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TomBrooklyn
08-08-2002, 09:16 AM
I was going to ask this in another recent thread where IQ was being discussed, but that thread seems long enough already.

Does anybody know who has the highest IQ that can be cited from a reliable source?

Lester
08-08-2002, 09:20 AM
<blockquote><font class="small">Quote: TomBrooklyn:</font><hr> I was going to ask this in another recent thread where IQ was being discussed, but that thread seems long enough already.

Does anybody know who has the highest IQ that can be cited from a reliable source? <hr></blockquote>
&gt;&gt;&gt;&gt;&gt;I can tell you it's not me, Tom. I'm as dumb as a nail, and maybe a little "bent" too. lol ***Lester***

08-08-2002, 09:25 AM
i would say your asking what pool player has the highest iq i would say johnny everlino he made a living out of pool for about 50 years

PQQLK9
08-08-2002, 09:46 AM
Most people have an IQ in the 90 - 109 range. You're considered a genius if your IQ is 132 or above. Chris Langan has an IQ of 195, the highest known IQ in the US. He started talking at 6 months and by age 4 could read and comprehend books. His IQ puts him in the same class as Sir Isaac Newton and Michelangelo. He's in his mid-forties, and he works as a part-time bouncer at a bar and lives in a one-room house on $6,000 a year. He's not a success by most modern standards. Then there's William James Sidis with his highest ever known IQ estimated at between 250 and 300. At eighteen months he could read The New York Times, at two he taught himself Latin, at three he learned Greek. By the time he was an adult he could speak more than forty languages and dialects. He spent most of his life wandering from one menial job to another.

Drake
08-08-2002, 09:48 AM
OR.....Who has run the most racks??? or the most balls in Straight POOL?? Be HONEST, and virtual pool doesn't count Patrick.

PQQLK9
08-08-2002, 09:51 AM
<blockquote><font class="small">Quote: finnegan:</font><hr> i would say your asking what pool player has the highest iq i would say johnny everlino he made a living out of pool for about 50 years <hr></blockquote>

As Johnny would say "Those Tables are playing BEEYOOOTEEFOOOLY" /ccboard/images/icons/smile.gif

Kato
08-08-2002, 09:52 AM
Would you believe it if I said it was me? No didn't think so.

Kato~~~sharp as a marble.

08-08-2002, 10:07 AM

nAz
08-08-2002, 10:10 AM
the average iq is 100, so 1/2 of the population is over 100, and 1/2 is under 100.

84-116 is normal, and anything above and below are obvious. anything under 70 is mental retardation. (70 is the average IQ of most pool players i met... im sure you will agree with that lol)

in the standardized stanford/binet intel' test, 68.2% score normal, and 15.9% score in each direction. though the WAIS test is the most widely used, i only have info on the stanford-binet test, but you get the general idea.

also note that online tests are always wacked out to give you a score you probably don't deserve, so don't break out the champaigne yet. This particular online test is probably one of the more accurate ones though.

Tom try out this IQ test its pretty good. I scored 127 /ccboard/images/icons/frown.gif Not bad for a grade scool drop out

<a target="_blank" href=http://www.emode.com/tests/uiq/authorize/register.jsp?url=/tests/uiq/index.jsp>http://www.emode.com/tests/uiq/authorize/register.jsp?url=/tests/uiq/index.jsp</a>

Chris Cass
08-08-2002, 10:18 AM
<blockquote><font class="small">Quote: Lester:</font><hr>
&gt;&gt;&gt;&gt;&gt;I can tell you it's not me, Tom. I'm as dumb as a nail, and maybe a little "bent" too. lol ***Lester*** <hr></blockquote>

HAHAHAHHAHAHA Gosh, I like you Lester.

Regards,

C.C.

PQQLK9
08-08-2002, 10:40 AM
President Bush Has Lowest IQ of all Presidents of past 50 Years


The Pennsylvania Court Observer
http://207.69.141.215/BushIQ.shtml
7-10-01 12:32 PM CST
University Notes
Contributors: Cristina L. Borenstein, Lana Taamar

Report: President Bush Has Lowest IQ of all Presidents of past 50 Years

If late night TV comedy is an indicator, then there has never been as widespread a perception that a president is not intellectually qualified for the position he holds as there is with President GW Bush. In a report published Monday, the Lovenstein Institute of Scranton, Pennsylvania detailed its findings of a four month study of the intelligence quotient of President George W. Bush. Since 1973, the Lovenstein Institute has published it's research to the education community on each new president, which includes the famous "IQ" report among others. According to statements in the report, there have been twelve presidents over the past 50 years, from F. D. Roosevelt to G. W. Bush who were all rated based on scholarly achievements, writings that they alone produced without aid of staff, their ability to speak
with clarity, and several other psychological factors which were then scored in the Swanson/Crain system of intelligence ranking. The study determined the following IQs of each president as accurate to within five percentage points:

