My favorite brainteaser - vote on answer [Archive]

teddyFBI

03-17-2005, 01:32 PM

I still love the elegance of this one (no trick answers, btw)

You reach the final round of a game show, where the host shows you 3 doors and tells you there's a car behind one, and chickens behind the other 2. You get one pick and get whatever's behind that door. So you pick a door.

The host then does the following: he opens up one of the doors that you did NOT pick and reveals a chicken (you watch the game show frequently and know that he always opens up a door w/ a chicken -- he never reveals the car). He now says to you 'I'm going to give you the option to either stick with your original door, or SWITCH to the still un-opened door, and you'll get whatever's behind your final selection.'

What do you do to maximize your chance of winning the car? (and why? -- remember, there's no trick answer here)

Vote before viewing people's answers/comments below.

Patrick del Poker Grande

03-17-2005, 01:34 PM

I see that I'm the second person (out of 2 total votes) to get it right - I assume the OP voted before me, or did someone else who's been around OOT for more than a few months already vote here too? Do you actually want me to explain the answer when I'm the first one to post?

I remember there being a cool little java webpage illustrating this one. Who's got the link?

cjhellm

03-17-2005, 01:34 PM

I just read about this in the man who loved only numbers. pretty interesting problem. apparently it really stumped a lot of mathematicians.

edit- patrick.. first was me

Sophia

03-17-2005, 01:35 PM

mmbt0ne

03-17-2005, 01:36 PM

You're back?

Sophia

03-17-2005, 01:37 PM

Patrick del Poker Grande

03-17-2005, 01:38 PM

[ QUOTE ]
[ QUOTE ]
You're back?

[/ QUOTE ]

No.

[/ QUOTE ]
Yes you are. I can see you right now.

Sophia

03-17-2005, 01:40 PM

Patrick del Poker Grande

03-17-2005, 01:40 PM

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
You're back?

[/ QUOTE ]

No.

[/ QUOTE ]
Yes you are. I can see you right now.

[/ QUOTE ]

No, you cannot.

[/ QUOTE ]
See? There you are again!

Shajen

03-17-2005, 01:41 PM

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
You're back?

[/ QUOTE ]

No.

[/ QUOTE ]
Yes you are. I can see you right now.

[/ QUOTE ]

No, you cannot.

[/ QUOTE ]

I cannot? [censored]. I hate this damned game.

Sophia

03-17-2005, 01:41 PM

Patrick del Poker Grande

03-17-2005, 01:42 PM

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
You're back?

[/ QUOTE ]

No.

[/ QUOTE ]
Yes you are. I can see you right now.

[/ QUOTE ]

No, you cannot.

[/ QUOTE ]
See? There you are again!

[/ QUOTE ]

Drugs kill.

[/ QUOTE ]
So what you're trying to say is that you're back?

Sophia

03-17-2005, 01:43 PM

Patrick del Poker Grande

03-17-2005, 01:44 PM

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
You're back?

[/ QUOTE ]

No.

[/ QUOTE ]
Yes you are. I can see you right now.

[/ QUOTE ]

No, you cannot.

[/ QUOTE ]
See? There you are again!

[/ QUOTE ]

Drugs kill.

[/ QUOTE ]
So what you're trying to say is that you're back?

[/ QUOTE ]

No.

[/ QUOTE ]
That's what I thought. I think everyone here can see it's pretty clear you're back.

astroglide

03-17-2005, 01:46 PM

when you first pick you're picking one out of three so you have a 33% chance. when you're given the choice you have a 50% pick, so your odds are improved. if there are 100 doors and you pick one, you have a 1% chance of being right. even if 998 doors are flipped open and you can switch, you should switch because the other door is a 50% chance. it didn't make sense to me before being told to think about it like that. it's just based on the odds of your pick at the time you pick.

Sophia

03-17-2005, 01:46 PM

Patrick del Poker Grande

03-17-2005, 01:47 PM

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
You're back?

[/ QUOTE ]

No.

[/ QUOTE ]
Yes you are. I can see you right now.

[/ QUOTE ]

No, you cannot.

[/ QUOTE ]
See? There you are again!

[/ QUOTE ]

Drugs kill.

[/ QUOTE ]
So what you're trying to say is that you're back?

[/ QUOTE ]

No.

[/ QUOTE ]
That's what I thought. I think everyone here can see it's pretty clear you're back.

[/ QUOTE ]

They're wrong. So are you.

