A logic puzzle

lumpy

tcrossma wrote: »

Yeah, but increase the sample size. Let's say you have 1 million items to choose from, and you have to pick 1. That's a 1 in a million chance of you being correct. Then 999,998 of the remaining items are taken away and you are left with two items -- yours and one other.

Do you still think it's just 50/50 odds?

I would think that I must have made th correct choice the first time since you could so easily take all but one of the remaining

I wonder how many people who feel that swapping provides the best odds, still play the same lottery # every day

has anyone ever put this to a physical test with live people and actuall boxes? If so - from the vantage point of the beggining - do 66% of people actually win by switching? Also - from the vantage point of the start of the second choice - do 50% of people win no matter what choice they made?

tommyboy

lumpy wrote: »

I would think that I must have made th correct choice the first time since you could so easily take all but one of the remaining

I wonder how many people who feel that swapping provides the best odds, still play the same lottery # every day

has anyone ever put this to a physical test with live people and actuall boxes? If so - from the vantage point of the beggining - do 66% of people actually win by switching? Also - from the vantage point of the start of the second choice - do 50% of people win no matter what choice they made?

This reason for the test to begin with is the illusion that you have a 50/50 chance of winning. I'm not sure if this has been done commercially. But it ALL depends on the sample size (and luck I guess;)). If its done only few times, its almost guarenteed it won't be 66% win, 33% lose. If you took a test with 20 multiple choice question (4 answers each) and you guess on every one of them. That doesn't mean you automatically get a 25% grade.

This is why we have prob and stats classes;)

Disc Jockey

"After considerable discussion and vacillation here at the Los Alamos National Laboratory, two of my colleagues independently programmed the problem, and in 1,000,000 trials, switching paid off 66.7% of the time. The total running time on the computer was less than one second.

G.P. DeVault, Ph.D., Los Alamos National Laboratory
Los Alamos, New Mexico"

tommyboy

Also, instead of having this test be done, I think perfect example are casinos. I saw on history channel a while back how a casino increases its chances slightly from 50/50 to 52/48 ( how they found this number or I guess how they enforce it, I have no clue). But this small increase makes them millions of dollars a year. Does that mean you will always lose... of course not. But it only means the more you go, the much better chance you have of losing.

Haha ok I'll shut up

bobman1235

lumpy wrote: »

has anyone ever put this to a physical test with live people and actuall boxes? If so - from the vantage point of the beggining - do 66% of people actually win by switching? Also - from the vantage point of the start of the second choice - do 50% of people win no matter what choice they made?

Why would anyone do this test when anyone who has ever taken a statistics class can easily see the answer? You could just as easily "simulate" this in your head as do it for real; your suggestion that it needs "lab" time is idiotic.

virtualdean

bobman1235 wrote: »

Why would anyone do this test when anyone who has ever taken a statistics class can easily see the answer? You could just as easily "simulate" this in your head as do it for real; your suggestion that it needs "lab" time is idiotic.

I believe Will Rogers once said, " There are lies, damned lies, and statistics"

Who knows who said it? I got a 33% chance of being right.

bobman1235

virtualdean wrote: »

I believe Will Rogers once said, " There are lies, damned lies, and statistics"

Who knows who said it? I got a 33% chance of being right.

So not only do you not understand statistics but you also don't understand quotes about statistics? Awesome.

mrbigbluelight

virtualdean wrote: »

I believe Will Rogers once said, " There are lies, damned lies, and statistics"

Who knows who said it? I got a 33% chance of being right.

psssssstt....... try "Mark Twain" and you'll increase your chance of being right 67 % ......


Will Rogers did say, "A man only learns in two ways, one by reading, and the other by association with smarter people."

Maybe that's what you were thinking of.

arun1963

Going purely by logic, no I wouldn't switch boxes. The experimenter knows which box has the $ 10. Logic says he wouldn't want to lose the $ 10. So if he's giving me the option to switch, I must be holding the right box.

lumpy

I will admit that I was wrong about it being 50/50. the link a few posts back with the problem displayed on a spreadsheet convinced me.

arun1963

There were three boxes. You picked one so 1/3 chance of wining. Suddenly you discover that one one of the other boxes is empty. So thats down to 1 of 2 thats 50% don't let any of the audio geeks confuse you.

