Women, math, and the Monty Hall problem

[Evangelicalhumanist]

In deference to the OP by @IndigoChild5559, I have to note that it doesn't seem that RF men are all that more likely to understand this problem than women.

 

[Watchmen]

#Purex, it is not like flipping a coin. If you flip a coin repeatedly over time, eventually you get to 50/50. Not so with the changing the door scenario. It will be 2/3.

 

[Watchmen]

In deference to the OP by @IndigoChild5559, I have to note that it doesn't seem that RF men are all that more likely to understand this problem than women.

Lol

 

[Stevicus]

Which was what? Three boxes?

I think it was a case. I'm not sure, although I just remember looking in her cupboards and finding it packed full of Rice A Roni boxes.

 

[Foxfyre]

But the Monte Hall problem is NOT a choice between 2 things, so at no time in the game are the odds ever 50-50. That is what you are not paying attention to.

The fact that Hall eliminates one of the 3 choices part way through the game at no time ever makes this a binary choice -- it always remains trinary, but you are pretending that your first choice is past and no longer has anything to do with the game, when you are left with only 2. But those 2 are still -- like it or not -- out of 3.

I understand what the Monty Hall Paradox is. But I do not believe it changes the mathematical principle of odds no matter how much that is argued. You start out with three choices. Take away one of the three and you have a 1 in 2 chance of choosing correctly between the other two. That is 50-50 odds or so I was taught in elementary math class. It doesn't matter if a choice has already been made or the psychological dynamics involved. You still have a choice between two things, one good, one bad and a 50-50 chance of choosing the good over the bad.

It doesn't take away the odds just because of the psychological factors involved.

 

[Alien826]

May I submit a general observation?

It's important, when confronted with a puzzle like this, to understand that the "story" being presented is just a way to make it interesting. The actual puzzle depends on certain parameters, that you don't get to alter. I suspect if this one were presented as pure mathematics, those that don't get it would either say "I don't understand" or "please explain it better". Instead we get these diversions based on non-included factors. I'll try to illustrate what I mean with another puzzle.

A man is on one side of a river and needs to get to the other side with all his possessions intact. He has with him a bag of corn, a chicken and a fox. He has a small boat which can hold only two of these things beside himself. If he leaves the chicken with the bag of corn it will eat the corn. If he leaves the fox with the chicken it will eat the chicken. The fox won't eat the corn. If he is present he can stop the bad things happening. What does he do?

When confronted with this puzzle, it's important to stick with the given parameters. No, he can't swim across carrying all three. No he can't call his cousin Fred to help him. No the animals won't run away if he leaves them untended. The fox will catch the chicken, it won't escape up a tree. It doesn't matter what mood he is in, or what the weather is.

 

[Watchmen]

I understand what the Monty Hall Paradox is. But I do not believe it changes the mathematical principle of odds no matter how much that is argued. You start out with three choices. Take away one of the three and you have a 1 in 2 chance of choosing correctly between the other two. That is 50-50 odds or so I was taught in elementary math class. It doesn't matter if a choice has already been made or the psychological dynamics involved. You still have a choice between two things, one good, one bad and a 50-50 chance of choosing the good over the bad.

It doesn't take away the odds just because of the psychological factors involved.

And yet the clinical results show it is NOT 50/50.

 

[Alien826]

I understand what the Monty Hall Paradox is. But I do not believe it changes the mathematical principle of odds no matter how much that is argued. You start out with three choices. Take away one of the three and you have a 1 in 2 chance of choosing correctly between the other two. That is 50-50 odds or so I was taught in elementary math class. It doesn't matter if a choice has already been made or the psychological dynamics involved. You still have a choice between two things, one good, one bad and a 50-50 chance of choosing the good over the bad.

It doesn't take away the odds just because of the psychological factors involved.

That's true if what you said is all that happens, that is Monty simply removes one of the doors. The point is that by choosing to open a door that contains a goat, he has added information that helps the contestant to choose. Of course, that way would possibly remove the car entirely and that changes things.

Edit: It might help if you accepted the answer as presented. Otherwise you are pitting your intuition against a proven result.

