Women, math, and the Monty Hall problem

[Foxfyre]

Last attempt.

You can't assume that the odds are 50/50. You have to know something (or know that you know nothing) about the choices to assign probability. Once you knew nothing about the position of the car and goats (at the start of the game) the probability has to be assumed to be equal for each door. Once the door is opened, and with the knowledge that Monty will behave in a certain way, we have some information, which allows us to alter our calculation of the probability.

It seems to me that this idea that two choices always have equal probability is the main error being made.

One last example. If I told you that a bag contained 10 marbles, 9 black and 1 white and asked to bet on the possibility of randomly choosing a white marble, what odds would you give? 9-1 against, right? See how information changes probability?

The odds change with the number of options one has.

 

[Alien826]

Did you look at the graph on the Wiki page, given that this is the point. There was a recent article about the coin toss not being exactly 50/50, for the reasons I stated.

No, but I was essentially agreeing with you, and expanding the idea a little.

 

[Foxfyre]

I once worked at a life insurance company. My immediate boss was an actuary (essentially a mathematician that specializes in the probability of mortality). There was another guy who was the head of a different department. He hated all mathematics. In a meeting, if my boss tried to explain something in mathematical terms, he would say "X plus Y" and leave the room. Literally, I've seen him do it.

That is not what I'm doing here though. I simply refuse to see the psychological factor involved in the Monty Hall Paradox as somehow changing the actual odds that exist. One in two chances is one in two. One in ten chances is one in ten. The math doesn't change. The only variable is the psychological factor in play.

 

[Evangelicalhumanist]

That is not what I'm doing here though. I simply refuse to see the psychological factor involved in the Monty Hall Paradox as somehow changing the actual odds that exist. One in two chances is one in two. One in ten chances is one in ten. The math doesn't change. The only variable is the psychological factor in play.

And there you have it....

 

[Mock Turtle]

It's irrelevant information because it's not part of the ACTUAL choice.

For some reason many of you cannot seem to grasp the simple fact that there is only ONE ACTUAL CHOICE being offered. And it only involves two doors, and two possible results.

You seem to fail to grasp that real evidence exists as to the issue being as stated, and it is you who can't appreciate this. As mentioned by others - almost a religious belief in such too. How do you explain the real world results?

 

[Alien826]

That is not what I'm doing here though. I simply refuse to see the psychological factor involved in the Monty Hall Paradox as somehow changing the actual odds that exist. One in two chances is one in two. One in ten chances is one in ten. The math doesn't change. The only variable is the psychological factor in play.

But it's nothing to do with psychological factors. Nobody is suggesting that the tendency to stick with the original choice somehow affects the actual probabilities involved. It doesn't. Sure it affects what choices people actually make, but that's not what this is all about. The question is not what people would do in real life, but what should they do in order to maximize their chances to win the car.

Surely you can see that your gut feel (which at one time was shared by many, even experts) has been totally debunked? How about admitting that, and either making some effort to follow the mathematics (there have been numerous posts to help you) or simply stating that you don't understand it (no shame in that)?

To start, do you understand the principles behind the mathematics of probability? A simple level is all you need. Most people understand "odds" as applied to gambling. I have a feeling that if you did, all this would go away.

 

[Evangelicalhumanist]

Then you either didn't look at the simulation or didn't understand the numbers it generated.

You're essentially saying that all opinions are equal, so since yours is as good as the alternative, you'll stick with it. This is the sine qua non of the Dunning Kruger effect. We saw it often in the Covid vaccine days, when millions went with the opinion of Trump over Fauci, and said that Fauci's recommendation (and by extension, anybody else holding it) was just his opinion as if there were no such thing as expertise or being demonstrably correct.

Too bad you ignored all of the material about the difference between the contestant choosing which door to reveal and the host doing it, and instead, simply repeated yourself with no changes and no indication that you even saw those words much less read and understood them.

Well, you have a 100% chance of choosing the door you want, but only 1 chance in 3 of wining the car if you don't trade, and 2 chances in 3 of winning it if you do. That's what the simulation revealed.