Basic conditions have changed youre now evaluating 1/2 boxes instead of 1/3 boxes

concealer404

arun1963 wrote: »

There were three boxes. You picked one so 1/3 chance of wining. Suddenly you discover that one one of the other boxes is empty. So thats down to 1 of 2 thats 50% don't let any of the audio geeks confuse you.

Have you bothered to try to understand any of the explanations, or would you rather just make it personal because you don't understand?

I'll make this simple for you, there are only two possible scenarios:

1) You pick the car the first time. After being shown an empty box, you switch to the other empty box. This will happen 33.33% of the time.
2) You pick an empty box the first time. You are shown an empty box, you switch to the other box, that has a car. This will happen 66.67% of the time, because there are two empty boxes to start with.

Try to understand or at least ask questions before you start with the immature name-calling. Mkay? This has nothing to do with being an "audio geek," this is merely statistics/probability.

bobman1235

arun1963 wrote: »

There were three boxes. You picked one so 1/3 chance of wining. Suddenly you discover that one one of the other boxes is empty. So thats down to 1 of 2 thats 50% don't let any of the audio geeks confuse you.

Basic conditions have changed youre now evaluating 1/2 boxes instead of 1/3 boxes

Apart from the name-calling - you don't suddenly discover anything. You knew from the start one of the other boxes was empty. Only one box has something in it. No matter which box you choose, there will always be an empty one remaining. Someone with KNOWLEDGE OF WHICH IS WHICH just shows you that empty one. He shows you something you knew to be true from the very start. It changes NOTHING.

arun1963

concealer404 wrote: »

Have you bothered to try to understand any of the explanations, or would you rather just make it personal because you don't understand?

I'll make this simple for you, there are only two possible scenarios:

1) You pick the car the first time. After being shown an empty box, you switch to the other empty box. This will happen 33.33% of the time.
2) You pick an empty box the first time. You are shown an empty box, you switch to the other box, that has a car. This will happen 66.67% of the time, because there are two empty boxes to start with.

Try to understand or at least ask questions before you start with the immature name-calling. Mkay? This has nothing to do with being an "audio geek," this is merely statistics/probability.

Ummm no. You pick one box out of three, you have a 33.33% chance i.e. 1/3. Suddenly one of the boxes is exposed as a dud. So now there are two boxes and you hold one of them what are your chances? There is a major flaw in the argument. If you haven't caught it thats your problem.

THE ORIGINAL ODDS 1/3 DON'T STAY CONSTANT CAUSE YOU'RE DELETING ONE BOX. Don't you get it? Or do you have to suck up to the uninformed just to stay in the reckoning?

concealer404

arun1963 wrote: »

Ummm no. You pick one box out of three, you have a 33.33% chance i.e. 1/3. Suddenly one of the boxes is exposed as a dud. So now there are two boxes and you hold one of them what are your chances? There is a major flaw in the argument. If you haven't caught it thats your problem.

THE ORIGINAL ODDS 1/3 DON'T STAY CONSTANT CAUSE YOU'RE DELETING ONE BOX. Don't you get it? Or do you have to suck up to the uninformed just to stay in the reckoning?

Answer the original question: Have you checked out the links, including the very instructive video from youtube that explains this very situation to the point that a 3rd grader would understand?

There are no flaws in the argument. Either 1) you don't understand the scenario or 2) you don't understand statistics.

Neither of choice 1 or 2 should result in personal attacks.

Reported.

concealer404

Here, arun1963, i'll walk you through it one step at a time:

Please answer this first question:

What are the chances that you'll pick the car on your first try? Also what are the chances that you'll pick a dud on the first try?


Please answer these, and then we'll move to the next step.

wz2p7j

I believe this problem, if I'm not mistaken, is what's called a conditional probability.

Another example would be, flipping a coin and the probability of getting "heads."
Correct answer is 50/50
Now what if I tell you that I just flipped that same coin 8 times before you showed up and each time it was heads.
Now the question becomes what is the probability of getting heads knowing you just flipped and got heads 8 times in a row.

If I remember correctly a fellow named Thomas Bayes, an Englishman, was a pioneer in conditional stats and Baysian statistics. I remember it being pretty interesting in my stats classes but don't remember much else about it.

Chris

concealer404

wz2p7j wrote: »

I believe this problem, if I'm not mistaken, is what's called a conditional probability.

