Lecture Scene

[kennybenny]

Just curious, there was a lecture scene where Micky gave Ben 3 "doors" to choose and then Ben chooses one. After that, Micky gave away the result of one door and now gives Ben another choice to choose the "winning door." Ben decides to choose a new door instead of staying with his original decision. What was the math reason behind that?

Does it have something to do with how his original decision only gave him 1/3 chance of winning, but if he were to choose again, now he gets 1/2 chance to win whereas if he were to stay with his original decision he was keeping his 1/3 chance?

Thanks

[Guynoire]

This is the famous Let's Make a Deal Question discussed in most intro stats courses. The trick here is that the game show host knows which door the car is behind and therefore can and will always show a goat. If the game show host rolled dice to determine the door and just happened to show a goat then the probability would be 1/2, however that is not what he does.

The easiest way I can think to explain this as follows the origional probability of getting the car is 1/3. Because the host knows which door the car is behind, he can always show you a goat and does so. This in turn doesn't change the probability on your door. Since the probability that the car is behind your door is 1/3 and the sum of all probabilities must add up to 1 the probability that the car is behind the other door is 2/3 so it is beneficial to switch.

[godeem23]

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

[E-town-guy]

The fact is, if you choose door #1 then they eliminate door #3 how can there be a benefit to switching to #2. Both #1 and #2 have the same odds 50/50. There is just as much reason to switch as there is not to.

[mjbballar23]

If you guys dont believe that switching wins more than try it out for yourself. You'll quickly see that switching wins much more than staying.

[golfnut101]

So, how does this relate to blackjack ?

[Guynoire]

Originally Posted by golfnut101

So, how does this relate to blackjack ?

It doesn't. I was kinda suprised when he asked it. It had nothing to do with blackjack and nothing to do with non-linear equations, the name of the course.

[golfnut101]

Non-linear equations ? Blackjack ? I've always enjoyed stats, odds, etc. but by no means am a math guy. Sounds like you are. How are the two related ?
Just a pure interest question.

thnx for your time

[Guynoire]

I'm not really sure I understand you. If I recall the scene correctly Kevin Spacey was talking about Newton's method and said the name of the course was non-linear equations, so basically they were doing calculus. Then he asked Bill Campbell a famous stats problem that really just involves tricky algebra and a knowledge of conditional probability. I didn't really see a direct connection between the two.

I wouldn't put too much thought into this. I think it's just another case of what you see in movies all the time; they talk about a subject that most people won't have much knowledge about and try to sound technical, but if you do happen to have specific knowledge on the subject it doesn't make sense. It's not important to the movie as a whole in terms of its plot or its entertainment value and the best method is just to accept it and move on with the plot.

[Ploppy]

http://wizardofodds.com/askthewizard/122
and
http://wizardofodds.com/askthewizard/124