[/ QUOTE ]
That's not the vibe I'm picking up here. I think you're definitely back.

M2d

03-17-2005, 01:50 PM

[ QUOTE ]
when you first pick you're picking one out of three so you have a 33% chance. when you're given the choice you have a 50% pick, so your odds are improved. if there are 100 doors and you pick one, you have a 1% chance of being right. even if 998 doors are flipped open and you can switch, you should switch because the other door is a 50% chance. it didn't make sense to me before being told to think about it like that. it's just based on the odds of your pick at the time you pick.

[/ QUOTE ]
why wouldn't your original door be 50/50 as well? you're essentially getting a new choice after the third (incorrect) door is opened. You're making a decision if you stay, just as much as you make one if you change.

jimdmcevoy

03-17-2005, 01:51 PM

[ QUOTE ]
when you first pick you're picking one out of three so you have a 33% chance. when you're given the choice you have a 50% pick, so your odds are improved. if there are 100 doors and you pick one, you have a 1% chance of being right. even if 998 doors are flipped open and you can switch, you should switch because the other door is a 50% chance. it didn't make sense to me before being told to think about it like that. it's just based on the odds of your pick at the time you pick.

[/ QUOTE ]

So, one door has a 33% chance to be correct, and the other 50% chance?

Patrick del Poker Grande

03-17-2005, 01:53 PM

Do it (http://www.stat.sc.edu/~west/javahtml/LetsMakeaDeal.html)

Patrick del Poker Grande

03-17-2005, 01:54 PM

[ QUOTE ]
[ QUOTE ]
when you first pick you're picking one out of three so you have a 33% chance. when you're given the choice you have a 50% pick, so your odds are improved. if there are 100 doors and you pick one, you have a 1% chance of being right. even if 998 doors are flipped open and you can switch, you should switch because the other door is a 50% chance. it didn't make sense to me before being told to think about it like that. it's just based on the odds of your pick at the time you pick.

[/ QUOTE ]

So, one door has a 33% chance to be correct, and the other 50% chance?

[/ QUOTE ]
No. One has a 33% chance and the other has a 67% chance.

JoshuaD

03-17-2005, 01:55 PM

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
You're back?

[/ QUOTE ]

No.

[/ QUOTE ]
Yes you are. I can see you right now.

[/ QUOTE ]

No, you cannot.

[/ QUOTE ]
See? There you are again!

[/ QUOTE ]

Drugs kill.

[/ QUOTE ]
So what you're trying to say is that you're back?

[/ QUOTE ]

No.

[/ QUOTE ]
That's what I thought. I think everyone here can see it's pretty clear you're back.

[/ QUOTE ]

They're wrong. So are you.

[/ QUOTE ]
That's not the vibe I'm picking up here. I think you're definitely back.

[/ QUOTE ]

Seconded.

teddyFBI

03-17-2005, 01:57 PM

[ QUOTE ]
when you first pick you're picking one out of three so you have a 33% chance. when you're given the choice you have a 50% pick, so your odds are improved. if there are 1000 doors and you pick one, you have a 1% chance of being right. even if 998 doors are flipped open and you can switch, you should switch because the other door is a 50% chance. it didn't make sense to me before being told to think about it like that. it's just based on the odds of your pick at the time you pick.

[/ QUOTE ]

This reasoning is the classic 'incorrect' reasoning. Your odds if you switch in the 1000 doors example is NOT 50% but rather 999 / 1000. Even though you get the answer right, your reasoning is deeply flawed. When you switch in the 3 door example you're NOT improving your odds from 33% to 50% but rather from 33% to 66%.

Patrick del Poker Grande

03-17-2005, 01:57 PM

Basically, if there are three doors, each door has a 1/3 chance of being the right door at the start, including the door you pick. That means you have a 2/3 chance of being wrong. That 2/3 chance represents the chance that the right answer is one of the other two doors. Now when the host reveals that one of the other two doors is the wrong answer, you still only have a 1/3 chance of being right and that 2/3 chance is all in the remaining door.

Maybe think of it like this. Forget that the host reveals what's behind one of the other doors. Your second decision is essentially whether you want your original door or both the other doors. It's clearly better to have both the other doors.

