Follow the Maths

The place for discussions that don't fit into any of the above categories
Post Reply
User avatar
A. Spruce
Posts: 2225
Joined: Tue Aug 16, 2016 5:23 pm
Location: California, USA

Follow the Maths

Post by A. Spruce » Wed Oct 11, 2017 10:38 pm

I'd like to hear your take on the classic "Monty Hall" problem. Here are three videos to tell you what the problem is and the math behind it. Do you agree with the math and why? Do you disagree with the math, and why?

The original Monty Hall problem.
https://www.youtube.com/watch?v=4Lb-6rxZxx0


The "explanation" of why the maths. You watch the vids and tell me if you agree with your original assessment or agree with the explanation.
https://www.youtube.com/watch?v=7u6kFlWZOWg

Another explanation, may or may not change your mind
https://www.youtube.com/watch?v=mhlc7peGlGg

Here's a movie clip, maybe this will help make sense of the problem?
https://www.youtube.com/watch?v=Zr_xWfThjJ0
I'm CDO, it's the same thing as OCD, but in alphabetical order like it should be! I've also got a touch of AD/OS, Attention Deficit . . . Oh, Shiny!


User avatar
Shannon
Posts: 8645
Joined: Fri Nov 25, 2011 11:58 pm
Location: Canada
Contact:

Re: Follow the Maths

Post by Shannon » Thu Oct 12, 2017 9:38 am

Well I think the math is right even though I have never thought of it in those terms. I think most people would say after the first "goat" is revealed that their chances are 50/50 not 33/66. Very interesting thing look at.
If you've found our videos or website information helpful, please considering pledging us on Patreon

User avatar
Aaron
Posts: 1570
Joined: Sat Jan 03, 2015 4:03 pm
Location: St. Paul, MN

Re: Follow the Maths

Post by Aaron » Thu Oct 12, 2017 9:44 am

It's hard to understand, but I accept its truth!

User avatar
A. Spruce
Posts: 2225
Joined: Tue Aug 16, 2016 5:23 pm
Location: California, USA

Re: Follow the Maths

Post by A. Spruce » Thu Oct 12, 2017 9:56 am

I'm of the 50/50 camp.

Let's suppose you walk into a room and are given a choice between two doors, there are only two door, your odds of winning are 50/50. There is no third door, it never existed.

Now, if you walk into a room with three doors and one of those doors is revealed to you to be fake, you STILL only have two working doors to choose from, do you not? So, how have your odds changed simply because a fake door was revealed? If all doors are left in play, sure, maybe the odds move around a bit, but this is simply not the case, there are only two doors in play.
I'm CDO, it's the same thing as OCD, but in alphabetical order like it should be! I've also got a touch of AD/OS, Attention Deficit . . . Oh, Shiny!

User avatar
Mpmarvin
Posts: 40
Joined: Mon Sep 11, 2017 11:36 pm

Re: Follow the Maths

Post by Mpmarvin » Thu Oct 12, 2017 10:39 am

I would assume they have all the episodes of this game show on tape somewhere. And it should be a large enough sampling size to draw some conclusions. This may hold up. I've seen the new revised show a couple of times just to see if they changed things up and oddly this situation is one of the things they did change. Now you only get one pick at a door. They don't let you switch. My conspiracy side tells me that they've looked at enough samples of the original show to know that this actually holds up in the real world thus the change.

User avatar
Aaron
Posts: 1570
Joined: Sat Jan 03, 2015 4:03 pm
Location: St. Paul, MN

Re: Follow the Maths

Post by Aaron » Thu Oct 12, 2017 12:06 pm

A. Spruce wrote:
Thu Oct 12, 2017 9:56 am
I'm of the 50/50 camp.
I was for a really long time but I think I get it now. I'll try and persuade you.
A. Spruce wrote:
Thu Oct 12, 2017 9:56 am
Let's suppose you walk into a room and are given a choice between two doors, there are only two door, your odds of winning are 50/50. There is no third door, it never existed.
Yes, that would be 50/50 for sure. Two doors, one choice.
A. Spruce wrote:
Thu Oct 12, 2017 9:56 am
Now, if you walk into a room with three doors and one of those doors is revealed to you to be fake, you STILL only have two working doors to choose from, do you not?
But you got the order wrong. You need to make the choice of which of the three doors is fake BEFORE it is revealed to you which of the two remaining doors are fake, then you can elect whether to stay with or switch your choice.

