The Monty Hall Paradox

I gotta mention, where I live goats are almost as valuable as cars, and ya can't milk a car...

RH

0 Replies

Oh yea? where you come from, there's other stuff you can't do with a car either, and some things people from other places wouldn't do with a goat.

foxy...here's where you're having the problem....

you've got to stop thinking that you're being given a new situation. It IS all based on your initial 3 choices.

There a 1/3 chance that you will pick the car, a 1/3 chance Monty will pick the car, and 1/3 chance no one will pick the car.

Monty always picks a goat, so his 1/3 is subtracted from the equation....

3/3 minus 1/3 = 2/3's

so you can stick with your choice, staying with your 1/3 chance of getting the car, or, realizing that you now have 2/3 of a chance at picking the car, you make another choice, picking the other.

In other words the 3 doors still exist, that's the common denominator. That 3rd door, which is the one Monty picks, would have to have ceased to exist before Monty even made his choice, in order for it to be a choice between 2 doors, not 3.

What if there were 15 doors, and both you and monty could each pick 5?

You need to pick 3 doors with cars in order to win one.

you pick 5 doors, he picks 5 doors, all with goats.

Now, you have the chance to stay, or chose up to 5 different doors....you would obviously make at lease a couple of switches, knowing you have a better chance of ensuring you have 3 cars.

Same principle.

0 Replies

Fox,

Did you bother to read the "How it works" tab on the site?

It explains it with pictures.

0 Replies

First of all, to get me to watch a game show would involve ropes or several strong humans.

I did watch the 64,000 question, at the time. And, years later, one of my life's good friends was associated with the van doren family. But past all that, I apparently have had a growing-over-decades distaste for the shill talk on many tv shows, including news, whatever channel. I am now allergic to circus barker vocalization, no matter who from. Or whom from.

It also happened that a girlfriend in my classes, now a lifelong friend, fell in love with a guy, and married him, and somewhere around that time, he was a long time winner on some show where they couldn't get him off. Weeks and weeks went by, close to a season. I was told what happened, but, hey, I forget, truthfully, since I wasn't following it - I think I had moved by then. Maybe they worked out some deal to get him off. Fortunately I forget the name of the show, but it was one of the early ones. He won everything under the kazoo, and maybe even the kazoo, a very bright fellow.

Anyway, those shows do award people stuff.

0 Replies

Right.

When I got to switch/don't switch I tossed a coin.

Heads for switch, tails for don't switch.

I got 11 heads and 9 tails in 20.

My prizes were 13 goats and 7 cars.

You're a bunch of saps as I said at first. 'Cept Foxy of course.

Intelligent design proponents know best.

0 Replies

This is an old one but a good one because it's counter intuitive so most people get it wrong.

You should always switch.

The easiest way to visualize this is to increase the number of doors in the game. Imagine the same rules applied to 100 doors. You pick a door at random. Monty then reveals 98 doors but he is only allowed to reveal doors with goats behind them. There are two doors remaining, the door you picked and the one Monty didn't open. Obviously you switch to the remaining door because the chance you picked the right door in the beginning is very small leaving the probability for the last remaining door very high.

0 Replies

Foxfyre wrote:

So gut level, Joe, do you think the on line game was rigged to demonstrate "proof" for the theory of probability here? Or is the theory of probability the real deal?

The game is not rigged (they don't need to rig it to make it work). And the "theory" is a fact.

0 Replies

The explaanation on Wikipedia actually makes more sense to me than the one from the original NY Times article.

http://en.wikipedia.org/wiki/Monty_Hall_problem

I do find the whole thing confusing though because, unless my mind is playing tricks on me, there were never 2 goats on Let's Make a Deal. For some reason I seem to recall that there was usually a car (or boat) as the "big prize", furniture or appliances as a mid-level prize and a goat or donkey as the booby prize.

I'll have to watch some old episodes on the Game Show Network to refresh my memory. Maybe I'm thinking of some other show...

