Women, math, and the Monty Hall problem

[PureX]

Both the math and extensive simulations demonstrate that the odds double by switching doors after one door is revealed to not contain the prize.

Saying that the odds remain 50-50 is like saying that 1 + 1 = 3; the former is just as factually and experimentally incorrect as the latter, albeit far more intuitive.

You tell a story using numbers, and then when the numbers reiterate the story you made them tell you think you've proved some truth that you believed from the start. It's the classic confirmation bias of the "scientism" way of thinkIng. And to prove this, just look at how adamantly those who believe in it hold onto their belief. No degree of skepticism whatever. Which is clearly not a scientific view in any sense of that term. It's more akin to religiosity.

The odds don't "remain" 50/50. They simply are 50/50 for the actual result of the choice that the contestant is actually given.

And 1 + 1 = 3 is correct when it's telling a different story than the one you presumed.

 

[Revoltingest]

How so? Einstein's biggest blunder was that he called the cosmological constant his biggest blunder.

https://pubs.aip.org/physicstoday/Online/30082/Investigating-the-legend-of-Einstein-s-biggest

 

[Revoltingest]

And 1 + 1 = 3 is correct when it's telling a different story than the one you presumed.

This says it all.

 

[ImmortalFlame]

The odds don't "remain" 50/50. They simply are 50/50 for the actual result of the choice that the contestant is actually given.

Except they weren't. They were given a 1/3 chance, and then one of the doors that wasn't picked that didn't contain the prize was opened. The fact that one of the doors was opened to reveal no prize doesn't change the probability related to this choice, the only difference being that one of the doors that DIDN'T contain the prize was opened, essentially meaning the same thing as giving someone 2 attempts at a 1/3 chance - provided they change their door.

Look, you can do this experiment yourself very easily to prove it is mathematically and logically true.

There are three possibilities. Either the prize (green number) is behind door one, door two or door three:

1 2 3
1 2 3
1 2 3

Let's say that the contestant initially picks door 3 (underlined):

1 2 3
1 2 3
1 2 3

In response, Monty opens one of the two doors the contestant didn't pick that DOESN'T contain the prize (red number):

1 2 3
1 2 3
1 2 3

Now, notice above how if the contestant chooses to stick with the door they initially picked, they will have a 1/3 chance of winning the prize. But look below at what happens if the contestant chooses to change their door in all three scenarios:

1 2 3
1 2 3
1 2 3

So, if the contestant changes their choice, they have a 2/3 chance of winning the car.

 

[Heyo]

https://pubs.aip.org/physicstoday/Online/30082/Investigating-the-legend-of-Einstein-s-biggest

It may be that he never said "blunder", instead he used the German term "Eselei", i.e. he called it asinine.

 

[anotherneil]

I wrote a program a long time ago to test this claim and the results showed that it is correct.

An easier way to think of this is to exaggerate the problem. There are 10 doors instead of just 3.




You pick door # 5, and all the doors open except for door # 5 and the door with the car (door # 7).



Now what do you think?

 

[PureX]

Except they weren't. They were given a 1/3 chance,

No, they were never given a 1 in 3 chance of anything. There are no odds of something happening that was never going to happen, and did not, in fact, happen. It amazes me that you all just cannot see this. You have a story in your heads and you just cannot see past it. Nor will you let go of it.

and then one of the doors that wasn't picked that didn't contain the prize was opened. The fact that one of the doors was opened to reveal no prize doesn't change the probability related to this choice, the only difference being that one of the doors that DIDN'T contain the prize was opened, essentially meaning the same thing as giving someone 2 attempts at a 1/3 chance - provided they change their door.

Look, you can do this experiment yourself very easily to prove it is mathematically and logically true.

There are three possibilities. Either the prize (green number) is behind door one, door two or door three:

1 2 3
1 2 3
1 2 3

Let's say that the contestant initially picks door 3 (underlined):

1 2 3
1 2 3
1 2 3

In response, Monty opens one of the two doors the contestant didn't pick that DOESN'T contain the prize (red number):

1 2 3
1 2 3
1 2 3

Now, notice above how if the contestant chooses to stick with the door they initially picked, they will have a 1/3 chance of winning the prize. But look below at what happens if the contestant chooses to change their door in all three scenarios:

1 2 3
1 2 3
1 2 3

So, if the contestant changes their choice, they have a 2/3 chance of winning the car.

 

[PureX]

I wrote a program a long time ago to test this claim and the results showed that it is correct.

An easier way to think of this is to exaggerate the problem. There are 10 doors instead of just 3.




You pick door # 5, and all the doors open except for door # 5 and the door with the car (door # 7).



Now what do you think?

Two doors, two possible results. 50/50 odds of getting either result. Because you don't know whether you picked the car or not, the first time. So you don't know that Monty left the door with the car behind it or not. Yet for some reason, you want to imagine that you do know it. Why?

 

[ImmortalFlame]

No, they were never given a 1 in 3 chance of anything. There are no odds of something happening that was never going to happen, and did not, in fact, happen. It amazes me that you all just cannot see this. You have a story in your heads and you just cannot see past it. Nor will you let go of it.