If one door is revealed fake BEFORE you make your choice, that revealed door becomes mathematically irrelevant among the remaining two doors.

For example, pretend it's 100 doors instead of just three. If 98 of them are revealed to be fake before you make any choice, then you are just left with two doors. Same thing.
A. Spruce wrote:
Thu Oct 12, 2017 9:56 am
So, how have your odds changed simply because a fake door was revealed? If all doors are left in play, sure, maybe the odds move around a bit, but this is simply not the case, there are only two doors in play.
So going back to 100 doors. You pick Door 1. Then doors 2-33 are revealed fake, and 35-100 are fake. Do you stay with Door 1 or do you declare Door 34 to be fake?

User avatar
A. Spruce
Posts: 2225
Joined: Tue Aug 16, 2016 5:23 pm
Location: California, USA

Re: Follow the Maths

Post by A. Spruce » Thu Oct 12, 2017 12:37 pm

The problem is, once a door is revealed, it removes it from play, it becomes irrelevant and can no longer be factored into the equation. The choice is narrowed to 2 doors, both have an equal chance of having the prize.

Part of the problem is that virtually any viewpoint can be supported by math, basically, math can be twisted to create the results the observer chooses. IMHO, that is what is going on with this scenario.
I'm CDO, it's the same thing as OCD, but in alphabetical order like it should be! I've also got a touch of AD/OS, Attention Deficit . . . Oh, Shiny!

User avatar
A. Spruce
Posts: 2225
Joined: Tue Aug 16, 2016 5:23 pm
Location: California, USA

Re: Follow the Maths

Post by A. Spruce » Thu Oct 12, 2017 12:51 pm

I found another video by the same guy explaining the problem a different way.
https://www.youtube.com/watch?v=C4vRTzsv4os

I can see how the 33/66 camp arrives at their statistical advantage, unfortunately, they're still wrong! :lol:
I'm CDO, it's the same thing as OCD, but in alphabetical order like it should be! I've also got a touch of AD/OS, Attention Deficit . . . Oh, Shiny!

User avatar
Dia
Posts: 165
Joined: Mon Aug 07, 2017 10:29 am
Contact:

Re: Follow the Maths

Post by Dia » Thu Oct 12, 2017 1:38 pm

This just hurt my brain a little. Like that time Shannon made me calculate the hypotenuse of a triangle for the first time in about a decade to figure out dimensions for my future shed. You trying to keep us sharp, Spruce?

User avatar
A. Spruce
Posts: 2225
Joined: Tue Aug 16, 2016 5:23 pm
Location: California, USA

Re: Follow the Maths

Post by A. Spruce » Thu Oct 12, 2017 2:03 pm

He was teasing you, triangles don't have hippopotamus'! :mrgreen:

Nah, just wondering what your perspective of the game problem is.8-)
I'm CDO, it's the same thing as OCD, but in alphabetical order like it should be! I've also got a touch of AD/OS, Attention Deficit . . . Oh, Shiny!

User avatar
Aaron
Posts: 1570
Joined: Sat Jan 03, 2015 4:03 pm
Location: St. Paul, MN

Re: Follow the Maths

Post by Aaron » Thu Oct 12, 2017 2:16 pm

A. Spruce wrote:
Thu Oct 12, 2017 12:37 pm
The problem is, once a door is revealed, it removes it from play, it becomes irrelevant and can no longer be factored into the equation. The choice is narrowed to 2 doors, both have an equal chance of having the prize.
No! It's not irrelevent at all. That reveal is very important because it completely eliminates any probability *within* the 2/3 probability. Keep with me...

So you have three doors. You pick one. There's ONLY a 1/3 chance it's the good door, right? That means there is a 2/3 chance the two remaining doors you did not pick are good doors. Still with me?

A 2/3 chance is better than a 1/3 chance. The other two doors have a greater possibility of being a good door than just the one door you picked.