147 Franklin D. Roosevelt (D)
132 Harry Truman (D)
122 Dwight D. Eisenhower (r)
174 John F. Kennedy (D)
126 Lyndon B. Johnson (D)
155 Richard M. Nixon (r)
121 Gerald Ford (r)
175 James E. Carter (D)
105 Ronald Reagan (r)
098 George HW Bush (r)
182 William J. Clinton (D)
091 George W. Bush (r)

The six Republican presidents of the past 50 years had an average IQ of 115.5, with President Nixon having the highest IQ, at 155. President G. W. Bush was rated the lowest of all the Republicans with an IQ of 91. The six Democrat presidents had IQs with an average of 156, with President Clinton having the highest IQ, at 182. President Lyndon B. Johnson was rated the lowest of all the Democrats with an IQ of 126.

Among comments made concerning the specific testing of President GW Bush, his low ratings were due to his apparent difficulty to command the English language in public statements, his limited use of
vocabulary (6,500 words for Bush versus an average of 11,000 words for other presidents), his lack of scholarly achievements other than a basic MBA, and an absence of any body of work which could be studied
on an intellectual basis. The complete report documents the methods and procedures used to arrive at these ratings, including depth of sentence structure and voice stress confidence analysis. "All the Presidents prior to George W. Bush had a least one book under their belt, and most had written several white papers during their education or early careers. Not so with President Bush," Dr. Lovenstein said. "He has no published works or writings, so in many ways that made it more difficult to arrive at an assessment. We had to rely more heavily on transcripts of his unscripted public speaking." The Lovenstein Institute of Scranton Pennsylvania think tank includes high caliber historians, psychiatrists, sociologists, scientists in human behavior, and psychologists. Among their ranks are Dr. Werner
R. Lovenstein, world-renowned sociologist, and Professor Patricia F. Dilliams, a world-respected psychiatrist.
This study was commissioned on February 13, 2001 and released on July 9, 2001 to subscribing member universities and organizations within the education community.

SpiderMan
08-08-2002, 10:55 AM
That's disgusting - Bill Clinton's was the highest of all. Maybe he figured he was so much smarter than the rest of us that he could repeatedly betray public trust and get away with it. Of course, we proved him right. Sort of implies that we shouldn't base our choice of leaders on IQ. Too bad there's not an HQ (honesty quotient) /ccboard/images/icons/wink.gif

SpiderMan

08-08-2002, 10:57 AM
<blockquote><font class="small">Quote: PQQLK9:</font><hr>
President Bush Has Lowest IQ of all Presidents of past 50 Years
<hr></blockquote>
As much as this fits with my view of the man ;&lt;), it is an urban legend. See http://www.snopes2.com/ and search for Bush, IQ.

SpiderMan
08-08-2002, 10:58 AM
Yet she made an obvious mistake in her newspaper column, then compounded it by defending her incorrect answer in future columns. Something tells me she may be overrated. Is the name "Savant" correct from birth?

SpiderMan

Vapros
08-08-2002, 11:09 AM
Hey everybody, see the post from nAz. He has provided a link to an online IQ test. You can take it in just a few minutes and get your IQ score and a little analysis almost immediately - at no cost. Give it a shot, and post your own score if you want to.

Ross
08-08-2002, 11:13 AM
<blockquote><font class="small">Quote: SpiderMan:</font><hr> Yet she made an obvious mistake in her newspaper column, then compounded it by defending her incorrect answer in future columns. Something tells me she may be overrated. Is the name "Savant" correct from birth?

SpiderMan <hr></blockquote>
What mistake was that?

08-08-2002, 11:17 AM
Yea.. I actually took that test a few weeks ago (bored at work). Now I know Im a relatively smart guy... but my IQ is NOT 170 /ccboard/images/icons/smile.gif

Holly
08-08-2002, 11:41 AM
I believe at this time the person with the highest recorded IQ is Marilyn VosSavant, who writes that little column in the Parade magazine distributed as an insert in newspapers all over the country. If I remember correctly it is around 240 something. She is the poster child for Mensa also.

Tootles,

Holly

SpiderMan
08-08-2002, 12:26 PM
The actual details can probably be found somewhere on the internet, but as I recall it was a game-show scenario. There are three doors, behind one is a grand prize. You are asked to pick door #1, #2, or #3. Then the host asks you if you would like to change your guess. Should you?