...

Are you just anti-maths now? Why does this upset you so much? Also, that was literally my only post on this thread. I'm clearly not "not letting go" of anything. I'm just very reasonably and rationally explaining to you the problem, which is an extremely well-known and well-understood mathematical problem that illustrates the separation between cognitive intuition and actual mathematical reality.

Why can't you just admit that you were wrong? Literally, the whole point of the illustration in the first place is to demonstrate natural human fallibility when something seems so obvious and intuitive but is not true. It's perfectly fine to be mislead by the premise - that's what it was designed to do.

 

[ImmortalFlame]

Two doors, two possible results. 50/50 odds of either result.

How do you not get this when it as been illustrated and explained for you as clear as day?

 

[Koldo]

No, they were never given a 1 in 3 chance of anything. There are no odds of something happening that was never going to happen, and did not, in fact, happen. It amazes me that you all just cannot see this. You have a story in your heads and you just cannot see past it. Nor will you let go of it.

The issue is that it is trivial to settle this. We can go over a very simple experiment to check whether there is a 50% chance to make the right choice. But you refuse to do so... why is that? Why do you refuse to verify whether you are thinking about it correctly?

 

[Debater Slayer]

You tell a story using numbers, and then when the numbers reiterate the story you made them tell you think you've proved some truth that you believed from the start. It's the classic confirmation bias of the "scientism" way of thinkIng. And to prove this, just look at how adamantly those who believe in it hold onto their belief. No degree of skepticism whatever. Which is clearly not a scientific view in any sense of that term. It's more akin to religiosity.

The odds don't "remain" 50/50. They simply are 50/50 for the actual result of the choice that the contestant is actually given.

And 1 + 1 = 3 is correct when it's telling a different story than the one you presumed.

Math is not science; it is logic. Mathematical proofs are not a matter of opinion or "telling a story [in the subjective sense]" given that they rely on the facts of logic.

More than one post in this thread includes the solution to the Monty Hall problem with demonstrations of why it is correct, and there are simulations that are readily available online to illustrate that the larger the number of attempts, the more the instances of winning after switching follow the 2/3 odds.

In other posts, you have criticized non-artists for critiquing art or trying to dismiss it. I think dismissing mathematical facts as "scientism" or as a matter of personal opinion can accurately be described as an opposite but similar position—"artism," perhaps: a position whereby mathematical and logically rigorous facts are likened to the subjective and personal as if they were a matter of opinion or subjective assessment similar to art.

 

[Whateverist]

You fell for the illusion that there was a 1/3 - 2/3 option. There never was.

Haven't finished reading this thread but here is another way to look at it.

At the beginning each door had a 1/3 chance of holding the big prize, which is your probability of winning it if there is no switching allowed.

But it is also true that without switching your chance of picking a goat prize is 2/3.

If switching is allowed then probability is still 2/3 that your initial pick was wrong and so switching is the way to go, doubling your chance of winning.

Edited to say, PureX, that your intuition is exactly what makes this problem so hard for so many. I had the same one at first myself.

 

[It Aint Necessarily So]

An illusion was set to numbers and the numbers maintained the illusion. That’s all that happened. And the believers believed it because they believed it to start with.

It's you suffering from an illusion, and it's a common one, which is why the problem has been raised so often and sparks controversy and prolonged discussion. If you were right, nobody would have heard of the Monty Hall problem.

You tell a story using numbers, and then when the numbers reiterate the story you made them tell you think you've proved some truth that you believed from the start. It's the classic confirmation bias of the "scientism" way of thinkIng.

I have no idea where you get these notions or why you believe them. What you saw was a claim well-supported by argument and evidence, but somehow, you describe it like that.

And to prove this, just look at how adamantly those who believe in it hold onto their belief. No degree of skepticism whatever ... You have a story in your heads and you just cannot see past it. Nor will you let go of it.

What we have is solid evidence that trading is always correct. You don't have that evidence because of YOUR confirmation bias, which blinds you to the demonstration that you are wrong.

That is the function of such a confirmation bias - to protect susceptible minds from falsifying evidence. Under the influence of a faith-based confirmation bias, there is no way to demonstrate to one that he is wrong. Having no means of recognizing or correcting an error, he's locked into his wrongness. Such is faith.

Here are some other locked-in minds who are proud to announce that no evidence could ever change those minds - the definition of closed-mindedness and a hallmark of zealous faith-based beliefs like yours:

[1] The moderator in the debate between Ken Ham and Bill Nye on whether creationism is a viable scientific pursuit asked, “What would change your minds?” Scientist Bill Nye answered, “Evidence.” Young Earth Creationist Ken Ham answered, “Nothing. I'm a Christian.” Elsewhere, Ham stated, “By definition, no apparent, perceived or claimed evidence in any field, including history and chronology, can be valid if it contradicts the scriptural record."