Another example would be, flipping a coin and the probability of getting "heads."
Correct answer is 50/50
Now what if I tell you that I just flipped that same coin 8 times before you showed up and each time it was heads.
Now the question becomes what is the probability of getting heads knowing you just flipped and got heads 8 times in a row.

If I remember correctly a fellow named Thomas Bayes, an Englishman, was a pioneer in conditional stats and Baysian statistics. I remember it being pretty interesting in my stats classes but don't remember much else about it.

Chris

Ehhh... that's something different. The difference with your scenario is that it's still 50/50 because the probability of getting heads is ALWAYS 50%, no matter how many times it's come up before. Each flip is it's own separate entity with no previous outcomes affecting it. There's only two possibilities.

What we're talking about is known as "Variable Change," a two step process that originally had two outcomes spread across three choices.

wz2p7j

concealer404 wrote: »

Ehhh... that's something different. The difference with your scenario is that it's still 50/50 because the probability of getting heads is ALWAYS 50%, no matter how many times it's come up before. Each flip is it's own separate entity with no previous outcomes affecting it. There's only two possibilities.

What we're talking about is known as "Variable Change," a two step process that originally had two outcomes spread across three choices.

Negative - read up on Bayes.

Chris

concealer404

wz2p7j wrote: »

Negative - read up on Bayes.

Chris

Give me a few minutes, i'm up to learn new stuff.


(EDIT)

Alright, i see what that is.

It's closer related to the Monty Hall problem than a coin toss, but here's why it won't work with a standard coin toss. (One coin, multiple tosses.)

Conditional Probability would say that if you tossed and got a head, the head is now REMOVED from the probability of the next toss. Since you're tossing the same coin again, you can still get either heads, or tails. Still a 50/50.

Conditional Probability would dictate that if you just got a head, then the next toss HAS to be tails, because you already got a head, and the head is now removed from the equation. No dice.

wz2p7j

Actually concealer, I think there might be a bone of contention among "classic" stats and Baysian stats. The classic stats would argue it's always 50/50. Bayes argued if you had prior knowledge of, say, 8 straight heads, that needed to be considered. I don't remember much more - it was long time ago!

Chris

concealer404

wz2p7j wrote: »

Actually concealer, I think there might be a bone of contention among "classic" stats and Baysian stats. The classic stats would argue it's always 50/50. Bayes argued if you had prior knowledge of, say, 8 straight heads, that needed to be considered. I don't remember much more - it was long time ago!

Chris

Yes, Bayes does seem to argue that, but that's not conditional probability.

FiveORacing

arun1963 wrote: »

There were three boxes. You picked one so 1/3 chance of wining. Suddenly you discover that one one of the other boxes is empty. So thats down to 1 of 2 thats 50% don't let any of the audio geeks confuse you.

Basic conditions have changed youre now evaluating 1/2 boxes instead of 1/3 boxes

I was thinking along those lines as well, assuming the eliminated box was random and could even be yours or the winner. But it's not. The examiner will always avoid two boxes in exposing an empty one, the winner and yours. The million box example got me on the right track. Let's say you initially pick #7 (a loser) and the winner is #8. The chance you picked the winner was 1 in a million to start. The examiner will now start revealing boxes, always avoiding 7 and 8. When it gets down to two boxes the chances you picked the right one is still one in a million, but the chances that the other box is the winner are pretty darn good, as he needed to avoid that for 999,998 reveals.

If the reveals were truly random, and not "chosen" by the examiner, including possibly being yours or the winner every time, and you got down to 2 boxes, then the chances you were right is now one in two. But that would have been a one in a million guess from the onset.

Sorry I missed that important little fact the first time.

concealer404

What i think the people that don't understand are missing is that the examiner KNOWS which box has the prize.

(EDIT)

FiveORacing got it.

wz2p7j

concealer404 wrote: »

Yes, Bayes does seem to argue that, but that's not conditional probability.

OK - probably wasn't using the right word. (no pun intended) :)

Chris

concealer404

wz2p7j wrote: »

OK - probably wasn't using the right word. (no pun intended) :)

Chris

Bayes seems to be the equivalent of those of us who believe in cables. I've got some fundamental issues with what he says, though. I can get behind the theory, but i don't understand how he seems to be able to calculate the probability of something without knowing the sample size. But i think that's my problem with it right there, it's not true probability or statistics, it's more of an "educated guessing game."

Interesting reading material, though.