M2d

03-17-2005, 01:57 PM

If i was on a game show and got that far, I'd be trying to figure out how to score with the hottie, eye candy hostess anyway.

daryn

03-17-2005, 01:58 PM

<blockquote>In risposta di:<hr />
<blockquote>In risposta di:<hr />
<blockquote>In risposta di:<hr />
when you first pick you're picking one out of three so you have a 33% chance. when you're given the choice you have a 50% pick, so your odds are improved. if there are 100 doors and you pick one, you have a 1% chance of being right. even if 998 doors are flipped open and you can switch, you should switch because the other door is a 50% chance. it didn't make sense to me before being told to think about it like that. it's just based on the odds of your pick at the time you pick.

[/ QUOTE ]

So, one door has a 33% chance to be correct, and the other 50% chance?

[/ QUOTE ]
No. One has a 33% chance and the other has a 67% chance.

[/ QUOTE ]

this is correct. astro is wrong (for once)?

the door you originally picked gives you a 33% chance at success (why wouldn't it?). the fact that he reveals the chicken or whatever behind a door does nothing to your original choice.

however the other 2 doors 66% combined chance of success all goes into the one that he didn't open.

Patrick del Poker Grande

03-17-2005, 01:58 PM

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
You're back?

[/ QUOTE ]

No.

[/ QUOTE ]
Yes you are. I can see you right now.

[/ QUOTE ]

No, you cannot.

[/ QUOTE ]
See? There you are again!

[/ QUOTE ]

Drugs kill.

[/ QUOTE ]
So what you're trying to say is that you're back?

[/ QUOTE ]

No.

[/ QUOTE ]
That's what I thought. I think everyone here can see it's pretty clear you're back.

[/ QUOTE ]

They're wrong. So are you.

[/ QUOTE ]
That's not the vibe I'm picking up here. I think you're definitely back.

[/ QUOTE ]

Seconded.

[/ QUOTE ]
See?

teddyFBI

03-17-2005, 01:58 PM

[ QUOTE ]
Basically, if there are three doors, each door has a 1/3 chance of being the right door at the start, including the door you pick. That means you have a 2/3 chance of being wrong. That 2/3 chance represents the chance that the right answer is one of the other two doors. Now when the host reveals that one of the other two doors is the wrong answer, you still only have a 1/3 chance of being right and that 2/3 chance is all in the remaining door.

Maybe think of it like this. Forget that the host reveals what's behind one of the other doors. Your second decision is essentially whether you want your original door or both the other doors. It's clearly better to have both the other doors.

[/ QUOTE ]

Correct. For the record, 85% of university students given this brainteaser get it incorrect. It's quite elegant in its simplicity.

Shajen

03-17-2005, 01:59 PM

[ QUOTE ]
Do it (http://www.stat.sc.edu/~west/javahtml/LetsMakeaDeal.html)

[/ QUOTE ]

Even after doing this several times, I still say you have a 50 50 shot.

Its not rocket science.

But then again, I'm not a rocket scientist.

jimdmcevoy

03-17-2005, 02:00 PM

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
when you first pick you're picking one out of three so you have a 33% chance. when you're given the choice you have a 50% pick, so your odds are improved. if there are 100 doors and you pick one, you have a 1% chance of being right. even if 998 doors are flipped open and you can switch, you should switch because the other door is a 50% chance. it didn't make sense to me before being told to think about it like that. it's just based on the odds of your pick at the time you pick.

[/ QUOTE ]

So, one door has a 33% chance to be correct, and the other 50% chance?

[/ QUOTE ]
No. One has a 33% chance and the other has a 67% chance.

[/ QUOTE ]

dude, I asked the question so he could figure it out for himself

riffraff

03-17-2005, 02:00 PM

It's also old. As good as it is, I'm surprised not everyone has heard it before =)

teddyFBI

03-17-2005, 02:00 PM

[ QUOTE ]
[ QUOTE ]
Do it (http://www.stat.sc.edu/~west/javahtml/LetsMakeaDeal.html)

[/ QUOTE ]

Even after doing this several times, I still say you have a 50 50 shot.

Its not rocket science.

But then again, I'm not a rocket scientist.

[/ QUOTE ]

Nope - read the answers above; they've got it right. Don't believe me? set up 3 cups with a ball underneath and reproduce the experiment. You'll win by switching 2 out of 3 times, but only 1 out of 3 by staying.

Patrick del Poker Grande

03-17-2005, 02:00 PM

[ QUOTE ]
[ QUOTE ]
Do it (http://www.stat.sc.edu/~west/javahtml/LetsMakeaDeal.html)

[/ QUOTE ]

Even after doing this several times, I still say you have a 50 50 shot.