Marilyn stated that you should always change your guess, then subsequently went through a flawed mathematical analysis to "prove" that this would increase your chance of getting the correct door. Engineers worldwide were flabbergasted. It was almost comical. Obviously, with no more data than you had to begin with, your second choice has no different chance than your first. Otherwise, why not change your guess again and again until your chances approached certainty /ccboard/images/icons/wink.gif I'm sure someone eventually must have explained it in a way she could understand, as all comment on the subject stopped and all further inquiries ignored. She's just pretending she never said it (like Bill Clinton, IQ182).

SpiderMan

Lester
08-08-2002, 12:40 PM
She's just pretending she never said it (like Bill Clinton, IQ182).

SpiderMan <hr></blockquote>
&gt;&gt;&gt;&gt;&gt;Hey Spidey, "If you can't dazzle em with brilliance, Baffle em with BS"! I think they teach that at MENSA. ***Lester***

heater451
08-08-2002, 12:53 PM
I would say that it's the current crew of the International Space Station:

http://spaceflight.nasa.gov/station/crew/exp5/


Then again, maybe there's a bonafide genius out there, who's stoking up the mother of all doobies right now. . . .


===================

bluewolf
08-08-2002, 01:18 PM
<blockquote><font class="small">Quote: TomBrooklyn:</font><hr> I was going to ask this in another recent thread where IQ was being discussed, but that thread seems long enough already.

Does anybody know who has the highest IQ that can be cited from a reliable source? <hr></blockquote>

uhoh.here we go again! LOL

bluewolf

bluewolf
08-08-2002, 01:25 PM
wow. how did he make it through college. it is hard to get a hs diploma with that iq. not that it is impossible, but the person has to work like 'h

bluewolf

08-08-2002, 01:30 PM
Actually, hers is a true phenomenon. The complete example is:

You pick a door. The host then reveals ANOTHER door that is NOT the grand prize. He then asks you if you'd like to change your guess to the last door.

Believe it or not, you should. Your original guess was based on a 1 in 3, whereas now you are increasing your odds to 1 in 2.

That is a simple explanation of the math behind it. I'm sure it gets a little more complicated. Anyway, I have seen this on the Discovery channel; a famous mathematician came up with it as a puzzle.

In short, if this is how Marilyn explained it, she is not wrong.

- Steve Lipsky

bluewolf
08-08-2002, 01:42 PM
<blockquote><font class="small">Quote: Kato:</font><hr> Would you believe it if I said it was me? No didn't think so.

Kato~~~sharp as a marble. <hr></blockquote>

A few statements from CIA psychologists

research shows that when teachers are asked to rate their students they pick extrovers over introverts.

People with social charisma are rated higher than those who are socially clumsy.
----
How do they figure out all of these very high IQs

bluewolf

Doomsday Machine
08-08-2002, 01:42 PM
If you have a 1 in 3 chance with your first choice and then you have a 1 in 2 chance what would be the advantage of changing your original choice ?? This would be the same as changing your choice if you are flipping coins while the coin is in the air. I absolutely see NO advantage to this whatsoever.

08-08-2002, 01:48 PM
Well, the coin will always be a 1 in 2 prop, so I don't think that's a valid analogy.

Here it is: If the game show were to show you a door, BY RANDOMLY picking one of the two doors left, then you might as well stay with your first guess.

However, they're not doing that. They know which of the two doors left is a dud. So they're just showing it to you.

In essence (and here is the interesting part), your guess is STILL a 1 in 3 if you don't switch. It's still a 1 in 3 because your guess was made with the same information you now have (there were 2 duds)... now they're just showing you one of the duds. If you do switch, your guess has improved to a 1 in 2, because you're basing your guess on new information.

- Steve Lipsky

bluewolf
08-08-2002, 01:48 PM
&gt;&gt;&gt;&gt;&gt;I can tell you it's not me, Tom. I'm as dumb as a nail, and maybe a little "bent" too. lol ***Lester*** <hr></blockquote>

"Being smart is knowing what you are dumb at"

bluewolf

08-08-2002, 01:53 PM
ummm Patrick does stupid!

08-08-2002, 02:01 PM
Here's the simplest way to think about it. Take it to the limit... we have one million doors, only one of which has a prize behind it.

You pick one door. I open 999,998 doors, all revealing duds. (Keep in mind, I am NOT doing this randomly - I know which door has the prize in it). Would you then change your guess if I allowed you to? Of course you would! Your original guess is still a 1 in a million! It's true that there are only two doors left, BUT NO MATTER WHICH DOOR YOU CHOSE (out of the million) I as the host could always show you 999,998 that were worthless.

Changing your guess here is clearly the way to go. You've gone from 1 in a million to 1 in 2.

- Steve

Doomsday Machine
08-08-2002, 02:04 PM
If you have just 2 doors left and one is the "big deal" and one is not, I would classify that as a 1 in 2, 50-50, or 50% chance of picking the big deal. By eliminating one of the 3 doors and showing that it is not the big deal you are automatically making your original choice a 1 in 2 proposition, so changing your original choice will not improve your chances of picking the correct door. The coin flipping analogy does apply to this 50-50 proposition.

