-33 You're on a game show where there's a prize behind one of three doors, and you have to guess one. After you guess, the host (who knows where the prize is), opens one of the doors (other than the one you picked) that doesn't contain the prize, after which you may either change your guess or stay with the same door. You're equally likely to win if you change your guess as if you don't, amirite?

by Anonymous 12 years ago

I remember seeing this scenario in the movie 21 but I can't remember what the correct answer is.

by Anonymous 14 years ago

Mathematically, you should stay where you are. You have a 66.7% chance of winning as opposed to only 33.3% if you switch doors

by Anonymous 14 years ago

BZZZT wrong. You should actually always switch.

by Anonymous 14 years ago

It was the other way around :/

by Anonymous 14 years ago

For those of you who are still interested, this is called the "Monty Hall Problem" and you can look it up on Wikipedia. The answer is that you should always switch your guess. The basic reason is that your initial guess has a 1/3 chance of being correct, i.e. a 2/3 chance that the prize is behind one of the doors you didn't pick. Once one of the empty doors is opened, your chances of being correct do not change, but you now know that of the two remaining doors you didn't pick was wrong. So the only unopened door you didn't pick has a 2/3 chance of being correct.

by Anonymous 14 years ago

Yah I remember doing this problem in math in 7th grade.

by Anonymous 12 years ago

I JUST READ THIS IN A SCI-FI BOOK. Like, yesterday. This is creepy.

by Anonymous 12 years ago

Robert J Sawyer? He seems to have it in all his books.

by Anonymous 12 years ago

Yup. WWW: Watch. I love that series now. He also has a lot of shameless self-promotion.

by Anonymous 12 years ago

Yep, also has Old Sully's beer from Mindscan in a bunch of his books.

by Anonymous 12 years ago

Haha yeah. He's a great author though. Especially since I'm a sci-fi nerd :P

by Anonymous 12 years ago

They demonstrated this on numb3rs- and it is better to change your choice.

by Anonymous 12 years ago

I've done seen this problem in math about 15 different times. Always switch.

by Anonymous 12 years ago

i totally get the 'always' change thing but this was what came to my mind: there are two doors left so there's 50/50 chance

by Anonymous 12 years ago

if thats how you see it even when shown factually that you are twice as lkely to win by switching thn you are truly a moron

by Anonymous 12 years ago

It has to deal with conditional probability. Normally it would be 50/50, but taking into account that 1 out of three doors has been revealed, it changes because now the other two doors' probabilities are based off of the fact the other door was not the right choice. Take a stats class, they'll explain better.

by Anonymous 12 years ago

Didn't you see 21?

by Anonymous 12 years ago

I was in a statistics class and we proved that you have a better chance of winning after you switch. We proved it using this Bayes theorem equation but essentially, the short and simple version is when you chose your original door, you had a 1/3 chance of winning and after you switch you have a 1/2 chance of winning. It sounds like it's messed up logic but we took a sample of everyone in the class and people who switched the door won more times than people who stayed.

by Anonymous 12 years ago

You aren't much of a math nerd, are you?

by Anonymous 12 years ago

This was in The Curious Incident of the Dog in the Night-Time. There's two ways of solving it. One is a really long math problem and the other is making a tree. The tree will show you that, like said before,you have a 2/3 chance of winning by changing.

by Anonymous 12 years ago