Did you see my graphic on that taken from @Evangelicalhumanist's site?

If so, you didn't understand what it was telling you about your odds of winning the car if you traded versus not. The answer was right there, but only for those who can draw sound conclusions from data or understand that others can, i.e., recognize and have regard for expertise. It's the Dunning-Kruger set who can do neither and settle on wrong decisions because to them, there are no wrong opinions. Isn't that what, "That's just your opinion" means? It means "Mine is just as good."

Yes, that's what we're doing, although I think I'm doing more than just disagreeing with you. I'm also discussing why we disagree.

Dunning Kruger effect indeed!

 

[Evangelicalhumanist]

You seem to fail to grasp that real evidence exists as to the issue being as stated, and it is you who can't appreciate this. As mentioned by others - almost a religious belief in such too. How do you explain the real world results?

He doesn't explain the real-world results. He ignores them, in favour of his "theory."

(What makes this so sad, of course, is that he must then assume that the real world is somehow operating incorrectly -- and he's perfectly happy to do that.)

 

[Foxfyre]

But it's nothing to do with psychological factors. Nobody is suggesting that the tendency to stick with the original choice somehow affects the actual probabilities involved. It doesn't. Sure it affects what choices people actually make, but that's not what this is all about. The question is not what people would do in real life, but what should they do in order to maximize their chances to win the car.

Surely you can see that your gut feel (which at one time was shared by many, even experts) has been totally debunked? How about admitting that, and either making some effort to follow the mathematics (there have been numerous posts to help you) or simply stating that you don't understand it (no shame in that)?

To start, do you understand the principles behind the mathematics of probability? A simple level is all you need. Most people understand "odds" as applied to gambling. I have a feeling that if you did, all this would go away.

I have agreed to disagree. If I'm wrong I'm wrong. But so be it. Since how I perceive the Monty Hall Paradox will have zero effect on my or anybody else's life, can we just leave it at that?

 

[Heyo]

I just separate the psychological factor from the actual math.

Then you are off-topic. We are discussing the maths of the problem, not the psychology.

But we can agree to disagree.

When we can agree that we are talking about different problems.

 

[Revoltingest]

I have agreed to disagree. If I'm wrong I'm wrong.

You're wrong.

Since how I perceive the Monty Hall Paradox....

It's not a paradox.
Just a case of common sense failing
to comport with a mathematical fact.

....will have zero effect on my or anybody else's life, can we just leave it at that?

Why argue about it if it
doesn't matter to you?

 

[Heyo]

I have agreed to disagree. If I'm wrong I'm wrong. But so be it. Since how I perceive the Monty Hall Paradox will have zero effect on my or anybody else's life, can we just leave it at that?

The Monty Hall Problem specifically has no relevance on anybody's life who isn't playing "Let's Make a Deal" at the time.

The thing that does have serious impact on everybody's life is the attitude that's behind your refusal to face reality. It is what leads to very bad decisions.

 

[Foxfyre]

The Monty Hall Problem specifically has no relevance on anybody's life who isn't playing "Let's Make a Deal" at the time.

The thing that does have serious impact on everybody's life is the attitude that's behind your refusal to face reality. It is what leads to very bad decisions.

I accept that you seem to imply that my opinion about what the odds are will no doubt have a terrible influence on your life and the future of humankind. I have no such illusions about my influence on anybody or anything. Do have a pleasant day.

 

[It Aint Necessarily So]

the REASON you would be wrong 2/3 of the time is the propensity of a person to stick with his/her original choice.

Yes, people who never traded would drive home in a new car 1/3 of the time and be wrong the other 2/3 of the time. People whose propensity was to always trade would enjoy the opposite results. They'd be driving home in a new car 2/3 of the time.

And we can solve this combining the results of people who do both if we know their relative frequency, whether that be one person or many.

The odds change from 1 in 3 chances to 1 in 2 chances to make the better choice.