Its not rocket science.

But then again, I'm not a rocket scientist.

[/ QUOTE ]
That's the beauty in this one. It's painfully simple, yet so easy to get wrong. Even better is how logical the wrong answer appears to be.

daryn

03-17-2005, 02:01 PM

<blockquote>In risposta di:<hr />
It's also old. As good as it is, I'm surprised not everyone has heard it before =)

[/ QUOTE ]

especially since it is posted on 2+2 about once every 3 months for the last 2 years.

Patrick del Poker Grande

03-17-2005, 02:02 PM

[ QUOTE ]
[ QUOTE ]
It's also old. As good as it is, I'm surprised not everyone has heard it before =)

[/ QUOTE ]

especially since it is posted on 2+2 about once every 3 months for the last 2 years.

[/ QUOTE ]
Right. That's what I was getting at with my first post. It's still kindof cool though, at least the first one or two times you see it.

Shajen

03-17-2005, 02:03 PM

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Do it (http://www.stat.sc.edu/~west/javahtml/LetsMakeaDeal.html)

[/ QUOTE ]

Even after doing this several times, I still say you have a 50 50 shot.

Its not rocket science.

But then again, I'm not a rocket scientist.

[/ QUOTE ]
That's the beauty in this one. It's painfully simple, yet so easy to get wrong. Even better is how logical the wrong answer appears to be.

[/ QUOTE ]

I think the problem lies in how I am approaching it.

If there are 3 doors, I choose 1 and the host opens another, I have a 50/50 chance of being right between the remaining two doors.

This knowledge is throwing me off. After doing the applet several more times, I see the light. You are correct sir.

Cool.

daryn

03-17-2005, 02:05 PM

<blockquote>In risposta di:<hr />

If there are 3 doors, I choose 1 and the host opens another, I have a 50/50 chance of being right between the remaining two doors.

[/ QUOTE ]

this statement is incorrect

daryn

03-17-2005, 02:07 PM

the key is, the host knows where the prize is, and where the zonk is.

so if there were 1000 doors, and you picked one (1/1000 chance of being right), then the host opens up 998 doors with zonks.. you have to say to yourself:

he could ALWAYS show me 998 doors with zonks. so what's more likely here. either i picked the right door off the bat from 1000, or the other one he didn't open is the right one.

jimdmcevoy

03-17-2005, 02:09 PM

[ QUOTE ]
[ QUOTE ]

If there are 3 doors, I choose 1 and the host opens another, I have a 50/50 chance of being right between the remaining two doors.

[/ QUOTE ]

this statement is incorrect

[/ QUOTE ]

I'm not sure if this is what he means, but if you randomly pick a door of the remaining two left you do have a 50/50 of getting it right

Patrick del Poker Grande

03-17-2005, 02:10 PM

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]

If there are 3 doors, I choose 1 and the host opens another, I have a 50/50 chance of being right between the remaining two doors.

[/ QUOTE ]

this statement is incorrect

[/ QUOTE ]

I'm not sure if this is what he means, but if you randomly pick a door of the remaining two left you do have a 50/50 of getting it right

[/ QUOTE ]
No. The answer lies in several previous posts.

teddyFBI

03-17-2005, 02:10 PM

[ QUOTE ]
the key is, the host knows where the prize is, and where the zonk is.

so if there were 1000 doors, and you picked one (1/1000 chance of being right), then the host opens up 998 doors with zonks.. you have to say to yourself:

he could ALWAYS show me 998 doors with zonks. so what's more likely here. either i picked the right door off the bat from 1000, or the other one he didn't open is the right one.

[/ QUOTE ]

Want a fascinating twist to this though? You're correct in that it's crucial that you KNOW that the host will never open up a zonk door. What if you did NOT have that knowledge?? i.e. what if the host were NOT bound by the rules that he were never able to open up the door with the prize but rather chooses randomly?? It seems to me, then that the odds WOULD be 50/50 (that is, when the door he opens does not contain a prize).

Patrick del Poker Grande

03-17-2005, 02:12 PM

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
Do it (http://www.stat.sc.edu/~west/javahtml/LetsMakeaDeal.html)

[/ QUOTE ]

Even after doing this several times, I still say you have a 50 50 shot.

Its not rocket science.

But then again, I'm not a rocket scientist.

[/ QUOTE ]
That's the beauty in this one. It's painfully simple, yet so easy to get wrong. Even better is how logical the wrong answer appears to be.