0 Replies

Can't you read ros?

Or is 20 tries not enough for you to cease you gormless technical wizadry mumbo-jumbo.

I switched 11 times in 20.

You don't seem to be able to understand that once you are down to two door and you can choose your first choice is irrelevant. It's a time waster to provide space for more ads while you scientific nerds are trying to kid yourself that it's rocket science in order to be thought a rocket scientist as long as you restrict your relationships to thickies.

Think Occam and meanwhile keep away from classrooms.

0 Replies

spendius wrote:

Can't you read ros?

Or is 20 tries not enough for you to cease you gormless technical wizadry mumbo-jumbo.

I switched 11 times in 20.

You don't seem to be able to understand that once you are down to two door and you can choose your first choice is irrelevant. It's a time waster to provide space for more ads while you scientific nerds are trying to kid yourself that it's rocket science in order to be thought a rocket scientist as long as you restrict your relationships to thickies.

Think Occam and meanwhile keep away from classrooms.

And your experimental error was that you used a coin to decide whether to switch or not to switch. That supposedly random coin only undid the 2/3 advantage that Monty gave you when he showed you a door where the car wasn't.

Occam is the simpler logical explanation that is not necessarily the emotional response. With emotional logic like that---the sun would still be rotating around the earth.

Rap

0 Replies

And yes, yes, and yes to everybody who suggested that I read the explanations and look at the pictures, etc. etc. etc. I have done all that and I am still left with the original problem.

1. In the beginning I have three doors to choose from with a 1 in 3 chance to choose the right door.

2. It is an absolute certainty that at least one door that I didn't choose will be a goat. If I chose a goat initially, he will open the door with the other goat. If I chose the car initially he will choose one of the two goats. The door with the goat that he opens is then removed from the equation.

3. Now I have a choice between two doors. It really doesn't matter whether I chose right or wrong initially. I now am essentially choosing between two doors.

4. I now have a 1 in 2 chance of choosing the right door.

I'm sorry folks, but that is a 50-50 chance no matter how you slice it.

0 Replies

spendius wrote:

Right.

When I got to switch/don't switch I tossed a coin.

Heads for switch, tails for don't switch.

I got 11 heads and 9 tails in 20.

My prizes were 13 goats and 7 cars.

You're a bunch of saps as I said at first. 'Cept Foxy of course.

Intelligent design proponents know best.

You are mixing sardines and kumquats, and throwing in a bag of chips to boot.

Do you not see that you are creating more choices over and above the original switch/don't switch?

First you are tossing a coin, which only has 2 outcomes, heads or tails.

Then, based on this one out of 2 proposition, you switch or don't switch. Over 10 trys, the probability is half of the time you will do something that you would not have original done.

Try the experiment again, the proper way.

First you take your 10 chances, always sticking with "switch", then take another 10 chances, always switching.

You're throwing in extra conditions, thinking we are too dense to see it.

Surely you know you are doing that.

0 Replies

Foxfyre wrote:

3. Now I have a choice between two doors. It really doesn't matter whether I chose right or wrong initially. I now am essentially choosing between two doors.

4. I now have a 1 in 2 chance of choosing the right door.

I'm sorry folks, but that is a 50-50 chance no matter how you slice it.

NO, NO, NO!

You still have a choice among THREE doors.

Did the third door blink out of existance a nano second before Monty made his choice?

Whether or not you are permited to take Monty's door does not matter. It is there.

0 Replies

(You're doing a good job, Chai.)

(raprap and ros too...)

0 Replies

Foxfyre wrote:

And yes, yes, and yes to everybody who suggested that I read the explanations and look at the pictures, etc. etc. etc. I have done all that and I am still left with the original problem.

1. In the beginning I have three doors to choose from with a 1 in 3 chance to choose the right door.

2. It is an absolute certainty that at least one door that I didn't choose will be a goat. If I chose a goat initially, he will open the door with the other goat. If I chose the car initially he will choose one of the two goats. The door with the goat that he opens is then removed from the equation.