So the game host reveals one of the two remaining doors in the group of 2/3 probability that one of them is a bad door. That still does not change the outcome of the other door he did not reveal that you did not initally choose--it still has that original 2/3 probability that it had after you made your first choice!

It's counterintuitive, but it makes sense mathematically.
A. Spruce wrote:
Thu Oct 12, 2017 12:37 pm
Part of the problem is that virtually any viewpoint can be supported by math, basically, math can be twisted to create the results the observer chooses. IMHO, that is what is going on with this scenario.
Well you have to put on your math cap and really suppress your intuition to understand this problem. It helps to think of it at the much larger scale of, say, a million doors.

Say you pick Door #1 out of one million doors. The host reveals 999998 other doors are bad except Door #227443 which you still don't know is bad or good.

Are you going to stick with your Door #1, or switch to Door #227443?

You would be a fool not to switch. Because the first time you made your choice, your chances were a razor thin 1/1000000 it was a good door, and ONE *of* the doors among Door #2 through Door #1000000 are 999999/1000000, or nearly 99% chance it's a good door.

If all EXCEPT ONE of those OTHER doors are eliminated, there is still that 99.99% chance that Door #227443 is the good door, and only the vanishingly small 0.0001% chance your first choice is correct.

If you can apply that same logic to just 3 doors instead of a million doors, it begins to make sense.
Last edited by Aaron on Thu Oct 12, 2017 2:47 pm, edited 1 time in total.

User avatar
A. Spruce
Posts: 2225
Joined: Tue Aug 16, 2016 5:23 pm
Location: California, USA

Re: Follow the Maths

Post by A. Spruce » Thu Oct 12, 2017 2:46 pm

I'm still chewing on this . . .
I'm CDO, it's the same thing as OCD, but in alphabetical order like it should be! I've also got a touch of AD/OS, Attention Deficit . . . Oh, Shiny!

User avatar
Aaron
Posts: 1570
Joined: Sat Jan 03, 2015 4:03 pm
Location: St. Paul, MN

Re: Follow the Maths

Post by Aaron » Thu Oct 12, 2017 2:50 pm

Does the millions of doors make sense? You pick one, and then all but another one are eliminated so there are two left--just the first one you picked and one other?

User avatar
A. Spruce
Posts: 2225
Joined: Tue Aug 16, 2016 5:23 pm
Location: California, USA

Re: Follow the Maths

Post by A. Spruce » Thu Oct 12, 2017 3:25 pm

I am not sold on the idea just yet, however, I do believe that I have found the fly in the ointment that is creating the discord.

I am looking at the problem from the perspective of choice, in which case, it is 50/50 as to whether or not you have chosen the right one. You are coming in from the math side, which is indicating the higher probability that the "unchosen" door has the statistical advantage of winning.

I'm still chewing on it though. :mrgreen:
I'm CDO, it's the same thing as OCD, but in alphabetical order like it should be! I've also got a touch of AD/OS, Attention Deficit . . . Oh, Shiny!

User avatar
emtnut
Posts: 752
Joined: Mon Mar 02, 2015 7:21 am
Location: Canada
Contact:

Re: Follow the Maths

Post by emtnut » Thu Oct 12, 2017 4:04 pm

Aaron wrote:
Thu Oct 12, 2017 2:16 pm


If all EXCEPT ONE of those OTHER doors are eliminated, there is still that 99.99% chance that Door #227443 is the good door, and only the vanishingly small 0.0001% chance your first choice is correct.
What happened to the 0.0099 % :o :shock: :?

:mrgreen:
~~ This space for rent ... apply within :mrgreen: ~~

User avatar
Aaron
Posts: 1570
Joined: Sat Jan 03, 2015 4:03 pm
Location: St. Paul, MN

Re: Follow the Maths

Post by Aaron » Thu Oct 12, 2017 4:20 pm

A. Spruce wrote:
Thu Oct 12, 2017 3:25 pm
I am not sold on the idea just yet, however, I do believe that I have found the fly in the ointment that is creating the discord.

I am looking at the problem from the perspective of choice, in which case, it is 50/50 as to whether or not you have chosen the right one.
No, it's never 50/50.

