The scams of Statistics...

[Philosophy Explorer]

I'm always intrigued about how people's minds work, Phil. Are you honestly saying that you can't understand this?

The host knowing a priori doesn't change the relevant facts.

PhilX

[vegetariantaxidermy]

The reason why so many of the greatest mathematicians of our age have been caught out by this puzzle is because they don't listen to the scenario. They immediately see it as a mathematical problem instead of as a prior knowledge problem. The player has one door and thus a 1/3 chance of being right. However the host has two doors and thus a 2/3 chance that the car must lie behind one of them. if it does indeed lie behind one of them he already KNOWS this and is obliged by the terms of the game to pick the other door.

I'm begging you to say that you now get this,Scott, because this is so fucking obvious that it's driving me nuts.

It's also obvious Leo that by opening the third door to reveal the goat, it effectively changes the game to a choice between the first two doors hiding a goat and the car. It's like removing the third door out of play leaving just two doors now and the player doesn't know what the host has in his mind except that the player just knows one door now hides a goat and the other door hides a car making the odds 50/50 whether the car is behind door #1 or door #2.

PhilX

https://www.youtube.com/watch?v=mhlc7peGlGg

This video explains it pretty clearly. When you originally pick a door, your chances of getting a goat are 2/3. That doesn't change. I agree that logically it seems like 50/50 for changing or not changing, but that's not the case. It's been proven.

[Obvious Leo]

I'm always intrigued about how people's minds work, Phil. Are you honestly saying that you can't understand this?

The host knowing a priori doesn't change the relevant facts.

PhilX

It fucking DOES. The prior knowledge of the host IS the relevant fact.

[Philosophy Explorer]

I'm always intrigued about how people's minds work, Phil. Are you honestly saying that you can't understand this?

The host knowing a priori doesn't change the relevant facts.

PhilX

It fucking DOES. The prior knowledge of the host IS the relevant fact.

Are you saying whether or not the host knows what's behind door #3 makes a difference to the other two doors?

PhilX

[Obvious Leo]

This video explains it pretty clearly.

I agree, VT, the video keeps it nice and simple. Do you agree that it confirms what I've been saying all along and that it is the prior knowledge of the host which is the key here.

HE CANNOT OPEN THE DOOR THAT REVEALS THE CAR.

[Obvious Leo]

I do not agree with the claim made in the video that the correct solution is counter-intuitive because animals and small children intuit this scenario perfectly correctly. This is a story about the nature of human cognition and the psychological investment we make in our choices. Neurons that fire together wire together and most people are simply unable to change their minds, even when they're PROVEN WRONG.

[vegetariantaxidermy]

I do not agree with the claim made in the video that the correct solution is counter-intuitive because animals and small children intuit this scenario perfectly correctly. This is a story about the nature of human cognition and the psychological investment we make in our choices. Neurons that fire together wire together and most people are simply unable to change their minds, even when they're PROVEN WRONG.

I have to say I thought it was 50/50 before I saw the video. How did they test it on animals and children? And yes, the host's prior knowledge is crucial, since he bases his choice on what the contestant has chosen. He can't pick the car.

[Philosophy Explorer]

Let me add two more scenarios to see what you think:

Scenario #1: Suppose there were two cars and a goat as possible prizes. Now same as before, the host opens door #3 to reveal the goat. How does this change the odds?

Scenario #2: There are now only two doors hiding a goat and a car. The host tells the player "If there was a third door and I told you a goat was behind it which you accept, would that influence your decision to switch doors?" Does this scenario change the odds?

PhilX

[vegetariantaxidermy]

Let me add two more scenarios to see what you think:

Scenario #1: Suppose there were two cars and a goat as possible prizes. Now same as before, the host opens door #3 to reveal the goat. How does this change the odds?

Scenario #2: There are now only two doors hiding a goat and a car. The host tells the player "If there was a third door and I told you a goat was behind it which you accept, would that influence your decision to switch doors?" Does this scenario change the odds?

PhilX

You are the one changing the odds. When the first door was chosen the odds were 1/3. That doesn't change.

[Obvious Leo]

How did they test it on animals and children?

