And another puzzle

Originally Posted by wyrdness

Did you read the original question properly?



The host knows what's behind the doors. Therefore you have a 2/3 probability of getting the car if you change your mind.

You fell into the trap set by the writer of the question, which was to assume that you have a 50/50 chance, rather than working out what would really happen.

Nope, I fell in to the trap of reading the question too fast, obviously.

My bad, in that situation, yes, the advantage is in switching.

By your logic, you're more likely to pick the car by changing your mind, even if you actually picked the car first time. It doesn't matter what he says to you, you still have two doors to pick from.


Doors A-B-C
A and B have a goat, C has a car. (Why not).

You pick A, Host opens B. You choose between A and C (50:50) why would the car be behind C?
You pick B, Host opens A. You choose between B and C (50:50) why would the car be behind C?
You pick C, Host opens A. You choose between B and C (50:50)
You pick C, Host opens B. You choose between A and C (50:50)
So why would it be ever be more likely to be C and so a good idea to change your mind?

Am I missing something? How can you get extra information if the host is going to open a door with a goat behind whatever you do initially? You pick a goat first time, you see a goat, you pick the car first time, you see a goat.

Originally Posted by sinbad

By your logic, you're more likely to pick the car by changing your mind, even if you actually picked the car first time. It doesn't matter what he says to you, you still have two doors to pick from.


Doors A-B-C
A and B have a goat, C has a car. (Why not).

You pick A, Host opens B. You choose between A and C (50:50) why would the car be behind C?
You pick B, Host opens A. You choose between B and C (50:50) why would the car be behind C?
You pick C, Host opens A. You choose between B and C (50:50)
You pick C, Host opens B. You choose between A and C (50:50)
So why would it be ever be more likely to be C and so a good idea to change your mind?

Am I missing something? How can you get extra information if the host is going to open a door with a goat behind whatever you do initially? You pick a goat first time, you see a goat, you pick the car first time, you see a goat.

If the host doesn't know where the car is, there's a possibility of him opening a door & revealing the car. You loose. No choices.

Originally Posted by Baph

If the host doesn't know where the car is, there's a possibility of him opening a door & revealing the car. You loose. No choices.

But the host does know, it says so.

Originally Posted by sinbad

But the host does know, it says so.

Yes, and the probabilities only stay equal if the host doesn't know. That's the only way he's guranteed not to reveal the car, and so the odds are tipped.

Check out the first link by wyrdness, play the game, and click to have it explain. Read about the probability wheels etc. You'll get it.

Ahh I get it now. It still is 50:50 in isolation because there's two doors, but if you count on hitting a goat, and the chances are 2/3 you will, then whichever door is left after the one you picked and the one he opens are eliminated (by yourself) is the car.