SPetty
08-08-2002, 02:06 PM
hahahaha this is funny to me. I used to work with a very intelligent engineer who made this argument to me, and I just could not get it. I recognized it again when I saw it in Savant's column, and again, I just could not get it. Now, however, with your perfect explanation, I still just can't get it.

Ever have someone try to explain something to you that you just don't get? This, now, is probably one of those things that I'll never understand. Even when you explain the argument, it just doesn't compute.

I'm with Spiderman on this one - I think the answer is wrong.

08-08-2002, 02:07 PM
Doomsday, what do you think about the situation when it is applied to 1 million doors?

- Steve

SpiderMan
08-08-2002, 02:11 PM
No, she would still be wrong. And I do believe that was her argument. But here's the logic for dispute:

Consider that there are 3 doors, all equally likely to be the winner. Suppose you guess "A", and then he reveals "C" to be empty. If given the opportunity, should you switch your guess to "B"? No, it doesn't help at all. Since he's eliminated "C" then only "A" and "B" are left and one has to be the winner. You are at no advantage switching your guess to "B". You already have a 1 in 2 chance with "A".

Think about it this way ... suppose your original choice had been "B". Should you switch to "A"? Nothing has changed, and they both can't be "better" /ccboard/images/icons/wink.gif

SpiderMan

SPetty
08-08-2002, 02:12 PM
<blockquote><font class="small">Quote: Doomsday Machine:</font><hr> If you have just 2 doors left and one is the "big deal" and one is not, I would classify that as a 1 in 2, 50-50, or 50% chance of picking the big deal. By eliminating one of the 3 doors and showing that it is not the big deal you are automatically making your original choice a 1 in 2 proposition, so changing your original choice will not improve your chances of picking the correct door. <hr></blockquote>Yes, exactly! Steve, where is the flaw in this logic?

bluewolf
08-08-2002, 02:13 PM
<blockquote><font class="small">Quote: Doomsday Machine:</font><hr> If you have just 2 doors left and one is the "big deal" and one is not, I would classify that as a 1 in 2, 50-50, or 50% chance of picking the big deal. By eliminating one of the 3 doors and showing that it is not the big deal you are automatically making your original choice a 1 in 2 proposition, so changing your original choice will not improve your chances of picking the correct door. The coin flipping analogy does apply to this 50-50 proposition. <hr></blockquote>

they showed which of the two remaining doors was a dud. so that leaves a nice prize and the grand prize so you win either way.

bluewolf

SpiderMan
08-08-2002, 02:22 PM
Yet the "World's Highest IQ" couldn't understand this, or else thought everyone was so stupid that they could be convinced otherwise if only her argument was repeated enough times. Didn't work out that way.

SpiderMan

08-08-2002, 02:24 PM
Wait, here it is, one better. Let's say there are 80 million different lottery combinations. You pick one. One by one, the host shows you 79,999,998 of the losing combinations. He then shows you your original combination, and the last remaining combination. He tells you:

"Either your ticket, or the one I am currently holding, is the winning ticket. Choose which."

Can you really tell me that you would stick with your original ticket? The chances that your ticket wins are the SAME chances it wins before he showed you 79,999,998 losing combinations. Which is to say, virtually nil. In all lottery drawings, there MUST be 79,999,999 losing combinations. He is just showing you all of them but one (the ticket you are holding, which is of course the LAST losing combination). The new ticket MUST be the winning ticket.

In short, if someone did this with you every day for the rest of your life, and you ALWAYS stuck with your original lottery combination - you would die without ever having won. Even when it's down to two tickets! However, if you ALWAYS changed your choice when it was down to the last two, you would win the lottery one time every two days for the rest of your life.

- Steve

SPetty
08-08-2002, 02:32 PM
<blockquote><font class="small">Quote: Steve_Lipsky:</font><hr> "Either your ticket, or the one I am currently holding, is the winning ticket. Choose which."<hr></blockquote>Which, is, again, a 50/50 chance.

Even though I sometimes may disagree, I almost always understand the argument. In this case, still, I don't understand the argument. There is a fundamental way that you and Ms. Savant are seeing this that is way different than I can even attempt to see it. It is so clearly a 50/50 proposition to me that I just can't see what you're trying to say. Again, is there a flaw in the logic that Doomsday presented?

Thanks for hanging in there!