Actually, the odds change from 1 chance in 3 to 2 chances in 3 if he trades, and remains 1 chance in 3 if he doesn't. It is never 1 chance in two if the host chooses which door to reveal. As I explained earlier, the reveal only changes his odds from 1 in 3 to 1 in 2 when the exposed door was chosen by somebody who didn't know where the car was, and revealed a goat, which would happen 2/3 of the time since 2/3 of the doors have goats.

Why are these different? Because the guest will reveal the car 1/3 of the time and the host will never reveal it. The guest's choices of doors and his or her choice of curtains to open each have 1 chance in 3 of selecting the car. If the guest chooses the car with his reveal choice, his chances of having chosen right initially drop to zero. He can trade or not; he has already lost, so his odds remain zero either way.

But apparently, none of this is for you to understand. Like @PureX, you prefer your gut feeling (intuition) to reason, which would work just fine if your gut were a competent mathematician and directed you properly, but it's not.

And that's what faith is - unjustified belief, whether believed "to the bones" or just accepted uncritically form others - and why reason and empiricism are more reliable guides to truth and knowledge than either intuition or blind faith. Although these are each less reliable than critical analysis, they are not equal to one another. Intuition will be correct more often than blind guesses, but not as often as reason.

Spoiler: off-topic digression: What is intuition?

Off-topic digression: What is intuition?

It's a compelling idea that is the answer to a question never asked and comes as a conclusion with none of the work done arriving at it visible to the conscious agent. He can't review the unseen processing to look for errors of fact or logic the way he does with an argument. There is no argument, just a compelling belief that might be correct or not if it hasn't been tested yet, and some such beliefs such as irresistible god beliefs will be untestable.

Here's a good test for deciding when a thought is an intuition: You can't say why you believe it. You find yourself saying, "I can't demonstrate it, and I don't know why I believe it, but it feels right to me." That describes a lot. It describes the commandments from a conscience. Why don't I rape people? I have practical reasons that derive from reason applied to experience which compel me to not break the law, but they don't come from the conscience. The come from legal ramifications and from not wanting to make mortal enemies

The healthy conscience says that even if there would be no consequences - even if the rape victim couldn't retaliate nor the law reach me - I still don't want to do that to somebody, and Ican give no better reason than that my conscience would punish me forever for that because IT considers rape wrong apart from worldly consequences. Why? No reason that I can give. I'm grateful for those moral intuitions, but I can't tell you why my conscience chose what it did.

Here's another intuition: That there is a world on the other side of consciousness. I believe that as do most people reading these words, but why? All we know immediately is our conscious content. We have a compelling intuition that it represents something out there on the other side of the conscious content, but we don't know that, and no experiment can decide whether reality is what we infer it to be from our experience, which we understand intuitively as being a representation of external reality. If your answer to "How do you know that this isn't all a dream or that you aren't a brain in a vat or in some matrix?" What answer can you give better than "I don't know how Iknow that, I just do." None. THAT's intuition.

Instinct is also intuition but related more to behavior than thought. How does an infant know to suckle, and how does it know how to do that? If it could speak and answer, it would have to say, "I don't know how I know either of those. I just do."

Dunning Kruger effect indeed!

A classic example.

You've seen the comment about known knowns, known unknowns, and unknown unknows, right? Rumsfeld got roasted for saying something similar in the Bush years, but it's a valid description of ideas in general.

It's applicable here by analogy:

• Known knowns: We have people who know and know that they are correct, such as the people who could use the data from your Monte Hall problem site do decide what the correct answer is. They're right and they know their right even if some others don't. They possess some degree of expertise.
• Known unknowns: Then we have people who don't know but know that about themselves and know that some others do know. They consult that first group, because they recognize that expertise exists, know where to find it, and know that that will result in a good outcome much more often than consulting a palm reader or vaccine denier, for example.
• Unknown unknowns: This brings us to D-K: "Well, that's just Fauci's opinion. Nobody knows any more than anybody else, and all opinions are equal." They don't know what they don't know.

