This is a good puzzle - except I can't solve it!

[Hypersmurf]

I believe that to be flawed reasoning.

You're wrong, and hopefully the hundred door variation will illustrate it for you.

Spoiler

There are now a hundred doors, and one prize. Pick one door; the host will eliminate 98 that do not have the prize. There now remain two doors - the one you picked, and the one he didn't eliminate. One of the two has the prize. Do you switch?

Can you see that the odds of your picking the correct door first time are 1 in 100? It doesn't matter whether or not you know he'll be eliminating 98 doors... you still choose one out of a hundred.

There's a 99% chance that the door is not the one you picked first. And once 98 doors have been eliminated, that means there's a 99% chance that the door he left is the one with the prize, and still only a 1% chance that your original pick is correct.

Does that make more intuitive sense to you?

-Hyp.

 

[Lord Pendragon]

How interesting.

Spoiler

I found it very difficult to grasp at first, but I found that it's easier, for me, to understand if the probabilities and percentages are removed and it's stated like this:

There are 100 doors, and 1 prize. Pick one. It's most likely not the right door.

The host eliminates 98 doors, leaving the one you picked originally, and one other door. Since the door you picked originally was most likely not the right door, the one remaining door is almost certainly the one with the prize.

Very neat.

 

[Hypersmurf]

... if the probabilities and percentages are removed...

Heathen.

-Hyp.

 

[Lord Pendragon]

Heathen.

Well, you know what they say. Once an English major...

Spoiler

Or, another way to think of it is that there are really only two options for where the prize can be. "Your door" and "not your door." The host has merely consolidated the "not your door" option into a single door, but it doesn't change anything. The chances are still better that the prize was behind "Not your door" all along.

 

[Hypersmurf]

Spoiler

Or, another way to think of it is that there are really only two options for where the prize can be. "Your door" and "not your door." The host has merely consolidated the "not your door" option into a single door, but it doesn't change anything. The chances are still better that the prize was behind "Not your door" all along.

Spoiler

Yup. The problem is when you get people who say "Right! Your door, or not your door. That's 50/50."

-Hyp.

 

[Lonely Tylenol]

The thread of THE DARK SPEECH

I believe that to be flawed reasoning. Here's why:

Spoiler

If the host always, no matter what, opens a wrong door after the guest chooses and then gives the guest the chance to change his mind, then the first guess is entirely irrelevent. It is, for all intents and purposes, a choice between 2 doors, not 3, as you can be 100% sure that one of the wrong choices will be eliminated before you have to make your final decision. It is therefore a simple 50/50 chance.

A lot of people run up against that difficulty, but it's actually pretty simple.

Spoiler

The thing is, that a randomly selecting player will in fact get the right answer 50% of the time. But that assumes a randomly selecting player, which is not what we're assuming here.

Look at it this way. When you choose a door, there's a 1/3 chance you chose the right door, and a 2/3 chance it was one of the other doors. When Monty reveals one of the doors, that doesn't change any probabilities. It's still a 2/3 chance that it was one of the other doors, and a 1/3 chance it's your door. Only now you have an extra bit of information that you didn't have to begin with. You know that it wasn't a certain door. You're still picking from three doors, but you're "cheating" because you know one of the doors isn't the prize.

No matter what, you know that the chance that Monty's doors contain the prize are 2/3. Let's say a second contestant came on, who hadn't seen which door had been revealed. He knows that you picked a door, and that Monty still had two doors. We ask him, "what's the chance that the prize is still behind one of Monty's doors?" He will say "2/3." Because Monty has two doors and you have one and the prize was randomly placed, regardless of what you know about Monty's doors.

Anyway, if you pick randomly, you'll win 50% of the time. But you will win 66% of the time if you switch every time you play.

The other thread had a very good example (a bit messed up on first writing due to a missing line) involving eggs. But the fact of the matter is that my argument is supported by not only a solid mathematical proof, but also empirical evidence. The link I posted above has both.

 

[Lonely Tylenol]

Or here's another way of looking at it...

Spoiler

Let's say you pick one door out of three. Then Monty doesn't reveal a door, but he asks you if you would rather switch and take both other doors rather than the one you picked. It is plainly obvious that the chance of your door being correct is 1/3, but the chance you have if you switch to both other doors is 2/3. If you switch, you have a 66% chance of winning.

But this is identical to the way the problem was originally set up. In that version Monty doesn't eliminate a door. He does in fact give you the choice of both other doors over your single door by revealing a door.

 

[Vrecknidj]

Three Gods - A, B and C - are called, in some order, True, False and Random. True always speaks truly, False always speaks falsely, but whether Random speaks truly or falsely is a completely random matter. Your task is to determine the identities of A, B and C by asking three yes-no questions; each question must be put to exactly one God. The Gods understand English, but will answer all questions in their own language, in which the words for 'yes' and 'no' are 'da' and 'ja', in some order. You do not know which word means which.

Okay, I never did work this one out. What's the solution?

Dave

 

[The Other Librarian]

What stops me from opening both doors and deciding from the two views? Nothing in the puzzle says the guards will not allow the doors to be opened.

The Mind is its own place and in itself, can make a Heaven of Hell, a Hell of Heaven.

-Uncle Miltie

 

[Abstraction]

I had a problem like this in a game I ran once. There were two faceplates on a treasure chest which talked. They told you that one of covered a lock and the other covered a deadly trap. Each said that it was the one that always told the truth and the other one always lied. The classic problem. Of the three players, one sat down and puzzled it out for TEN MINUTES. The other two knew the classic answer. The problem was that 1) the faces didn't answer yes/no. When asked "what would the other say?" they just gave a wild answer, which would be (obviously) a lie. Frex: If I asked the other one where the deadly trap was, what would he say? Answer: Ooh, he would say a terrible lie, like it was under the bed!

Problem 2) They both lied anyways.