But i guess you can call me Woger Wussel in this one. ;)

tommyboy

arun1963 wrote: »

Ummm no. You pick one box out of three, you have a 33.33% chance i.e. 1/3. Suddenly one of the boxes is exposed as a dud. So now there are two boxes and you hold one of them what are your chances? There is a major flaw in the argument. If you haven't caught it thats your problem.

THE ORIGINAL ODDS 1/3 DON'T STAY CONSTANT CAUSE YOU'RE DELETING ONE BOX. Don't you get it? Or do you have to suck up to the uninformed just to stay in the reckoning?

School is your friend. (or just read the many posts that explain exactly why you are wrong, trolling maybe?)

hearingimpared

Well, I've read every post and every scenario given by each poster and what I've deduced from all the banter is;

Abbott: Well, Costello, I'm going to New York with you. Bucky Harris the Yankee's manager gave me a job as coach for as long as you're on the team.

Costello: Look Abbott, if you're the coach, you must know all the players.

Abbott: I certainly do.

Costello: Well you know I've never met the guys. So you'll have to tell me their names, and then I'll know who's playing on the team.

Abbott: Oh, I'll tell you their names, but you know it seems to me they give these ball players now-a-days very peculiar names.

Costello: You mean funny names?

Abbott: Strange names, pet names...like Dizzy Dean...

Costello: His brother Daffy

Abbott: Daffy Dean...

Costello: And their French cousin.

Abbott: French?

Costello: Goofe'

Abbott: Goofe' Dean. Well, let's see, we have on the bags, Who's on first, What's on second, I Don't Know is on third...

Costello: That's what I want to find out.

Abbott: I say Who's on first, What's on second, I Don't Know's on third.

Costello: Are you the manager?

Abbott: Yes.

Costello: You gonna be the coach too?

Abbott: Yes.

Costello: And you don't know the fellows' names.

Abbott: Well I should.

Costello: Well then who's on first?

Abbott: Yes.

Costello: I mean the fellow's name.

Abbott: Who.

Costello: The guy on first.

Abbott: Who.

Costello: The first baseman.

Abbott: Who.

Costello: The guy playing...

Abbott: Who is on first!

Costello: I'm asking you who's on first.

Abbott: That's the man's name.

Costello: That's who's name?

Abbott: Yes.

Costello: Well go ahead and tell me.

Abbott: That's it.

Costello: That's who?

Abbott: Yes. PAUSE

Costello: Look, you gotta first baseman?

Abbott: Certainly.

Costello: Who's playing first?

Abbott: That's right.

Costello: When you pay off the first baseman every month, who gets the money?

Abbott: Every dollar of it.

Costello: All I'm trying to find out is the fellow's name on first base.

Abbott: Who.

Costello: The guy that gets...

Abbott: That's it.

Costello: Who gets the money...

Abbott: He does, every dollar of it. Sometimes his wife comes down and collects it.

Costello: Who's wife?

Abbott: Yes. PAUSE

Abbott: What's wrong with that?

Costello: I wanna know is when you sign up the first baseman, how does he sign his name?

Abbott: Who.

Costello: The guy.

Abbott: Who.

Costello: How does he sign...

Abbott: That's how he signs it.

Costello: Who?

Abbott: Yes. PAUSE

Costello: All I'm trying to find out is what's the guys name on first base.

Abbott: No. What is on second base.

Costello: I'm not asking you who's on second.

Abbott: Who's on first.

Costello: One base at a time!

Abbott: Well, don't change the players around.

Costello: I'm not changing nobody!

Abbott: Take it easy, buddy.

Costello: I'm only asking you, who's the guy on first base?

Abbott: That's right.

Costello: OK.

Abbott: Alright. PAUSE

Costello: What's the guy's name on first base?

Abbott: No. What is on second.

Costello: I'm not asking you who's on second.

Abbott: Who's on first.

Costello: I don't know.

Abbott: He's on third, we're not talking about him.

Costello: Now how did I get on third base?

Abbott: Why you mentioned his name.

Costello: If I mentioned the third baseman's name, who did I say is playing third?

Abbott: No. Who's playing first.

Costello: What's on base?

Abbott: What's on second.

Costello: I don't know.

Abbott: He's on third.

Costello: There I go, back on third again! PAUSE

Costello: Would you just stay on third base and don't go off it.

Abbott: Alright, what do you want to know?

Costello: Now who's playing third base?

