So imagine you're on a TV game show

You're given a choice of three doors: Behind one door is a car; behind the others, goats. After you pick pick a door, the host (who knows what's behind the doors) will open one of the other doors to reveal a goat. He will then give you a choice of staying with your initial choice or switching to the other door.

Should you stay or switch? Or does it not matter?

(I absolutely love this puzzle.)

(Those who have seen this one before might want to hold off replying for a little while.)

It doesn't matter..........

The suspense is killing me.

Graybeard asked a good question....

I think you stay, but I forget why.

but can you remember any of your reasoning?

wrong place

But it doesn't matter, to my reasoning. There's a 33% chance that you'll chance you you'll choose correctly the first time. After the host reveals one of the goats, your initial choice and the initial odds are moot. You now have to make a new choice between a) sticking with your initial selection, or b) switching your selection. Now it's two options, two doors, two outcomes, and a 50/50 chance of winning the car.

For that person, he is facing a 50-50 proposition. But that person does not have the same information that you do.

Remember that the host did not open a door at random. He only opens a goat door. Further, the host's actions are also dependent upon your choice.

Look at it this way: The initial choice divides the space in two, one subspace contains one door and has a probability of 0.3333 and the other contains two doors and has a probability = 0.6667.

You are essentially be given a chance to switch from the one-door space to the two-door space. The fact that one of the doors has been revealed to contain a goat doesn't change anything as you knew that at least one of the doors contains a goat.

The ONLY way you win by staying with your initial choice is when your initial choice was correct and that only occurs 1/3 of the time.

If that doesn't convince you, trying playing with a deck of cards with the Ace of Spades representing the prize. Pick a card at random but don't look at it. Now have someone else go through the remaining fifty-one cards and lay fifty of them face up on the table, leaving one face down. The only constraint is that he must not reveal the Ace of Spades.

You now have two choices. By your logic, it's 50-50: two cards remaining, two choices, both equally valid. And indeed, if you were to bring a third party into the room at that point and ask him which of the two remaining cards is the Ace of Spades, he would only have a 50-50 chance because he lacks the information as to how the two cards were chosen. But in reality, your initial choice had only a 1/52 probability of being correct. That means that it had a 98.1% probability (1-1/52) of being wrong.

Thanks pokerfan! :crazy: :shrug:

and illustrates how counter-intuitive probability can be. Which is why I love poker as so much of it is just probability.

I didn't get that puzzle the first time I heard it either. I don't think many do.

shows how goddamned counterintuitive statistics can be :D

The chances of it being a car if you switch is 2/3 :D

but the 50-50's will agree that it's 1/3 & 2/3 at the start, they believe that it changes to 50-50 once the host opens a door. And that it would be true if the door was opened randomly ala Deal or No Deal.

It's a good reminder that things aren't always as they appear.

Now if "Let's Make a Deal" could only come back...

but I don't think it would be the same without Monty.

As to the puzzle: In her book The Power of Logical Thinking, vos Savant (1996:15) quotes cognitive psychologist Massimo Piattelli-Palmarini as saying "... no other statistical puzzle comes so close to fooling all the people all the time" and " that even Nobel physicists systematically give the wrong answer, and that they insist on it, and they are ready to berate in print those who propose the right answer."

The best part are all the Math PHD's (close to a thousand) who berated Marilyn in letters:

http://query.nytimes.com/gst/fullpage.html?res=9D0CEFDD1E3FF932A15754C0A967958260

The link also includes an interview with Monty Hall regarding the problem.