-k

bilkie
Posts: 21
Joined: Wed Sep 19, 2012 5:29 pm UTC

Re: 1282: "Monty Hall"

Postby bilkie » Fri Oct 25, 2013 9:16 pm UTC

I learned about the Monty Hall problem about three years ago, the same week I learned about the McGurk Effect.
Now there is a week to remember.

User avatar
Eebster the Great
Posts: 3484
Joined: Mon Nov 10, 2008 12:58 am UTC
Location: Cleveland, Ohio

Re: 1282: "Monty Hall"

Postby Eebster the Great » Fri Oct 25, 2013 9:41 pm UTC

One really important thing to remember about the Monty Hall problem is that the host knows in advance where the car is and therefore intentionally and always reveals a goat. If this were not the case, and the host simply opened a door at random that happened to be a goat, swapping would give no advantage. This is because if the host is ignorant, and you see him reveal a goat, it either means you picked the car (a 33% probability) or both that you picked a goat and that the host got lucky and picked a goat (a 66% * 50% = 33% probability). The other possibility (that you picked a goat and the host picked the car) just wasn't realized this time, and the remaining possibilities are equally likely, so you have a 50/50 chance either way.

Of course, if you don't know whether the host knew in advance or just got lucky, then you might as well switch anyway, because staying with the first choice will never be beneficial.

mathmannix wrote:Were I to be on the show, I would probably like the goat - especially if I had no need for the car! I mean, if the car is a little sports car, it wouldn't be that practical for me. Plus we already have two cars, and IIRC, when you win a car on a television game show, you still have to pay for taxes, tags, and to get it home from Hollywood Studios, CA to the other side of the country where you live.

Not sure about shipping, but you definitely have to pay taxes, and presumably also title and registration fees. Taxes are the big one though.

Thankfully, at least in theory you only have to pay taxes on the actual value of the car, not the unrealistic, inflated value they advertise on the show.

Goats may be difficult to take care of, but worse case scenario, the goat dies and you eat it, nice family barbecue style. I've had goat, and it's good gravy. Not a bad worse-case scenario. If you can take care of it properly, you at least have a free lawnmower/fertilizer for your lawn, not that the HOA where I live would allow it, but my rural in-laws could definitely make use of it and all these other aspects if that happens, so it's a very nice present.

Yeah, but you're getting a maybe $200 goat rather than a $20,000+ new car. You could always just sell the car.

Bonus: we can think of it as a pet, too - providing companionship just like an outdoor dog.

That's pretty much the point of this comic.

So, overall, the goat at least should decrease my gas/effort/time spent mowing the lawn, decrease my need for Permalawn to fertilize the grass, and decrease my trash output. And, when it dies, be that a week or ten years after I win it, I get a few good barbecues out of it. Let's see a car do all that.

I don't see how putting a goat in your yard is going to be good for the grass . . .
Last edited by Eebster the Great on Fri Oct 25, 2013 9:53 pm UTC, edited 2 times in total.

User avatar
Monika
Welcoming Aarvark
Posts: 3673
Joined: Mon Aug 18, 2008 8:03 am UTC
Location: Germany, near Heidelberg
Contact:

Re: 1282: "Monty Hall"

Postby Monika » Fri Oct 25, 2013 9:52 pm UTC

bilkie wrote:I learned about the Monty Hall problem about three years ago, the same week I learned about the McGurk Effect.
Now there is a week to remember.

They show the McGurk effect with a fairly boring example, ba/fa. The ba/da/ga example is so much better! http://www.youtube.com/watch?v=jtsfidRq2tw
#xkcd-q on irc.foonetic.net - the LGBTIQQA support channel
Please donate to help these people

User avatar
Klear
Posts: 1965
Joined: Sun Jun 13, 2010 8:43 am UTC
Location: Prague

Re: 1282: "Monty Hall"

Postby Klear » Fri Oct 25, 2013 10:26 pm UTC

Eebster the Great wrote:Of course, if you don't know whether the host knew in advance or just got lucky, then you might as well switch anyway, because staying with the first choice will never be beneficial.


Not in the case when the host only ever offers you the switch if you've chosen the car in your initial pick, as a schmuck bait.

Eebster the Great wrote:Yeah, but you're getting a maybe $200 goat rather than a $20,000+ new car. You could always just sell the car.


And buy 100 goats!

Monika wrote:
bilkie wrote:I learned about the Monty Hall problem about three years ago, the same week I learned about the McGurk Effect.
Now there is a week to remember.

They show the McGurk effect with a fairly boring example, ba/fa. The ba/da/ga example is so much better! http://www.youtube.com/watch?v=jtsfidRq2tw


Didn't work for me. I heard "pa pa pa", but if I would have to choose between ba and da (as I knew I should from your post), I'd choose ba.

Might be some oddity in my brain, or possibly it only works for native English speakers...


Return to “Individual XKCD Comic Threads”

Who is online

Users browsing this forum: Google Feedfetcher, Leovan and 105 guests