Your first choice is 33.33/33.33/33.33. Then it's 33.33/66.67 after all the bad doors among your unchosen (which happens to be just one) are revealed. You should switch to the door on the 66.7 side of the probability, rather than remaining on the 33.3 side.

But of course that could be the wrong choice if you luckily picked the good door in the first place despite your odds. Switching would then be a mistake, and you should stay. The host will never tell you that, obviously, and he will reveal at random just one of the two remaining bad doors. But statistically you are always better off switching in the long run.
You are coming in from the math side, which is indicating the higher probability that the "unchosen" door has the statistical advantage of winning.
To be crystal clear, it's a greater probability ONE of the doors AMONG the unchosen doors is a good door. Whether those unchosen doors number two or more (millions), the group of unchosen doors has a higher probability of containing ONE GOOD DOOR than just the door you picked BEFORE all the BAD DOORS among the unchosen are revealed. That is the key. 8-)
I'm still chewing on it though. :mrgreen:
If you don't get it by now, you're just being difficult. ;)
ac47770c-1ac5-4def-8611-ece728401487.jpg
ac47770c-1ac5-4def-8611-ece728401487.jpg (16.84 KiB) Viewed 85 times

User avatar
Aaron
Posts: 1570
Joined: Sat Jan 03, 2015 4:03 pm
Location: St. Paul, MN

Re: Follow the Maths

Post by Aaron » Thu Oct 12, 2017 4:23 pm

emtnut wrote:
Thu Oct 12, 2017 4:04 pm
What happened to the 0.0099 % :o :shock: :?
Got lost in my head. lol

User avatar
Shannon
Posts: 8645
Joined: Fri Nov 25, 2011 11:58 pm
Location: Canada
Contact:

Re: Follow the Maths

Post by Shannon » Thu Oct 12, 2017 4:35 pm

Dia wrote:
Thu Oct 12, 2017 1:38 pm
This just hurt my brain a little. Like that time Shannon made me calculate the hypotenuse of a triangle for the first time in about a decade to figure out dimensions for my future shed. You trying to keep us sharp, Spruce?
I think he has gone off on anther bender and is not thinking straight :o :o
If you've found our videos or website information helpful, please considering pledging us on Patreon

User avatar
A. Spruce
Posts: 2225
Joined: Tue Aug 16, 2016 5:23 pm
Location: California, USA

Re: Follow the Maths

Post by A. Spruce » Thu Oct 12, 2017 4:45 pm

Aaron wrote:
Thu Oct 12, 2017 4:20 pm
you're just being difficult. ;)
The probability is extremely low that I have a choice of being any other way! :P :lol: :lol:

Suffice it to say, I get what the math is saying, I just don't agree with it quite yet.
I'm CDO, it's the same thing as OCD, but in alphabetical order like it should be! I've also got a touch of AD/OS, Attention Deficit . . . Oh, Shiny!

User avatar
A. Spruce
Posts: 2225
Joined: Tue Aug 16, 2016 5:23 pm
Location: California, USA

Re: Follow the Maths

Post by A. Spruce » Thu Oct 12, 2017 4:46 pm

Shannon wrote:
Thu Oct 12, 2017 4:35 pm
I think he has gone off on anther bender and is not thinking straight :o :o
This assumes that I finished the first bender . . . :| :? :shock: :lol: :lol:
I'm CDO, it's the same thing as OCD, but in alphabetical order like it should be! I've also got a touch of AD/OS, Attention Deficit . . . Oh, Shiny!

User avatar
Aaron
Posts: 1570
Joined: Sat Jan 03, 2015 4:03 pm
Location: St. Paul, MN

Re: Follow the Maths

Post by Aaron » Thu Oct 12, 2017 4:47 pm

A. Spruce wrote:
Thu Oct 12, 2017 4:45 pm
Suffice it to say, I get what the math is saying, I just don't agree with it quite yet.
Well just don't go out buying lottery tickets thinking that you have a 50/50 chance of winning. :twisted:

User avatar
A. Spruce
Posts: 2225
Joined: Tue Aug 16, 2016 5:23 pm
Location: California, USA

Re: Follow the Maths

Post by A. Spruce » Thu Oct 12, 2017 4:55 pm

Aaron wrote:
Thu Oct 12, 2017 4:47 pm
Well just don't go out buying lottery tickets thinking that you have a 50/50 chance of winning. :twisted:
Oh, don't worry, I only buy winning lottery tickets. :mrgreen:
I'm CDO, it's the same thing as OCD, but in alphabetical order like it should be! I've also got a touch of AD/OS, Attention Deficit . . . Oh, Shiny!