 

[Stevicus]

I found this on the page for Monty Hall on Wikipedia, in which he comments on the Monty Hall Problem directly: Monty Hall - Wikipedia

Hall explained the solution to that problem in an interview with The New York Times reporter John Tierney in 1991.[31] In the article, Hall pointed out that because he had control over the way the game progressed, playing on the psychology of the contestant, the theoretical solution did not apply to the show's actual gameplay. He said he was not surprised at the experts' insistence that the probability was 1 out of 2. "That's the same assumption contestants would make on the show after I showed them there was nothing behind one door," he said. "They'd think the odds on their door had now gone up to 1 in 2, so they hated to give up the door no matter how much money I offered. By opening that door we were applying pressure. We called it the Henry James treatment. It was 'The Turn of the Screw.'" Hall clarified that as a game show host, he was not required to follow the rules of the puzzle as Marilyn vos Savant often explains in her weekly column in Parade, and did not always allow a person the opportunity to switch. For example, he might open their door immediately if it was a losing door, might offer them money to not switch from a losing door to a winning door, or might only allow them the opportunity to switch if they had a winning door. "If the host is required to open a door all the time and offer you a switch, then you should take the switch," he said. "But if he has the choice whether to allow a switch or not, beware. Caveat emptor. It all depends on his mood."[31]

So, it didn't always go the same way. There was psychological pressure on the contestant by offering more and more money to switch.

 

[Alien826]

I've decided that I would prefer a goat. I already have a car that I am totally happy with, and I've always wanted a pet goat. What should I do to make my odds better? (Don't try to answer, I'm joking!!!)

 

[Evangelicalhumanist]

I understand what the Monty Hall Paradox is. But I do not believe it changes the mathematical principle of odds no matter how much that is argued. You start out with three choices. Take away one of the three and you have a 1 in 2 chance of choosing correctly between the other two. That is 50-50 odds or so I was taught in elementary math class. It doesn't matter if a choice has already been made or the psychological dynamics involved. You still have a choice between two things, one good, one bad and a 50-50 chance of choosing the good over the bad.

It doesn't take away the odds just because of the psychological factors involved.

Look at what I hilighted -- Nobody "took away" one of your choices: you already made it before you were shown the door with the goat. Your first choice was to guess a door, and you had a 1 in 3 chance -- no more, no less. And your choice, plus what Hall revealed, left with a very different choice: not to pick a door, but to decide whether to change your FIRST choice -- which has already been made and remains part of the problem.

@IndigoChild5559 explained it very well in the OP. After Hall asks you to either stay with your first choice or change it you have a choice between two options, but one of those options is more likely to win than the other -- because of your first choice and what Hall reveals.

Your first choice is just pick a door, and 2/3 of times, that will be a goat, and only 1/3 it will be a car.

So 2/3 of the time, your first choice will be wrong, and only 1/3 of the time will be right.

So if you stay with your first choice, you will be wrong 2/3 of the time.

Who wants to be wrong 2/3 of the time?

 

[Evangelicalhumanist]

Look at what I hilighted -- Nobody "took away" one of your choices: you already made it before you were shown the door with the goat. Your first choice was to guess a door, and you had a 1 in 3 chance -- no more, no less. And your choice, plus what Hall revealed, left with a very different choice: not to pick a door, but to decide whether to change your FIRST choice -- which has already been made and remains part of the problem.

@IndigoChild5559 explained it very well in the OP. After Hall asks you to either stay with your first choice or change it you have a choice between two options, but one of those options is more likely to win than the other -- because of your first choice and what Hall reveals.

Your first choice is just pick a door, and 2/3 of times, that will be a goat, and only 1/3 it will be a car.

So 2/3 of the time, your first choice will be wrong, and only 1/3 of the time will be right.

So if you stay with your first choice, you will be wrong 2/3 of the time.

Who wants to be wrong 2/3 of the time?

Let me sum that up, very briefly.

Choose a door --- 2 out of 3 times you will be wrong.
Decide whether to switch your choice --- if you stay with the choice that had 2 out of 3 chances to be wrong, you're likely to lose.

The second choice you were given was NOT "pick the door with the prize," it was to choose whether to change your first choice. And that is a very, very different thing. It's a lop-sided choice.