[/ QUOTE ]

I think the problem lies in how I am approaching it.

If there are 3 doors, I choose 1 and the host opens another, I have a 50/50 chance of being right between the remaining two doors.

This knowledge is throwing me off. After doing the applet several more times, I see the light. You are correct sir.

Cool.

[/ QUOTE ]
Awesome. Now that this is all settled, I'm gonna go get me some Chipotle.

jimdmcevoy

03-17-2005, 02:13 PM

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]

If there are 3 doors, I choose 1 and the host opens another, I have a 50/50 chance of being right between the remaining two doors.

[/ QUOTE ]

this statement is incorrect

[/ QUOTE ]

I'm not sure if this is what he means, but if you randomly pick a door of the remaining two left you do have a 50/50 of getting it right

[/ QUOTE ]
No. The answer lies in several previous posts.

[/ QUOTE ]

Okay miscommunication I think, let me rephrase:

I'm not sure if this is what he means, but if you randomly pick a door of the remaining two left you will pick the right door 50% of the time

teddyFBI

03-17-2005, 02:14 PM

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]

If there are 3 doors, I choose 1 and the host opens another, I have a 50/50 chance of being right between the remaining two doors.

[/ QUOTE ]

this statement is incorrect

[/ QUOTE ]

I'm not sure if this is what he means, but if you randomly pick a door of the remaining two left you do have a 50/50 of getting it right

[/ QUOTE ]
No. The answer lies in several previous posts.

[/ QUOTE ]

Okay miscommunication I think, let me rephrase:

I'm not sure if this is what he means, but if you randomly pick a door of the remaining two left you will pick the right door 50% of the time

[/ QUOTE ]

Correct.

daryn

03-17-2005, 02:15 PM

<blockquote>In risposta di:<hr />
<blockquote>In risposta di:<hr />
<blockquote>In risposta di:<hr />
<blockquote>In risposta di:<hr />
<blockquote>In risposta di:<hr />

If there are 3 doors, I choose 1 and the host opens another, I have a 50/50 chance of being right between the remaining two doors.

[/ QUOTE ]

this statement is incorrect

[/ QUOTE ]

I'm not sure if this is what he means, but if you randomly pick a door of the remaining two left you do have a 50/50 of getting it right

[/ QUOTE ]
No. The answer lies in several previous posts.

[/ QUOTE ]

Okay miscommunication I think, let me rephrase:

I'm not sure if this is what he means, but if you randomly pick a door of the remaining two left you will pick the right door 50% of the time

[/ QUOTE ]

clearly.

edtost

03-17-2005, 02:15 PM

teddyFBI

03-17-2005, 02:16 PM

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
[ QUOTE ]

If there are 3 doors, I choose 1 and the host opens another, I have a 50/50 chance of being right between the remaining two doors.

[/ QUOTE ]

this statement is incorrect

[/ QUOTE ]

I'm not sure if this is what he means, but if you randomly pick a door of the remaining two left you do have a 50/50 of getting it right

[/ QUOTE ]
No. The answer lies in several previous posts.

[/ QUOTE ]

Okay miscommunication I think, let me rephrase:

I'm not sure if this is what he means, but if you randomly pick a door of the remaining two left you will pick the right door 50% of the time

[/ QUOTE ]

only if you do not know which one was picked originally.

[/ QUOTE ]

See word: RANDOMLY.
It doesn't matter what you "know" if you pick at random.

daryn

03-17-2005, 02:16 PM

key word = randomly

andyfox

03-17-2005, 02:18 PM

We went over this "Monty Hall" problem a few years back and I embarrassed myself with a flood of incorrectness. At least I can now explain the answer in a way that made sense to me.

Bottom line: you switch.

The way it was explained to me was to imagine you're at a golf driving range. Someone asks you to guess which ball he has picked out from the range out of the 10,000 that are there. You pick one. He now tells you that 9,998 are not the ball he picked. So that leaves the one you picked plus one other one left over. He asks if you want to stay with your original pick or switch to the other one.

When you picked yours, your odds were 9.999 to 1. Now the one he's offering you is 1:1. Makes sense to switch.

He's eliminated 9,998 out of the 9,999 wrong answers for you at this point.

daryn

03-17-2005, 02:21 PM

the one he's offering you is not 1:1. that is important! it's still 9,999-1 if you stick with the original.