User avatar
Aaron
Posts: 1570
Joined: Sat Jan 03, 2015 4:03 pm
Location: St. Paul, MN

Re: Follow the Maths

Post by Aaron » Thu Oct 12, 2017 4:59 pm

A. Spruce wrote:
Thu Oct 12, 2017 4:55 pm
Oh, don't worry, I only buy winning lottery tickets. :mrgreen:
You might get the winning ticket, but you'll still have to pick the right door to the lottery HQ building to claim your prize. :lol:

User avatar
A. Spruce
Posts: 2225
Joined: Tue Aug 16, 2016 5:23 pm
Location: California, USA

Re: Follow the Maths

Post by A. Spruce » Thu Oct 12, 2017 5:12 pm

Now who's being difficult, hmmmmm???? :lol:
I'm CDO, it's the same thing as OCD, but in alphabetical order like it should be! I've also got a touch of AD/OS, Attention Deficit . . . Oh, Shiny!

User avatar
Dia
Posts: 165
Joined: Mon Aug 07, 2017 10:29 am
Contact:

Re: Follow the Maths

Post by Dia » Thu Oct 12, 2017 6:05 pm

A. Spruce wrote:
Thu Oct 12, 2017 5:12 pm
Now who's being difficult, hmmmmm???? :lol:
Are you calling Aaron difficult?! Is hell freezing?

User avatar
A. Spruce
Posts: 2225
Joined: Tue Aug 16, 2016 5:23 pm
Location: California, USA

Re: Follow the Maths

Post by A. Spruce » Thu Oct 12, 2017 6:15 pm

He started it! He started it!!


:mrgreen:
I'm CDO, it's the same thing as OCD, but in alphabetical order like it should be! I've also got a touch of AD/OS, Attention Deficit . . . Oh, Shiny!

diytexas
Posts: 41
Joined: Thu Sep 21, 2017 11:39 pm

Re: Follow the Maths

Post by diytexas » Sun Oct 15, 2017 4:36 am

Here ya go spruce

"Actually Monty does you a confusing (to most people) disservice by throwing one away early. If he left the unpicked two doors closed and said you could open them simultaneously, and if you see a car … you win. Almost all would then trade for the two doors." - Don M from https://betterexplained.com/articles/un ... l-problem/


The key is knowing that your first choice is probably wrong. 2/3rds chance. By monty opening a door, the field is narrowed and the odds are increased that the door nobody chose is the car ONLY because the odds are your first choice is wrong.

With monty opening the inevitable goat, and factoring that your first choice is probably wrong, its more likely that its the unchosen door.

User avatar
A. Spruce
Posts: 2225
Joined: Tue Aug 16, 2016 5:23 pm
Location: California, USA

Re: Follow the Maths

Post by A. Spruce » Sun Oct 15, 2017 10:29 am

Thanks for the input, DT, I'll check out the link. 8-)
I'm CDO, it's the same thing as OCD, but in alphabetical order like it should be! I've also got a touch of AD/OS, Attention Deficit . . . Oh, Shiny!

User avatar
emtnut
Posts: 752
Joined: Mon Mar 02, 2015 7:21 am
Location: Canada
Contact:

Re: Follow the Maths

Post by emtnut » Sun Oct 15, 2017 7:26 pm

diytexas wrote:
Sun Oct 15, 2017 4:36 am

If he left the unpicked two doors closed and said you could open them simultaneously, and if you see a car … you win. Almost all would then trade for the two doors."
Hit the nail on the head Texas ;) To me, this makes it a no brainer..... I'm not sure if Sprucey will get it yet, thou :o

:evil: :twisted: :mrgreen:
~~ This space for rent ... apply within :mrgreen: ~~

Post Reply