Women, math, and the Monty Hall problem

[beenherebeforeagain]

but she ended up with a year's supply of Rice-A-Roni.

Which was what? Three boxes?

 

[Subduction Zone]

It's still just a shell game. A guessing game.

Besides, as I recall in "Let's Make a Deal," the final three doors usually contained one "zonk," while there was usually a mid-level prize, like a living room set or a refrigerator, while the "big deal" was the car. They also had consolation prizes, usually provided by the sponsors. My mom was on a game show and lost, but she ended up with a year's supply of Rice-A-Roni.

Okay, in real life it was not like that. But the host in the Monty Hall problem always has three boxes with two goats and he always reveals one box after the person makes his choice. One has to remember that in the Monty Hall problem that Monty obviously knows.

 

[Evangelicalhumanist]

It's also false. The odds remain 50/50 regardless what door you choose, or what door Monty opens.

The 3 doors are just theater because one is eliminated before you choose. And the one eliminated is always a goat. So the proposition was always 2 doors, and one with a car. This is why there is no mathematical way of proving your odds increased. Because there was no change in the odds. It was just irrelevant theater. There is only one choice, and two possible outcomes ... therefor 50/50 chance that the outcome will be the car and 50/50 that it will be the goat.

You are too sure of yourself. See:

Monty Hall problem - Wikipedia

en.wikipedia.org

 

[Foxfyre]

And your math is bad. Like most people you forgot that Monty knows. When there are two doors left he can always show a contestant a goat. In effect you are changing from only have one chance to having two.

Do you remember the TV show Mythbusters? They did an episode where they tested this and it works. The problem is a bit misleading because people forget the fact that Monty is not totally honest since he knows.

How does that make my math bad? Introducing a psychological element does not change the math. If one of two choices is the correct one, I have a one in two chance of making the correct choice. And that is regardless of anything Monty says that influences my choice.

 

[Subduction Zone]

How does that make my math bad? Introducing a psychological element does not change the math. If one of two choices is the correct one, I have a one in two chance of making the correct choice. And that is regardless of anything Monty says that influences my choice.

It tells us that you do not understand the problem.

Here is a simple question. If after a contestant made his choice he or she was always given a chance to change their original choice for the other two boxes would their odds change?

 

[Foxfyre]

It tells us that you do not understand the problem.

Here is a simple question. If after a contestant made his choice he or she was always given a chance to change their original choice for the other two boxes would their odds change?

The odds no even though I know that is the argument presented in the OP. The psychological element guiding one's choice, yes.

 

[Eddi]

That's some mind-bending stuff

 

[Subduction Zone]

The odds no even though I know that is the argument presented in the OP. The psychological element guiding one's choice, yes.

The first concept dealt with in this video covers this problem:

Let me change the problem just a bit for you. Instead of three doors there are 100. There is one car and 99 goats. You pick a door. The host then opens 98 doors, all of them have goats behind them. There is one door left. Do you switch or do you stick with your first door.

EDIT: Okay, you have to skip to 13:05 in the video when part one ends.

 

[Mock Turtle]

Both logically and mathematically the odds are 50/50 for and against choosing the car.

The test results are irrelevant because the odds are equal. Flip a coin 100 times and the "test results" will almost certainly not be 50/50. Nevertheless, the odds remain 50/50 for every coin flip, no matter how many times we test it.

Perhaps flexible thinking is involved here rather than being dogmatic, especially with having to explain the practical results obtained - which demonstrate the truth of changing. Would you ignore practical demonstrations for anything similar that coincided with theory?

 

[Foxfyre]

The first concept dealt with in this video covers this problem:

Let me change the problem just a bit for you. Instead of three doors there are 100. There is one car and 99 goats. You pick a door. The host then opens 98 doors, all of them have goats behind them. There is one door left. Do you switch or do you stick with your first door.

EDIT: Okay, you have to skip to 13:05 in the video when part one ends.

Whether I switch or not depends on what I psychological, mental, emotional importance I put on how I read Monty or whether I put any importance on it at all. But the fact remains that I have a 1 in 2 chance of making the correct choice. The criteria that determines my choice does not change that.

The "Monty Hall Paradox" involves statistical probability of the choice made based on observable human nature and the skill to manipulate that, but it does not change the odds involved in the choice. Once people are told they should switch, the calculated manipulation of human nature will of necessity change as well.

 

[Evangelicalhumanist]

Look, it really is quite simple:

At the start, when you have 3 doors to choose from, each door has a 1/3 chance that there's a prize behind it:

Door A = 1/3, Door B = 1/3, Door C = 1/3

Once you choose a door (let's say Door A), there is a 1/3 chance the prize is behind it, and a 2/3 chance that the prize is behind one of the other two doors (B and C). When the host opens another door (let's say C), with no prize, there is still a 2/3 chance that the prize is behind B or C, but now you know it's not C. So that 2/3 chance is now all on door B.

So your odds are now

A = 1/3 (nothing changed about that first choice)
B = 2/3

So change your choice..

 

[Subduction Zone]

Whether I switch or not depends on what I psychological, mental, emotional importance I put on how I read Monty or whether I put any importance on it at all. But the fact remains that I have a 1 in 2 chance of making the correct choice. The criteria that determines my choice does not change that.

The "Monty Hall Paradox" involves statistical probability of the choice made based on observable human nature and the skill to manipulate that, but it does not change the odds involved in the choice. Once people are told they should switch, the calculated manipulation of human nature will of necessity change as well.

No, psychology does not enter into the problem at all. It is simply a matter of statistics. If one switches the odds are two out of three that one will win. If one does not switch the odds are only one out of three that one will win.