She's right that in this case, her beliefs won't hurt her because they don't bleed into daily life or any decisions she will make just as a belief in angels is harmless unless it causes you to make bad decisions such as driving drunk under the assumption that a guardian angel will protect you, which is what I mean by bleeding into real life and real life decision making.

 

[Heyo]

I accept that you seem to imply that my opinion about what the odds are will no doubt have a terrible influence on your life and the future of humankind. I have no such illusions about my influence on anybody or anything. Do have a pleasant day.

I guess the "Do have a pleasant day" means that you think the debate is over?
I answer non-the-less, as I'm not only arguing with you, or about the odds of the Monty Hall Problem.

It's not important if you understand the maths, and it's not about you. You are just an example. When I say "you" here, I mean everybody with the same attitude.
You ignore the consensus of experts. You ignore the results of experiments. You think your opinion is more important than expert consensus or reality.
That is a very dangerous attitude, and I think it is worthwhile to point that out.

 

[Stevicus]

Of course. It's all theater to raise the excitement of the audience and to confuse the thinking of the contestant. But in the end, it's two doors and two possible outcomes. (Unless he opts to take the cash buyout.)

Yes, it seems there's a great deal of pressure and other psychological elements in play, which makes it more than just a mathematical puzzle. That's why shell games and three-card monte type games are considered unscrupulous, unethical, and illegal in most jurisdictions I'm aware of. They also use confederates and shills, with a less than honest dealer, to confuse the player and influence his/her bet. The difference in "Let's Make a Deal" is that the contestants aren't gambling anything. They have nothing to lose, except maybe their dignity. Some people thought it was fun.

I think "The Price is Right" was actually more popular. Of course, every game had its own mini-commercials, as every product up for grabs was touted to the audiences at home. A much more lucrative scam than a petty game of three-card monte.

 

[Foxfyre]

I guess the "Do have a pleasant day" means that you think the debate is over?
I answer non-the-less, as I'm not only arguing with you, or about the odds of the Monty Hall Problem.

It's not important if you understand the maths, and it's not about you. You are just an example. When I say "you" here, I mean everybody with the same attitude.
You ignore the consensus of experts. You ignore the results of experiments. You think your opinion is more important than expert consensus or reality.
That is a very dangerous attitude, and I think it is worthwhile to point that out.

If nobody ever challenged the consensus of 'experts', we would still be living in the dark ages.

 

[Evangelicalhumanist]

If nobody ever challenged the consensus of 'experts', we would still be living in the dark ages.

Not quite. People with better information can challenge the consensus of experts, to our general benefit. People ignorant of the workings of the expert's field are far more likely to be wrong than right, and end up doing more harm than good. That's why so many conspiracy theories and medical disinformation are so harmful.

 

[Foxfyre]

Not quite. People with better information can challenge the consensus of experts, to our general benefit. People ignorant of the workings of the expert's field are far more likely to be wrong than right, and end up doing more harm than good. That's why so many conspiracy theories and medical disinformation are so harmful.

I'm sympatico with Joe Manchin who recently declared Nobel Laureates who were advising Biden on COVID policy as "17 educated idiots." I yield to the experts on things I don't know. and accept that consensus can be a reasonable method of reaching a decision But I still maintain that when it is deemed improper or stupid or illegal to logically challenge an 'expert' opinion, we are not dealing with science or math or anything credible but are rather dealing with dogma. And logical people have long known that consensus is not always a reliable factor. That something is popular does not necessarily make it right.

 

[Revoltingest]

I guess the "Do have a pleasant day" means that you think the debate is over?
I answer non-the-less, as I'm not only arguing with you, or about the odds of the Monty Hall Problem.

It's not important if you understand the maths, and it's not about you. You are just an example. When I say "you" here, I mean everybody with the same attitude.
You ignore the consensus of experts. You ignore the results of experiments. You think your opinion is more important than expert consensus or reality.
That is a very dangerous attitude, and I think it is worthwhile to point that out.

Worse....to not know the math,
but to claim to know it, & apply it,
getting the incorrect result despite
having been shown simple proofs.