Doomsday Machine
08-08-2002, 02:33 PM
Steve, Let me give you an example and hopefully you will agree with the logic behind it. Let's say you have 3 cards, two face cards and one ace. You place all 3 cards face down on a flat surface and they are mixed blindly by a neutral party and neither the "dealer" or you, the player, has a chance to look at the shuffling of the 3 cards on the table. You are asked to place $20 on top of one of the cards that you think is the ace and the dealer turns over one of the 2 remaining cards showing you a face card. At this point he asks you if you want to keep your original choice or pick the last remaining card. I cannot imagine where the advantage of changing your original choice is to the remaining card as you have reduced your original 1 in 3 chance to pick the ace to a 1 in 2 chance so the act of changing to the remaining card (out of 2 possible choices) will NOT increase your chance of picking the ace. Do not confuse the original 1 in 3 example by increasing the choice to 1,000,000. Changing your guess when you have a 50% chance will not increase your chance to pick the correct card, door, number or anything else.

SpiderMan
08-08-2002, 02:33 PM
<blockquote><font class="small">Quote: Steve_Lipsky:</font><hr> Wait, here it is, one better. Let's say there are 80 million different lottery combinations. You pick one. One by one, the host shows you 79,999,998 of the losing combinations. He then shows you your original combination, and the last remaining combination. He tells you:

"Either your ticket, or the one I am currently holding, is the winning ticket. Choose which."

Can you really tell me that you would stick with your original ticket? The chances that your ticket wins are the SAME chances it wins before he showed you 79,999,998 losing combinations. Which is to say, virtually nil. In all lottery drawings, there MUST be 79,999,999 losing combinations. He is just showing you all of them but one (the ticket you are holding, which is of course the LAST losing combination). The new ticket MUST be the winning ticket.
- Steve <hr></blockquote>

No - By that same logic, the "new" ticket also has the same chances as it did before the elminations. It is no better or worse than your original ticket. Both have a 50% chance of being the winner. You could stick or switch depending on your emotions or superstitions, it wouldn't affect your chances either way.

SpiderMan

SpiderMan
08-08-2002, 02:43 PM
The dead horse has been exhumed for a new flogging.

If you want to presuppose subterfuge on the part of the host, then you must also consider that he is TRYING to get you to switch. Either way, it's still a 1 in 2 proposition at that point. My original choice upgraded with every opening.

SpiderMan

08-08-2002, 02:43 PM
What you have to realize is that he is not choosing doors AT RANDOM... if he was, and there was a one in three chance that he would show you that the door you chose was the wrong one, then yes... your odds would not change. BUT.. he would never do that. He is intentionally showing you one of the doors that is not right, therefore, your odds do not improve at all if you don't change your choice

08-08-2002, 02:44 PM
Doomsday, your example with the cards is completely different. The dealer in your example does not know which has the ace. In Marilyn's example, the host KNOWS which has the grand prize. In your example, I would not change my choice.

This fact is central to the argument. Go back to my lottery example, reading all the way to the end (because I recently edited in a new paragraph). The fact that your ticket "hung in there" until there were only two left doesn't mean anything, because the host was not revealing the losing tickets randomly . He revealed every losing ticket but one (yours).

Taking things to the limit, as I'm doing here with the lottery, is an accepted way to see principles. As long as none of the tenets of the argument are being violated, it is an accurate way to better understand subtle concepts.

However, let's go down to a smaller example now. Pretend that YOU are the host. You are offering your friend to guess a number that you have chosen between 1 and 10. You choose 2 as the "winning" number. He guesses 8. You then say:
"1 is not the winning number!"
"3 is not the winning number!"
"4 is not the winning number!"
"5 is not the winning number!"
"6 is not the winning number!"
"7 is not the winning number!"
"9 is not the winning number!"
"10 is not the winning number!"

You intentionally left 8 off the list because that's what your friend guessed. Now you offer him the choice to change his number from 8 (which he originally guessed) to 2, the only other number you didn't mention. Do you NOW see why he should change it??? For 9 of the 10 available numbers, his guess will be wrong, but there's always a way for you to keep his guess "down to the last two".

- Steve




- Steve Lipsky

SpiderMan
08-08-2002, 02:48 PM
No, Steve, even if the dealer knew which of the two remaining cards is the ace, it still wouldn't matter. He could just as easily be trying to get you to change from the winner as anything else. Once the third card is taken out, you have a 1 in 2 chance. You don't have any idea whether the dealer would prefer you to switch or not.

SpiderMan

08-08-2002, 02:53 PM
OK, here's an open challenge. If anyone on this board can refute the logic in the "guessing a number from 1 to 10" example, I'd love to hear it.

And... please don't refute it on the grounds that it is not the same example. It is.

- Steve

08-08-2002, 02:58 PM
Spiderman, forget about this "sneaky" dealer fascination you have /ccboard/images/icons/smile.gif

That is not what I am talking about. The same could be done with a computer program, which I plan to write tonight and somehow publish on the web tomorrow.