Why are you even bringing psychology into this discussion? Yes, people will often make the error of not switching due to an inherent resistance to change. But that does not affect the odds at all.

 

[Foxfyre]

No, psychology does not enter into the problem at all. It is simply a matter of statistics. If one switches the odds are two out of three that one will win. If one does not switch the odds are only one out of three that one will win.

Why are you even bringing psychology into this discussion? Yes, people will often make the error of not switching due to an inherent resistance to change. But that does not affect the odds at all.

I bring psychology into it because that is what is being described in the video and hypothesis. If I have a choice of two hidden things, one being good and the other not, no amount of mathematical equations changes the fact that I have a one in two chance of choosing the good thing. It doesn't matter how many choices I started with. The only intangible factor is the psychology involved in a game show or similar situations.

 

[Alien826]

No, psychology does not enter into the problem at all. It is simply a matter of statistics. If one switches the odds are two out of three that one will win. If one does not switch the odds are only one out of three that one will win.

Why are you even bringing psychology into this discussion? Yes, people will often make the error of not switching due to an inherent resistance to change. But that does not affect the odds at all.

There's one aspect of psychology that does stand out here. That is that some people will stick rigidly to a given perception regardless of how many facts that point to something different are presented. That may be a more valuable observation than the puzzle itself.

 

[Kathryn]

All I know is that I am going to switch most likely.

 

[Evangelicalhumanist]

I bring psychology into it because that is what is being described in the video and hypothesis. If I have a choice of two hidden things, one being good and the other not, no amount of mathematical equations changes the fact that I have a one in two chance of choosing the good thing. It doesn't matter how many choices I started with. The only intangible factor is the psychology involved in a game show or similar situations.

Please look at Post #31. The explanation shows that there is no psychology involved. Only that you first choice is always just 1 chance in 3 of being correct. That leaves 2 chances in 3 of one of the other doors, which you did not choose, is the correct one. The fact you are shown that one of those 2 is incorrect does not change that.

By showing you that one of those other 2 choices is wrong does not change the odds that 1 of them is still correct -- and since that is 2 chances in 3, the host has actually given you help to make the optimal choice, which is to change your first pick.

 

[Foxfyre]

Please look at Post #31. The explanation shows that there is no psychology involved. Only that you first choice is always just 1 chance in 3 of being correct. That leaves 2 chances in 3 of one of the other doors, which you did not choose, is the correct one. The fact you are shown that one of those 2 is incorrect does not change that.

By showing you that one of those other 2 choices is wrong does not change the odds that 1 of them is still correct -- and since that is 2 chances in 3, the host has actually given you help to find make the optimal choice, which is to change your first pick.

But sticking with one's first choice is a psychological thing, not a mathematical thing. The only mathematics involved are the statistics of people who stick with their first choice.

I am not one who usually does that at least as a rule. So based on my own experience, I might question whether the statistics cited about choice are really that accurate. But my experience could certainly also be an anomaly. I just know that regardless of how many choices I start with, once I'm down to the last two, the odds I have to make the best choice or one in two.

 

[Evangelicalhumanist]

But sticking with one's first choice is a psychological thing, not a mathematical thing. The only mathematics involved are the statistics of people who stick with their first choice.

I am not one who usually does that at least as a rule. So based on my own experience, I might question whether the statistics cited about choice are really that accurate. But my experience could certainly also be an anomaly. I just know that regardless of how many choices I start with, once I'm down to the last two, the odds I have to make the best choice or one in two.

You may think that you know that -- but you would be wrong. And that is easily demonstrated in an experiment. Just have somebody you know to be honest hide a prize behind one of 3 doors (you don't need real doors or a real prize -- this can all be done in the imagination). Then:

You choose a door.
Your friend says "let me show you another door (which they know isn't correct) -- and there is no prize behind it. Do you want to change your guess?"
You say "no," and then have your friend "reveal" what's behind your choice.

Do the above 100 times, and then repeat it 100 times except that you say "yes" when asked to change doors.

You will find that if you say "no, don't change," you will win about 33 times, and lose about 66 times And you will find that if you say "yes, change doors," you will win about 66 times and lost about 33 times.

There is no psychology in the above test -- none at all.

By the way, if you vary your choice, sometimes saying "change" and sometimes "don't change," you might get as high as 50 times out of a hundred. But 66 times is still better than 50 times.

 

[Foxfyre]

You may think that you know that -- but you would be wrong. And that is easily demonstrated in an experiment. Just have somebody you know to be honest hide a prize behind one of 3 doors (you don't need real doors or a real prize -- this can all be done in the imagination). Then:

You choose a door.
Your friend says "let me show you another door (which they know isn't correct) -- and there is no prize behind it. Do you want to change your guess?"
You say "no," and then have your friend "reveal" what's behind your choice.

Do the above 100 times, and then repeat it 100 times except that you say "yes" when asked to change doors.

You will find that if you say "no, don't change," you will win about 33 times, and lose about 66 times And you will find that if you say "yes, change doors," you will win about 66 times and lost about 33 times.

There is no psychology in the above test -- none at all.

By the way, if you vary your choice, sometimes saying "change" and sometimes "don't change," you might get as high as 50 times out of a hundred. But 66 times is still better than 50 times.

We can agree to disagree.

 

[Evangelicalhumanist]

We can agree to disagree.

Yes, I'm sure we can. But since I gave you the means to test the truth for yourself, and you choose to believe without bothering to try it, you've lost a learning opportunity. I myself try never to miss those.