Shajen

03-17-2005, 02:23 PM

[ QUOTE ]
[ QUOTE ]

If there are 3 doors, I choose 1 and the host opens another, I have a 50/50 chance of being right between the remaining two doors.

[/ QUOTE ]

this statement is incorrect

[/ QUOTE ]

Yeah, I know it was. I was explaining my reasoning and then how I came to understand it.

andyfox

03-17-2005, 02:23 PM

Try this: I ask you to pick a star in the sky. There are billions and billion of them. You pick one. I now eliminate out of the, say, 100 hundred billion, 99,999,999,998 of the wrong answers. Now I ask you if you want to stick with your original guess or switch to the other remaining possible correct answer.

The odds that your star was a correct guess are 999,999,999,999 to 1. You still want to stick with your original answer?

teddyFBI

03-17-2005, 02:24 PM

[ QUOTE ]
We went over this "Monty Hall" problem a few years back and I embarrassed myself with a flood of incorrectness. At least I can now explain the answer in a way that made sense to me.

Bottom line: you switch.

The way it was explained to me was to imagine you're at a golf driving range. Someone asks you to guess which ball he has picked out from the range out of the 10,000 that are there. You pick one. He now tells you that 9,998 are not the ball he picked. So that leaves the one you picked plus one other one left over. He asks if you want to stay with your original pick or switch to the other one.

When you picked yours, your odds were 9.999 to 1. Now the one he's offering you is 1:1. Makes sense to switch.

[/ QUOTE ]

Nope - this is again incorrect (and another reason I love this teaser; even people who THINK they get it don't really). The odds on the other golf ball would not be 1:1 but rather much, much, much, much better: 1:9999. In other words, you'll win 9,999 times if you switch (not 50/50 as your 1:1 ratio implies).

You're correct though in that once the # of doors is increased beyond 3, it's much easier to see why u should switch.

teddyFBI

03-17-2005, 02:25 PM

[ QUOTE ]
the one he's offering you is not 1:1. that is important! it's still 9,999-1 if you stick with the original.

[/ QUOTE ]

daryn, we're sharing a brain right now - we've duplicated each others posts at least 3 times in this thread.

Shajen

03-17-2005, 02:25 PM

daryn

03-17-2005, 02:26 PM

ok i will quit this thread since we seem to be posting the exact same answers /images/graemlins/grin.gif

andyfox

03-17-2005, 02:26 PM

Yes, my bad, thanks.

daryn

03-17-2005, 02:27 PM

WTF.. we even posted the same post about posting the same posts

andyfox

03-17-2005, 02:27 PM

Thanks.

astroglide

03-17-2005, 02:52 PM

yeah i figured i shouldn't have said anything about percentages. logically it makes sense that it would be more likely to win than the other one so i pick it. i slept through algebra 2 and flunked it and that's as far as i went. didn't go to college.

for the record though it's utterly gay to say "BUT YOU ARE COMPLETELY WRONG SIR AND HERE IS WHY..." if somebody says the wrong answer about not switching here. i would be surprised if anybody in this thread answered correctly and for the right reasons the first time they were told about it. it's like jumping on somebody for making a guess at a riddle and being wrong. every time i see somebody present this they give the answer as if they figured it out themself.

it's ok to jam on my math skills though.

daryn

03-17-2005, 02:56 PM

it's less about jumping on someone for the wrong answer and more about just telling them how to arrive at the correct one.

it's not like HAHA U R WRONG IDIOT!

jimdmcevoy

03-17-2005, 03:00 PM

[ QUOTE ]
yeah i figured i shouldn't have said anything about percentages. logically it makes sense that it would be more likely to win than the other one so i pick it. i slept through algebra 2 and flunked it and that's as far as i went. didn't go to college.

for the record though it's utterly gay to say "BUT YOU ARE COMPLETELY WRONG SIR AND HERE IS WHY..." if somebody says the wrong answer about not switching here. i would be surprised if anybody in this thread answered correctly and for the right reasons the first time they were told about it. it's like jumping on somebody for making a guess at a riddle and being wrong. every time i see somebody present this they give the answer as if they figured it out themself.

it's ok to jam on my math skills though.