You will pick a number from 1 to 10. Immediately, the computer will list 8 numbers that are NOT correct.

You will then get the choice to keep your number, or switch to the last number. After playing the game a bunch of times, you will see that staying with your number "wins" exactly 1 in 10, while switching wins 1 in 2.

And I promise, the computer won't be sneaky.

- Steve

Ross
08-08-2002, 03:04 PM
Spiderman, I thought that was the example you were going to give about Marilyn. However, Steve and Marilyn are correct. I teach statistics at Duke and I've used this as a motivating example when I cover probability. And believe me, it always generates a lot of heated debate. In fact, I was on vacation with a couple of friends and they spent 3 days arguing with me (over beer) that it doesn't help to switch.

Here is the most direct explanation I have found:

If your original guess was correct and you switch, you lose.
If your original guess was wrong and you switch, you win.
Since your original guess would be wrong two out of three times, if you switch you'll win two out of three times.

To test the question empirically, go to
http://cartalk.cars.com/Tools/monty.pl
and try the two strategies and see which works best.

You can also find a mathematical proof that the prob of winning by switching is 2/3 at that site.

Spiderman, I agree Marilyn may not be a super-genius but she is correct here! Sorry! :&lt;)

NH_Steve
08-08-2002, 03:07 PM
Another question might be how did he get into Yale??? And how did he ever get elected president?? Oh, same answer: Um, well, it might possibly have had something to do with his family status /ccboard/images/icons/smile.gif /ccboard/images/icons/smile.gif Plus a little cheatin' for good measure...
Nah, couldn't be, could it????

08-08-2002, 03:09 PM
Ross, I kissed the screen when I read your post.

That link you sent is incredible. It's virtually 2/3 exactly in practice.

Thanks,
Steve

08-08-2002, 03:17 PM
Steve, I see that the opposition has quieted /ccboard/images/icons/smile.gif

Ross
08-08-2002, 03:28 PM
Steve, no problem, glad I could help!
If anyone remains unconvinced, I offer the following to anyone who wants to take me up on it:
I will be at the US Open and will set up the Monty Hall situation with 3 cards. The person can play Monty as described and I will follow the switching strategy every time. I will pay the person $125 ever time I lose, if the person will pay me $100 every time I win. I will play all night if I have to! Any takers?

heater451
08-08-2002, 03:29 PM
As I was reading this thread (or the part about "pick a door", at least), I was originally on the Spiderman side of it. Then, the other side of the argument made more sense, once Steve_Lipsky posted this: <blockquote><font class="small">Quote: Steve_Lipsky:</font><hr>Here's the simplest way to think about it. Take it to the limit... we have one million doors, only one of which has a prize behind it.

You pick one door. I open 999,998 doors, all revealing duds. (Keep in mind, I am NOT doing this randomly - I know which door has the prize in it). Would you then change your guess if I allowed you to? Of course you would! Your original guess is still a 1 in a million! It's true that there are only two doors left, BUT NO MATTER WHICH DOOR YOU CHOSE (out of the million) I as the host could always show you 999,998 that were worthless.

Changing your guess here is clearly the way to go. You've gone from 1 in a million to 1 in 2.

- Steve <hr></blockquote>The important parts to understand, are that you are making your original choice "in a vacuumm", and the elimination of incorrect doors is NOT AT RANDOM.

And although I would have to argue that the final decision appears to be 50-50, think of it visually:

If I say, pick "the Magic dot" from the following(70 dots):
.................................................. ....................

Your chances are 1 in 70. (PICK ONE, then scroll down)
/
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/
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.................................................. ....................
(the correct answer was the one in bold--which should be the 81st)

You're chances of getting it right was very low.

Now, suppose I had done this:

I ask you to pick a dot, with a 1-in-70 chance. Odds are, you picked wrong, but since only I know for sure, I can eliminate all the dots down to two:
. (the one you picked) . (the Magic dot).

If I ask you to pick again, you now have a 50% chance, but since your original guess was based on low odds, you are sort of 50%+, for abandoning your original guess.

So, by the numbers, you would still have a 50-50 chance, but you would be better off taking the new offering, if you consider this:

In another scenario, I ask you to pick 5 dots from the 70. Then, I eliminate every other dot, but one. If the choice is between keep 5, or go with the one, your odds seem better to hold. Butsince I've eliminated all BUT the Magic dot, logic says that you should re-choose the only other dot unpicked by you. This makes it appear that a 1-in-6 choice is better than a 5-in-6, but, again, you have to consider your picks came from the original field of 70.

If you re-apply the choices to 1-in-3, and then consider the final choice as 50-50-50plus, then you are "more" likely to win by changing your decision.

