21 - I am confused

[oracleslave]

Watched a movie called 21 last night. Kevin Spacey plays a lecturer that teaches his clever students to beat casino's at blackjack. In the movie he poses a question to his students that I didn't understand.

A quizmaster offers you the chance to select any of the 3 doors. Behind 2 of the doors are goats and behind the remaining door is a car. You select the door behind which you believe is the car. The quizmaster then opens one of the other doors and reveals a goat. To my mind this leaves you with a 50/50 shot at winning the car or so I thought. The quizmaster then offers you the opportunity to change your original selection prior to him opening the next door. The movie argues that statistically you should change your selection to give you a better shot at winning the car. That bit I don't get.

Can someone explain the reasoning or is the movie just kidding?

[crack_ho]

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

[Menelaus]

http://en.wikipedia.org/wiki/File:Monty_tree_door1.svg

Good decision tree explanation

[Pondlife]

Film is not as good as the book IMHO. The guy has two others that I'm aware of; one on the creation of the Mercantile Oil exchange in Dubai and the other on the Japanese stock market about the time of Nick Leeson.

As for the logic:

You originally pick a door (a) and you have a 1/3 chance of being correct, therefore a 2/3 chance of the car being behind the other doors (b,c).

Guy shows you door (b) has a goat behind it. So, logically there is a 2/3 chance that door c has a car and a 1/3 chance that door a does.

[sasguru]

Watched a movie called 21 last night. Kevin Spacey plays a lecturer that teaches his clever students to beat casino's at blackjack. In the movie he poses a question to his students that I didn't understand.

A quizmaster offers you the chance to select any of the 3 doors. Behind 2 of the doors are goats and behind the remaining door is a car. You select the door behind which you believe is the car. The quizmaster then opens one of the other doors and reveals a goat. To my mind this leaves you with a 50/50 shot at winning the car or so I thought. The quizmaster then offers you the opportunity to change your original selection prior to him opening the next door. The movie argues that statistically you should change your selection to give you a better shot at winning the car. That bit I don't get.

Can someone explain the reasoning or is the movie just kidding?

Yes the classic opening example in any course of probability. Completely counter-intuitive yet true. Don't worry several maths profs have got it wrong too.

[oracleslave]

Film is not as good as the book IMHO.

They seldom are.

Ta for the explanation. Been bothering me since I saw the film.

[Pondlife]

The Author is Ben Mezrich and the two others are Rigged (Mercantile exchange) and Ugly Americans (stock market). They're classed as non fiction but he's been accused of making bits up. Ugly Americans is the better one IMO.

[FSM with Cheddar]

Basically:
If you select a door that has a goat for the first choice, the host is forced to choose the other door that has the goat. So in this case, by swapping you win.

You have a 2/3 chance of picking a goat for your first choice. Therefore you have a 2/3 chance of winning in this case.

If you select a door that has the car for the first choice, then the host can pick any other door. This leaves you with a 50/50 chance.

So by always switching you are improving your chances in the first case, and not affecting them in the second.

[TimberWolf]

Monte Hall game for oracleslave

1. Cgg 2. ggC 3. Cgg 4. gCg 5. ggC 6. gCg 7. ggC 8. Cgg 9. Cgg 10. gCg 11. gCg 12. ggC 13. gCg 14. ggC 15. Cgg
Monte Hall game for oracleslave. Playing 15 games should be enough to see the pattern. I think you can see that you have 1/3 chance of winning a car if you don’t swap doors? So you would win 5 cars after 15 games in that case. So lets play 15 games where you always swap doors after the first door is revealed. I’ve written the answers at the top so that you can see I don’t cheat, and we’ll rely on you not cheating by looking.

So… game on...

[TimberWolf]

Game 1

Game 1
Pick a door oracleslave...