 

[We Never Know]

I understand what the Monty Hall Paradox is. But I do not believe it changes the mathematical principle of odds no matter how much that is argued. You start out with three choices. Take away one of the three and you have a 1 in 2 chance of choosing correctly between the other two. That is 50-50 odds or so I was taught in elementary math class. It doesn't matter if a choice has already been made or the psychological dynamics involved. You still have a choice between two things, one good, one bad and a 50-50 chance of choosing the good over the bad.

It doesn't take away the odds just because of the psychological factors involved.

Switching doors after one has been revealed leaving only two doesn't increase your odds between the only two doors left. Those two doors are 50/50.

The whole idea rest upon keeping three doors in the mix.

Using the three doors and two choices(the second is you can switch doors) increases your odds mathematically because you got two choices of the three doors.

 

[blü 2]

Okay, let's try it one post at a time. There are 3 doors, A, B and C. Behind one of them is a car, and behind the other 2 is a goat.

You have to pick a door -- so please tell us which door you've chosen, and what you think the chances are that it has a goat behind it.

(To prevent my cheating, there's a way to show how I chose which door to put the car behind, but I'm keeping it secret for now.)

The middle door.

 

[Koldo]

I think the fallacy of your test is that with 50-50 odds you should win 50% of the time. With 50-50 odds, any person may choose rightly or wrongly 100% of the time in many guesses. But for each guess the odds remain the same. If No. 1 is a good choice and No. 2 is a bad choice I have a 50-50 or 1 in 2 chance of making a good choice. No matter how many times I get to choose between a #1 and a #2, the odds remain the same. Again the Monty Hall Paradox is based on observations that people in a given scenario will behave in a particular way. But it does not change the odds of the choice to be made.

While it is true that 50-50 odds doesn't entail that in the outcome being exactly 50-50, the outcome tends towards that whenever we have large simple size.

If you flip a fair coin ten times in a sequence, how often would you expect to see a sequence of 9 or even 10 equal outcomes? It is a very rare occurence, right? I am going to show the same happening, but regularly.

Give my proposed experiment a try. We can do it multiple times in a row. I don't mind. Tell me 10 numbers from 1 to 100.

 

[Evangelicalhumanist]

The middle door.

What do you think the chances are that Door B has either a goat or a car behind it?

 

[IndigoChild5559]

I understand what the Monty Hall Paradox is. But I do not believe it changes the mathematical principle of odds no matter how much that is argued. You start out with three choices. Take away one of the three and you have a 1 in 2 chance of choosing correctly between the other two. That is 50-50 odds or so I was taught in elementary math class. It doesn't matter if a choice has already been made or the psychological dynamics involved. You still have a choice between two things, one good, one bad and a 50-50 chance of choosing the good over the bad.

It doesn't take away the odds just because of the psychological factors involved.

My friend, it has nothing to do with psychology and everything to do with math. I'm very sorry that you didn't understand the math reasoning; not everyone will.

 

[IndigoChild5559]

What you have to figure out is... Is Monty trying to get you to switch from your door because its a winner or because its a loser.

I think he's just trying to run a highly interesting game show so that his network can make more money.

As an adult, I hate game shows. But I remember being sick at home from school, and Let's Make a Deal was a highlight of my day. That and Twilight Zone reruns. LOL

 

[IndigoChild5559]

But isn't the key, as @PureX said, that the first door eliminated is ALWAYS a NO?

That is, at no stage in the game are the true odds ever 1 in 3.

Your not following.

First, what do you mean "at no stage of the game are the true odds ever 1 in 3"??? Perhaps I'm misunderstanding you, but this is just basic elementary school probability. Second, when you made your first choice, you had a 1/3 chance and that doesn't change just because one door is opened.

Like I said, this is backed up by both computer simulations, and actual experimentation. It's proven every which way you can.

 

[IndigoChild5559]

Okay, let's try it one post at a time. There are 3 doors, A, B and C. Behind one of them is a car, and behind the other 2 is a goat.

You have to pick a door -- so please tell us which door you've chosen, and what you think the chances are that it has a goat behind it.

(To prevent my cheating, there's a way to show how I chose which door to put the car behind, but I'm keeping it secret for now.)

Uhhhhhh Z? j/k I'm sure sometimes you feel like those are the only kinds of answers you get. LOL