I don't know how the experiments were performed but this is a fact I've come across several times in my research into cognitive neuroscience, which is where I first came across this puzzle.

Cognitive neuroscience is a critically important discipline for a philosopher of physics to study because modern physics has countless logical paradoxes embedded within it which are likewise entirely due to crappy logic and our psychological investment in our eternal verities. Physicists also try to bulldoze their way through logical fallacies with clever mathematics but it never fucking works, VT. Bullshit is bullshit, whichever way you slice it, and you can't make a silk purse out of a sow's ear, as they say.

[Obvious Leo]

Phil. Try it this way. Let's say you and I are both playing this game and neither of us knows what's behind the doors. You get to pick first but you only get to pick one door whereas I get the other two doors by default. If I asked you to swap before proceeding with the game would you do it?

[Scott Mayers]

Hi guys,

I missed a day online. To get back into this, I originally mentioned to Leo that I see this problem is related to a similar factor concerning the concept of nothing, or zero, as it has been confusing throughout the ages. I'll try another way to show this.

If we begin with the number (or space) zero, we know that dividing it is left undefined because it leads to infinity, which is equally defined. But in using it as a value in a probability argument, it can cause problems. For example:

0 = 0 + 0

Obviously nothing is wrong with this statement. Yet, if these are being used to define an average of results where each thing is being represented as real distinct possibilities, we may run into problems. For instance, let us add the value '1' to each side:

0 + 1 = 0 + 0 + 1

Now, if we were to average the terms as events rather than simply doing what we'd normally do in the math above, we can see that there are 2 terms on the left, and 3 on the right. The averages are

(0 + 1)/2 = 1/2

and

(0 + 0 + 1)/3 = 1/3

This is the root type of cause of the problem occurring in the Monty Hall Problem I'll expand upon. So far, we recognize that the 1/3 average is similar to the initial game as the following possibilities:

0 0 1
0 1 0
1 0 0

Where the '1' is represents where the car would be in each of the above. Notice that these are similar to

0 + 0 + 1 = 0 + 1 + 0 = 1 + 0 + 0

That is, they both are equal representatives derived by the laws of Associativity and Communativity in basic algebra. If we represent the first of each possibility above with a bolded and colored font, and underline what is left over on the right, we have:

0 0 1
0 1 0
1 0 0

The Host can only choose what appears on the right as possibilities where there is a '0' to show. But the error in the puzzle begins when one ignores each '0' in all the underlined pairs as distinct. This is NOT a problem for the first and second '1' rows. But in the last row where there are TWO , not one 0, those believing in the 2/3 solution treats both distinct '0's as one possibility. Taking away the first column we have just the underlined representation:

0 1
1 0
0 0

In the first TWO game possibilities the Host obviously has to select those bolded '0's above. But the third game possibility is where the illusion of this puzzle comes from. They assume that since both a 0 + 0 => 0, they count this as only one possibility rather than two. If you don't get this, ask yourself if the Host can actually reveal both zeros at once in the game? Of course not. Thus, you have to treat this game possibility as two distinct ones such as (I'll underline & bold the Host's reveal):

0 0
0 0

Now do you guys understand the error? We actually end up having four, not three game possibilities. So to fix, it is not 2 wins / 3 possibilities, it is 2 2 wins / 4 possibilities!

[Obvious Leo]

Are we to assume that you refuse to concede that you are wrong, Scott.

How many times do you need to be told that this is not a maths problem?

Are you oblivious to proof?

[Obvious Leo]

As I suspected there might be there is a Monty Hall game running on the internet.

As of now 278,324 contestants decided to stay with their first choice and won a total of 93,286 pretend cars, a success rate of just below 34%

168,244 contestants decided to change their choice and won a total of 111,535 pretend cars, a total of 66%.

Scott. Would you care to name the parties responsible for staging such a massive global conspiracy or would you prefer to apologise to the members of this forum for treating them like morons.

[Scott Mayers]

I've given you sufficient charity with you here Leo and you appear to be only behaving with selective ignorance and abuse with me on this topic. I won't be engaging with you unless you're going to play fair. Either read what I wrote and participate in the arguments given or don't bother. I already know your position and you aren't adding anything new.