If you got lucky with the first pick this would only screw you over. . . .

{I am posting this after Ross's reply, and some others--it took me awhile to write it. Overall, I'm hoping that the dots help with visualizing why the odds are 'funny'.}


======================

SPetty
08-08-2002, 03:33 PM
<blockquote><font class="small">Quote: JasonG NYC:</font><hr> Steve, I see that the opposition has quieted /ccboard/images/icons/smile.gif <hr></blockquote>Yes, because as you have guessed, I give up.

I just don't get your argument. You keep saying the same thing over and over, and over and over I just don't get it. I've been through that with this puzzle before. Like I said, I normally at least understand the argument, but this one I'm missing. I am in the camp that the odds at the end when there are two things left are 50/50 for both things. Having everything eliminated before is eliminating them for both choices. It changes the odds. When there are two left, the odds are not now 1/10 or 1/3 or whatever, but 1/2 for each of the two that are left. You still have not refuted that argument, but rather, you again just say the same thing over and over. You know, that same thing that this feeble little mind just can't seem to grasp...

I liked Steve's idea of a computer program - of course, he'll have to share the source code so that I can see it's not rigged...

SPetty
08-08-2002, 03:46 PM
<blockquote><font class="small">Quote: heater451:</font><hr> Odds are, you picked wrong, but since only I know for sure, I can eliminate all the dots down to two:
. (the one you picked) . (the Magic dot).<hr></blockquote>No, the one I picked and another one that may or may not be the Magic dot. At this point, there are two dots. You are assuming that the one I picked is the wrong one and that only you can pick the Magic dot. At this point, there are two dots, each with a 50/50 chance of being the Magic dot.

<blockquote><font class="small">Quote: heater451:</font><hr> If I ask you to pick again, you now have a 50% chance, but since your original guess was based on low odds, you are sort of 50%+, for abandoning your original guess.<hr></blockquote>My original guess was based on low odds, but those odds have now been changed, by virtue of you eliminating all those other dots.

<blockquote><font class="small">Quote: heater451:</font><hr>Butsince I've eliminated all BUT the Magic dot...<hr></blockquote>See, assuming again that I didn't pick the right dot in the first place. That is the assumption that is wrong. By the time the choices get down to 5/6, hey baby, I've got the magic dot.

<blockquote><font class="small">Quote: heater451:</font><hr> logic says that you should re-choose the only other dot unpicked by you.<hr></blockquote>No, logic says that I have a 5/6 chance of having the Magic dot in my stable.

<blockquote><font class="small">Quote: heater451:</font><hr> Overall, I'm hoping that the dots help with visualizing why the odds are 'funny'.}<hr></blockquote>Thanks for trying. Sigh.

08-08-2002, 04:04 PM
SPetty, let's go back to the "guess the number between 1 and 10." I really think this is the easiest to "see".

Now, again, YOU are the host, the one that picks the magic number. Of course, you don't tell your friend. You make him guess.

No matter what he guesses, you can give him EIGHT wrong ones, and tell him so. Leave his guess out, and your "right" one out.

Do you still think, that from his end, he still has a 50% chance of getting it right if he sticks with his original number? In other words, if you and he played this game 100 times, do you think he would guess the right number (by sticking with his choice when it's down to 2) 50 times? The important thing to remember here, of course, is that in ALL 100 times playing this game, his number will be one of the two ones left.

- Steve

08-08-2002, 04:11 PM
Oh, and Ross, thanks for pointing out one thing that I was wrong about. When the host lets you change your choice, it doesn't become 1 in 2. It becomes n-1 in n, where n is the number of choices you had to begin with.

So if there are 10 numbers, changing will yield the correct answer 9 out of 10. If there were a million doors, changing will yield the correct answer 999,999 out of 1,000,000, and so on...

- Steve

phil in sofla
08-08-2002, 04:22 PM
At the time of this controversy, I was opposed to Marilyn's position, as in fact were significant numbers of both math and logic experts who wrote their opposition to her (which, to her credit, she published).

However, also at the time, my brother-in-law ran some trials, and reported that, to his surprise, the results were tracking Marilyn's predicted better odds if you switched.

Reconsidering the question, with the benefit of the example you gave and the explanation the logic or statistics teacher gave above in the thread, I think I'm beginning to understand the logic, and maybe the truth, of her position.

BTW, was her example 3 doors, or 4?

In trying to remember my letter to her, I recall that it seemed that the intention and knowledge of the host in picking the door to show it wasn't the one came up big. That is, we must assume he isn't just opening a door at random, prepared, if it should be, that it will immediately reveal where the big prize is. Rather, surely, the host would pick a door he knows is NOT the big prize door.