3. Now I have a choice between two doors. It really doesn't matter whether I chose right or wrong initially. I now am essentially choosing between two doors.

4. I now have a 1 in 2 chance of choosing the right door.

I'm sorry folks, but that is a 50-50 chance no matter how you slice it.

Try it using the example I gave... If you had 100 doors to choose from and after you picked one, Monty revealed 98 goats. Would you switch to the remaining unopened door, or keep your first guess? Then ask yourself the same question about 50 doors, 10 doors, 5 doors, 4 doors. The 3 door problem is the same, just a smaller difference.

0 Replies

If you end up with two doors and you don't know what's behind each it's 50-50. End of story. Emotions don't come into it. That's voodoo.

Your explanations mean you get the car every time. Not just mostly.

0 Replies

If you get the car everytime you switch then while the ads are playing and you saps are on the edge of your seats running your science number on yourself they just put the car where they want it to be.

Like I said--it's a prolonged ad for the car with others added for fun.

0 Replies

Foxfyre wrote:

And yes, yes, and yes to everybody who suggested that I read the explanations and look at the pictures, etc. etc. etc. I have done all that and I am still left with the original problem.

1. In the beginning I have three doors to choose from with a 1 in 3 chance to choose the right door.

2. It is an absolute certainty that at least one door that I didn't choose will be a goat. If I chose a goat initially, he will open the door with the other goat. If I chose the car initially he will choose one of the two goats. The door with the goat that he opens is then removed from the equation.

3. Now I have a choice between two doors. It really doesn't matter whether I chose right or wrong initially. I now am essentially choosing between two doors.

4. I now have a 1 in 2 chance of choosing the right door.

I'm sorry folks, but that is a 50-50 chance no matter how you slice it.

The question you are answering isn't the question that was asked. The question asked is "Are you better off switching?".

Since you admit in your step #1 that you have a 1 in 3 chance of picking the car then you also have to admit that you have a 2/3 chance of picking a goat on your first door.

That being the case, you are better off if you change your initial pick 2 out of 3 tries. The try attempts don't get reset half way through the process (which is where you get your 50/50). Each try starts when you are presented with the 3 doors.

0 Replies

spendius wrote:

If you end up with two doors and you don't know what's behind each it's 50-50. End of story. Emotions don't come into it. That's voodoo.

Your explanations mean you get the car every time. Not just mostly.

Where has anyone mentioned emotions?

You don't "end up" with 2 doors, you have 3 doors.

And the Lord spake, saying, "First shalt thou take out the Holy Pin. Then shalt thou count to three, no more, no less. Three shall be the number thou shalt count, and the number of the counting shall be three. Four shalt thou not count, neither count thou two, excepting that thou then proceed to three. Five is right out. Once the number three, being the third number, be reached, then lobbest thou thy Holy Hand Grenade of Antioch towards thy foe, who, being naughty in my sight, shall snuff it.

0 Replies

Chai wrote:

spendius wrote:
If you end up with two doors and you don't know what's behind each it's 50-50. End of story. Emotions don't come into it. That's voodoo.

Your explanations mean you get the car every time. Not just mostly.

Where has anyone mentioned emotions?

You don't "end up" with 2 doors, you have 3 doors.

And the Lord spake, saying, "First shalt thou take out the Holy Pin. Then shalt thou count to three, no more, no less. Three shall be the number thou shalt count, and the number of the counting shall be three. Four shalt thou not count, neither count thou two, excepting that thou then proceed to three. Five is right out. Once the number three, being the third number, be reached, then lobbest thou thy Holy Hand Grenade of Antioch towards thy foe, who, being naughty in my sight, shall snuff it.

Chai = Brother Maynard?? Shocked

0 Replies

The Monty Hall Paradox

Related Topics

Quick Links

My Account

able2know