Abbott: Why do you insist on putting Who on third base?

Costello: What am I putting on third.

Abbott: No. What is on second.

Costello: You don't want who on second?

Abbott: Who is on first.

Costello: I don't know. Together: Third base! PAUSE

Costello: Look, you gotta outfield?

Abbott: Sure.

Costello: The left fielder's name?

Abbott: Why.

Costello: I just thought I'd ask you.

Abbott: Well, I just thought I'd tell ya.

Costello: Then tell me who's playing left field.

Abbott: Who's playing first.

Costello: I'm not...stay out of the infield!!! I want to know what's the guy's name in left field?

Abbott: No, What is on second.

Costello: I'm not asking you who's on second.

Abbott: Who's on first!

Costello: I don't know. Together: Third base! PAUSE

Costello: The left fielder's name?

Abbott: Why.

Costello: Because!

Abbott: Oh, he's center field. PAUSE

Costello: Look, You gotta pitcher on this team?

Abbott: Sure.

Costello: The pitcher's name?

Abbott: Tomorrow.

Costello: You don't want to tell me today?

Abbott: I'm telling you now.

Costello: Then go ahead.

Abbott: Tomorrow!

Costello: What time?

Abbott: What time what?

Costello: What time tomorrow are you gonna tell me who's pitching?

Abbott: Now listen. Who is not pitching.

Costello: I'll break you're arm if you say who's on first!!! I want to know what's the pitcher's name?

Abbott: What's on second.

Costello: I don't know. Together: Third base! PAUSE

Costello: Gotta a catcher?

Abbott: Certainly.

Costello: The catcher's name?

Abbott: Today.

Costello: Today, and tomorrow's pitching.

Abbott: Now you've got it.

Costello: All we got is a couple of days on the team. PAUSE

Costello: You know I'm a catcher too.

Abbott: So they tell me.

Costello: I get behind the plate to do some fancy catching, Tomorrow's pitching on my team and a heavy hitter gets up. Now the heavy hitter bunts the ball. When he bunts the ball, me, being a good catcher, I'm gonna throw the guy out at first. So I pick up the ball and throw it to who?

Abbott: Now that's the first thing you've said right.

Costello: I don't even know what I'm talking about! PAUSE

Abbott: That's all you have to do.

Costello: Is to throw the ball to first base.

Abbott: Yes!

Costello: Now who's got it?

Abbott: Naturally. PAUSE

Costello: Look, if I throw the ball to first base, somebody's gotta get it. Now who has it?

Abbott: Naturally.

Costello: Who?

Abbott: Naturally.

Costello: Naturally?

Abbott: Naturally.

Costello: So I pick up the ball and I throw it to Naturally.

Abbott: No you don't you throw the ball to Who.

Costello: Naturally.

Abbott: That's different.

Costello: That's what I said.

Abbott: you're not saying it...

Costello: I throw the ball to Naturally.

Abbott: You throw it to Who.

Costello: Naturally.

Abbott: That's it.

Costello: That's what I said!

Abbott: You ask me.

Costello: I throw the ball to who?

Abbott: Naturally.

Costello: Now you ask me.

Abbott: You throw the ball to Who?

Costello: Naturally.

Abbott: That's it.

Costello: Same as you! Same as YOU!!! I throw the ball to who. Whoever it is drops the ball and the guy runs to second. Who picks up the ball and throws it to What. What throws it to I Don't Know. I Don't Know throws it back to Tomorrow, Triple play. Another guy gets up and hits a long fly ball to Because. Why? I don't know! He's on third and I don't give a darn!

Abbott: What?

Costello: I said I don't give a darn!

Abbott: Oh, that's our shortstop.

Costello: (makes screaming sound)

hearingimpared makes a screaming sound!!!:D:D:D:D:D

mrbigbluelight

^^^^ I believe Professor Joe has summed up this week's lesson most excellently. :D:D

PhantomOG

Just think about it this way. 3 boxes. 1 prize. Would you rather:

A) Choose 1 box?
or
Choose 2 boxes?

The statistics and numbers only reflect those choices. The 'not swapping' strategy is exactly the same as choosing one box... you win 33% of the time. The 'swapping' strategy is the same as choosing two boxes... you win 66% of the time.

By 'not swapping' you choose one box and get one box. By 'swapping' you effectively *get* two boxes, one guaranteed not to be the prize (by nature) and one which could be the prize.