[2] "The way in which I know Christianity is true is first and foremost on the basis of the witness of the Holy Spirit in my heart. And this gives me a self-authenticating means of knowing Christianity is true wholly apart from the evidence. And therefore, even if in some historically contingent circumstances the evidence that I have available to me should turn against Christianity, I do not think that this controverts the witness of the Holy Spirit. In such a situation, I should regard that as simply a result of the contingent circumstances that I'm in, and that if I were to pursue this with due diligence and with time, I would discover that the evidence, if in fact I could get the correct picture, would support exactly what the witness of the Holy Spirit tells me. So I think that's very important to get the relationship between faith and reason right..." - William Lane Craig

[3] “If somewhere in the Bible I were to find a passage that said 2 + 2 = 5, I wouldn't question what I am reading in the Bible. I would believe it, accept it as true, and do my best to work it out and understand it."- Pastor Peter laRuffa

 

[Foxfyre]

Well, at one time the 'experts' were the religious leaders - so many might agree with you. It just so happens that it is easier to challenge experts in science than in religions, even when the 'experts' in religions know that there are many other similar 'experts' but who have differing beliefs as to their expertise.

There are many differing opinions among those who are not religious as well and that continues to the present day. You may think a person with scientific credentials should have his word taken as the way it absolutely is. I see too much evidence to think that. In this case I am fully prepared to be wrong in my conclusions though I take a different approach than those trying to convince me I'm an idiot. I don't see that anybody's life will change regardless of who is right.

But you won't convince me that any scientific view is the correct one just because it is popular.

 

[PureX]

How do you not get this when it as been illustrated and explained for you as clear as day?

An illustrated fiction is still an illustrated fiction.

 

[PureX]

...

Are you just anti-maths now? Why does this upset you so much?

Why is it that when I disagree with some of you that you automatically imagine that I'm "upset"? I find that very weird.

Math is just a language we can use to express our experience of reality. It is not the mouth if God, or the fountain of truth, or the determiner of reality.

Also, that was literally my only post on this thread. I'm clearly not "not letting go" of anything. I'm just very reasonably and rationally explaining to you the problem,

There is no "problem". There is a fantasy that was created by a famous game show that some of you have fallen for and cannot see past.

which is an extremely well-known and well-understood mathematical problem that illustrates the separation between cognitive intuition and actual mathematical reality.

Lots of people fall for these things. Casinos are full of them.

Why can't you just admit that you were wrong?

Because I'm not.

Literally, the whole point of the illustration in the first place is to demonstrate natural human fallibility...

Well, your doing that very well.

 

[PureX]

Haven't finished reading this thread but here is another way to look at it.

At the beginning each door had a 1/3 chance of holding the big prize, which is your probability of winning it if there is no switching allowed.

But it is also true that without switching your chance of picking a goat prize is 2/3.

If switching is allowed then probability is still 2/3 that your initial pick was wrong and so switching is the way to go, doubling your chance of winning.

The problem here is that you are calculating probabilities based on something that never happened. You never chose one of three doors. Monty did. You may have intended to choose one, and said which one, but until a door is opened, no new information is being had. And because Monty will choose whichever door has a goat no matter what you do, and because there are two doors with a goat, this action also tells you nothing about which of the other two doors has the goat, or the car.

There is no "extra" information being gained from Monty's theatrics. There is only the illusion of it for those who have fallen for that illusion.

Edited to say, PureX, that your intuition is exactly what makes this problem so hard for so many. I had the same one at first myself.

It's not my intuition. It's just basic logic ... there are two doors and two possible outcomes. And you don't know which door will result in which outcome.

 

[Alien826]

There are many differing opinions among those who are not religious as well and that continues to the present day. You may think a person with scientific credentials should have his word taken as the way it absolutely is. I see too much evidence to think that. In this case I am fully prepared to be wrong in my conclusions though I take a different approach than those trying to convince me I'm an idiot. I don't see that anybody's life will change regardless of who is right.

But you won't convince me that any scientific view is the correct one just because it is popular.

You are absolutely correct that credentials are not any guarantee of accuracy. In fact science runs on this principle. Any theory can be challenged and that process is what enables science to progress towards a better understanding of the world. (Never to arrive at total accuracy, but to get better). What you are maybe missing is a couple of things. Very very basic things have been tested so many times that nobody wastes much time on them. Sometimes a very basic theory is shown to be wrong (like Newtonian physics) and it's true that there is a huge resistance from those that don't want to give up the work of a lifetime. This is not such a case. In this case you are (or would be) challenging very basic arithmetic. Successful challenges are reviewed very carefully by experts in the field before a new theory or a variation on an old one is accepted. That has happened in this thread, at a fairly trivial level. Challenge made. Challenge examined. Challenge rejected.

 

[Revoltingest]

It's not my intuition. It's just basic logic ... there are two doors and two possible outcomes. And you don't know which door will result in which outcome.

This post illustrates that math isn't the problem.
It's the erroneous belief that if there are 2 choices,
the probability of choosing correctly is always 50/50.
It ignores information about the choices.