[/ QUOTE ]

i also find it annoying when people are like this

i'm not sure if they feel the need to show how smart they are or if they have a small penis

astroglide

03-17-2005, 03:01 PM

what i'm saying is that in general people really do the equivalent of the "HAHA IDIOT" thing, they do the "OH, BUT YOU SEE MY FRIEND IT IS VERY CLEAR THAT..." thing. it's just as bad. i don't think anybody's an idiot if they get this one wrong. if they get it right they're probably not only good at math but into riddles/logic puzzles as well. but then how could they have not run into the monty hall thing?

anyway this isn't about my bad math, i accept that. i didn't calculate anything at all. i didn't say the wrong answer so nobody jumped on me for that, i'm just speaking about that subject.

it's just kind of a tangent about people who tell this thing unprovoked (not in response to other people telling puzzles/riddles). i would bet that an overwhelming majority of them are doing it to appear smart when the person says they wouldn't change the door and they explain why. then the person who guessed wrong goes and does it to somebody else. it's a cycle of abuse.

the phrasing of fbi's response reeks of intent though: "This reasoning is the classic 'incorrect' reasoning. Your odds if you switch in the 1000 doors example is NOT 50% but rather 999 / 1000. Even though you get the answer right, your reasoning is deeply flawed. When you switch in the 3 door example you're NOT improving your odds from 33% to 50% but rather from 33% to 66%."

look at the emphasis. and do you think he says "but rather" several times per utterance in real life? odds are he's one of those lame guys. patrick, for example, doesn't seem to be one of those lame guys.

private joker

03-17-2005, 03:16 PM

This is also one of my favorite brainteasers. I remember getting it in 8th grade math and everyone being stumped. I, of course, staunchly argued for the 50/50 answer, and then the teacher explained that the "second chance" essentially allows you to pick either the other 2 doors or the original one door. That one of the "other 2" is opened means nothing. Of the other 2, obviously at least one will be wrong, so showing it to you has no bearing on the odds of the right door. So once you start thinking of the second choice being a grouping of 2 doors, it's easy to see why switching is correct.

My life has not been the same since 8th grade.

(Note: this is because in 8th grade I was injured in a tragic blimp accident and lost the use of my arms, so I've been typing with my toes, but that has nothing to do with this brainteaser so forget I mentioned it).

Peca277

03-17-2005, 03:16 PM

http://img.photobucket.com/albums/v622/Peca277/game.jpg

Shajen

03-17-2005, 03:29 PM

[ QUOTE ]
http://img.photobucket.com/albums/v622/Peca277/game.jpg

[/ QUOTE ]

Insufficient sample size.

/images/graemlins/wink.gif

fluxrad

03-17-2005, 09:19 PM

[ QUOTE ]
Insufficient sample size.

[/ QUOTE ]

fluxrad@timmy:~/devel$ ./monty.pl
Running monty 1 million times

----Number of Wins----
Stay: 333882
Switch: 666118

SossMan

03-17-2005, 09:28 PM

[ QUOTE ]
[ QUOTE ]
It's also old. As good as it is, I'm surprised not everyone has heard it before =)

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especially since it is posted on 2+2 about once every 3 months for the last 2 years.

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yeah, this reminds me. Isn't it time to start a "Should I fold AA preflop" thread and a "What did KGB have in the final hand of Rounders" thread?

Skjonne

03-18-2005, 08:43 AM

[ QUOTE ]
[ QUOTE ]
[ QUOTE ]
It's also old. As good as it is, I'm surprised not everyone has heard it before =)

[/ QUOTE ]

especially since it is posted on 2+2 about once every 3 months for the last 2 years.

[/ QUOTE ]

yeah, this reminds me. Isn't it time to start a "Should I fold AA preflop" thread and a "What did KGB have in the final hand of Rounders" thread?

[/ QUOTE ]

No! We want nude pics!

Btw. The math who supports switching door is called Bayes' Theorem

Brian

03-19-2005, 11:52 PM

It took me about 30 minutes of reading and re-reading this thread before I finally understood this brain-teaser. Armed with the knowledge of how it worked, I decided to try unleashing it upon my family. My parents are pretty smart people, both with large math and chemistry backgrounds, though they are now in their mid-50's and have forgotten most of it. When I told them this brain-teaser, they argued with me for about 30 minutes before we finally decided to get out 3 cups and a small toy chicken and test it for ourselves.

We did about 50 trials with 3 cups, and even though that's a very small sample size, they began to see things more clearly. I then began adding on more and more cups, and they finally were able to grasp the concept.

Anyways, thanks for sharing this with us. I had certainly never heard it before, and no one to whom I have told it since had heard it either. And you are right, the elgeance of it and the fact that there aren't any trick answers really makes it great.

-Brian