I guess this goes in this section.

Has anyone seen that movie '21' where the MIT students count cards with help of their teacher?

There is one scene in the classroom where they talk about variable change in an example like this (I don't recall it exactly this is from my memory of it)

Game show where you have 3 doors to choose from, 2 have nothing and 1 has a prize. You choose your door and then the host opens one of the doors you didn't choose and reveals one of the nothing(s) he then asks you if you want to change your choice of door. The guy says yes and changes his choice to the other one.

They then go on to some little mathmatical explanation about variable change and why he increased his chances of winning and how everything was changed by this new option of changing his door #. I do not understand how it increased his chance of winning or how the whole thing was some how changed by this new option...

There is a 33.3 chance of winning, and a 66.6 chance of losing with all 3 doors. When there are two doors left there is 50/50 chance of winning/losing, I don't understand how accounting for variable change some how makes you have a better chance or even affects the 'problem' in anyway, the chances increase because one has been eliminated but changing your number from original to the other and some how getting a higher chance to win doesn't make sense to me =\

I was thinking about it when watching the movie and didn't understand it and then forgot about it but then today a similiar situation popped up in a real life game show and the guy was offered the chance to swap his # with another and he didn't and then he lost 'cos of that decision so it kinda came back to me and I was wondering again.

Please no use of overly 'smart' words to explain it, explain it how you would explain it to say a 15-18 year old. Thanks.

Edit: Oh wait... Just googled the theory and it seems it only applies if say the game show host knows where the prize is, however if he doesn't know what any of the doors hold then vairable change does not apply. Guess that 5 second google query helped me understand it lol.

This post was edited by JukeBOXX on Jun 10 2010 08:55am

It's not a variable change, it is an increase in the information available about a random variable. Don't worry about the formalism though, the intuition is really easy.

The reason this example seems unintuitive is actually because only three doors were chosen. Let's pretend the game was played with one thousand doors. We will play the same game: you pick a door, then the host opens all but one of the "wrong" doors and you are offered the opportunity to change your guess. When you first picked a door, you had a 1/1000 chance of being correct. By your logic, that chance increased to 1/2 when all but one of the "wrong" doors was opened. Obviously that is not correct though. The chance that you guessed correctly on the first try are only 1/1000, so 999/1000 times the door that the host leaves shut is going to be the winning door. Given that information, you have a 999/1000 chance of being right if you switch and only a 1/1000 chance of being right if you stay with the same door. The same logic applies in the 3 door case. You have a 2/3 chance of being right if you switch and a 1/3 chance of being right if you stay with your original choice, because of the additional information available to you.

Not everything in movies is made up, also I just wanted to understand it doesn't mean I believe it.



Thanks for explaining it.

i was trying to remember how the proposition of changing your choice fits in but yeah that was it lol, that was the only thing i remembered

i explained in to myself like this:
in 2 of 3 cases you would've won if you had just changed the door
in 1 of 3 cases you'll lose
same as wih 1000 doors..

Nope that is the exact problem.



It is still slightly mind boggling to me =\ 'cos it seems like common game show ploys; the guy would ask you if you want to change door even if your door is the losing one just because that is how gameshows work it makes them more interesting, but you still logically have the same chance of winning whether you change your door or not =\ I dunno maybe it is to complicated for me even when it was explained it kinda makes sense but still have like the way I think going against it.

There is 3 doors. You choose door 1, it stays closed. Host opens say door 3 and reveals that there was nothing behind it. So now door 1 and 2 are closed, one of them has nothing and the other has a prize.