let's say there are 3 doors. a prize is behind one. after you choose, one of the other 2 doors is ............

Question

let's say there are 3 doors, and a prize is behind only one of them. after you choose, one of the other 2 doors is revealed to be empty. now there are only 2 doors left. you are given the option to switch your door. what would you do??? would you keep the same door or switch??

before you answer, please read the rest of this:

this is called the monty hall conundrum. it is actually much smarter to switch. if you switch you will have a 2 in 3 chance of winning. if you don't switch though, you will only have a 1 in 3 chance of winning. if you don't believe me, then look it up on a search engine and read about it.

most people though will argue any mathematician and insist that it is 50/50 either way. they use the logic that "you never know, it MIGHT be the door you initially picked", which a terrible argument because it MIGHT be either door. what's smart is to use ockham's razor and go with what is MOST LIKELY.

invariably, some people will still insist that it's 50/50.

wow,, 4 people so far, and just as i predicted, one of them insisted that it would be 50/50. you're wrong though. i know you think you understand probability, but you're leaving out some key factors. it's not as simple as "welp,, 2 doors, so it's 50/50". you really should've researched this first.

just type "monty hall conundrum" into a search engine. it might take a while until you're able to grasp it fully, but in the mean time, you really should consider the possibility that you might be wrong.

well well well,,, we're up to 6 people now and 3 of them are arguing against mathematical expertise. i would love to do this with you guys in person. the only condition is that you HAVE to stick with the same door. you're not allowed to switch. and everytime you pick the wrong door, you owe me $10. but everytime you pick the right door, then i'd pay you $12. does that sound fair?? hey,, if it's really 50/50, then that means that you should average a dollar gain every time you play.

poolhottiette,

you're gonna kick yourself a lot harder if you stick with the same door and lose. this is what it comes down to. if you play the game 30 times, and you NEVER switch, then you'll win about 10 times. if you DO switch though, you'll win about 20 times. if you switch some of the time and don't switch others, then you'll get between 10 and 20. if you don't believe me, then try it at home. get one of your friends to perform this on you. you'll see,,, it's really, really stupid to go up against the odds. math beats intuition hands down. it's a hard lesson for people to learn.

4 of the people who answered insisted that mathematics doesn't matter simply because they don't like mathematics. these people will just have to learn the hard way that there's just no way to be smart enough to beat the odds in situations like these. they probably all play the lotto too.

the question is,, do you really wanna be one of these people?

Answer 1

I love the Monty Hall puzzle.

Yes, you should switch.

I think everyone agrees that you have a 1/3 chance to start with. Right?

You should also agree that Monty can always show you an empty door, regardless of which one you pick.
This means that he hasn't given you any new information, which implies that your chances if you stay with your original door are still 1/3. (This is really the big leap, right here.)

So, before switching, your chances are 1/3, and there's only one other door remaining. This other door must therefore have a 2/3 chance of hiding the prize.

Your chances of winning are therefore twice as good if you switch.

Answer 2

I'm one of the 50/50 people I'm afraid.

Essentialy what you have done in your explination is remove one of the doors. You have put yourself in a position where your chances are 1 out of 2.

You cant have a 2 out of 3 because the third choice has been removed from the equasion.

Edit--

I've taken the time ro do the recomended research on this, and I've come to the conclusion that all of the reasons for it being better one (Either way) are based on a gamblers falacy.

The best argument is that if you were to change the situation to one where there were originally 100 doors, then you pick one, then they open 98 wrong doors are you better off switching?

Just because you flip a coin and it comes up heads 10 times in a row.. doesn't mean your better off picking tails next time.

Edit 2 - After some further thought, I've come to see that it is much smarter to switch. And this is because the second choice is based on the original choice. To explain:

You see, when the scenerio started you had a 1 in 3 chance of being right. Which means the odds were 2 out of 3 that you would pick wrong. Nothing changed when you were shown one of the losing spots because no matter which one you pick, they can always show you an empty one.

When they offer to let you switch, they are really only asking if you want to bet that you picked right the first time (1 in 3 chance) or if you want to bet that you were wrong the first time (2 in 3 chance)

My own comment in my last edit cinched the solution for me when I spent the time thinking about it. Lets say it was 10 doors you had to pick from. After you pick they will open 8 losing doors, (remember they know where the right one is and they can always show you the 8 wrong doors reguardless of your choice) and now you have to decide if you picked right the first time or not. When it started you had a 1 in 10, nothing has changed because no matter what you do they can still open 8 wrong doors, they are not giving you any new information. They have not changed the fact that the original odds were 1 in 10. Now they are simply asking you if you want to stay with your 1 in 10 odds or if you want to be on the other side of those odds.

Answer 3

I've never really cared for probability. I can do it, but I think it's a royal pain. I think that's one of the reasons I didn't really like stats. But anyway... I would be choosing my door on intuition, not math, so there really wouldn't be any point in switching. That would just be second-guessing myself. Bad for self-esteem. Plus, it's more fun to be stubborn. Maybe even if I'm wrong, I can find some other way to get the prize. Heh...

Answer 4

okay, I follow you, I understand that it's 2/3 regardless of being shown an empty door....but wouldn't you kick yourself if you switched and it's the door you chose first? There is an element of chance involved.

Answer 5

Despite of all those mathematics, I'd stick to the one I picked at the first place. That's just how I am in my life!

Answer 6

have heard this before, mathematically better to switch, but you answered your own question

Answer 7

I would switch

Answer 8

switch

Answer 9

I'm with David D on this.