I thought at the time that it was this non-random nature of the door disclosed that made Marilyn wrong. But you say that if it WERE chosen at random, THAT would make her wrong? Could you fill me in on that line of reasoning?

Patrick
08-08-2002, 04:30 PM
IQ scores when you were a child don't count. If you had over a 200 IQ when you were a child, you will not have 200 IQ when you are an adult.
A child with 200 IQ is not smarter than an adult with less IQ.
Some evolve faster than others, that's why they get a too high score on IQ tests.

Patrick

08-08-2002, 04:33 PM
Phil, look at it this way:

Let's say you choose Door 1, out of 3 doors. Let's say you ALWAYS choose Door 1.

Let's also suppose that the grand prize is being distributed randomly.

Now, if you stick with Door 1, that is the only door that can win for you, right? But think about this: if you switch, you win WHENEVER it is not behind door 1. This is because if the prize were behind Door 2, the host would HAVE to open Door 3 (she can't open your door, and she can't open the door with the prize).

And if the prize were behind Door 3, she'd HAVE to open Door 2, for the same reasoning. Do you now see that by switching, regardless of which of the last two doors (i.e., Door 2 or Door 3) the prize is behind you will win? That is why switching yields a 2 out of 3.

If she were opening the doors at random (except for yours), she might open the right one. This would end the puzzle before it even began. The "trick" comes in that she will purposefully give you all this extra information in terms of wrong doors, and you can either use it (you should) or not use it (and suffer the consequences).

- Steve

Patrick
08-08-2002, 04:43 PM
This is from Paul Cooijmans frequently asked questions page:
http://members.chello.nl/p.cooijmans/FAQ.htm

"Child IQ scoring is a difficult area. I believe that children who have their IQ's measured when young should redo an IQ test in adult life for a more accurate assessment. What do you think? I agree. Childhood scores, and the everlasting quotation thereof, are a great source of confusion in the high-IQ world. There are several reasons why childhood scores are not good indicators of adult IQ: they are expressed agains age peers, while it is known that the younger the age group, the lower the correlation with adult IQ is. Also, when expressed as mental/biological age ratio IQs, high scores above about 130 are way overpresent and can therefore not be compared to deviation IQs as used for adults. In my opinion, scores of children should be expressed according to adult norms or unselected population norms. That would be much more clear and less confusing."


Patrick

Patrick
08-08-2002, 04:44 PM
From Paul Cooijmans FAQ page:
http://members.chello.nl/p.cooijmans/FAQ.htm

"How accurate are those free online IQ tests - not the high-range tests but the more normal one - for people of around average intelligence? The scores should not be taken seriously; such tests are only good for fun and education purposes, and for practicing for a real test. The IQs are not accurate at all, even for average people. The tests used by regular psychology are better. To create a good test and norm it takes a lot of expertise, work and money. You can't expect a good test to be offered for free on a commercial site."


Patrick

heater451
08-08-2002, 04:48 PM
Yes, the assumption is always made that you picked wrong to begin with, and that is only backed by the fact that the odds are higher for the first pick--Using a much higher number is just to help illustrate that.

There is also an assumption that the "host" will always eliminate down to the contestant pick and the prize--and not try to 'bait-and-switch'. (This is somewhat different for a gameshow, where there may be optional prizes.)

You are basically correct in believing that the reason the odds change to 50-50, is because you are reduced to the two choices. But, consider this, if you were not given another choice, your pick is still based on the original odds, and more likely to be wrong.

I think part of the confusion is that you are not right or wrong 100% of the time, by switching, but that you will be more likely to 'win', because the first pick has the greater chance of being the wrong one, since it was random, compared to the final.

--The whole "Magic Dot" bit, was an attempt to reach the more visual thinkers. You might try imagining picking someones favorite star out of the sky. . . .



=================

NH_Steve
08-08-2002, 04:53 PM
In the pool world, clearly all the One Pocket players /ccboard/images/icons/smile.gif /ccboard/images/icons/smile.gif /ccboard/images/icons/smile.gif

SpiderMan
08-08-2002, 05:06 PM
Ross, that's expressed in such a way that it is impossible to sensibly refute. I now agree with you. Steve, no need to write that computer program for my sake!

SpiderMan

<blockquote><font class="small">Quote: Ross:</font><hr>
If your original guess was correct and you switch, you lose.
If your original guess was wrong and you switch, you win.
Since your original guess would be wrong two out of three times, if you switch you'll win two out of three times.
<hr></blockquote>

Doomsday Machine
08-08-2002, 05:16 PM
In the website you are offering for "proof" they have made several mistakes !! If you take that 27,161 people have picked the correct door on their first choice you see that the percentage of the first picks that are correct are 25.52% (which seems somewhat low considering that 33% would be expected). For the remaining 79,251 that picked the wrong door and then had the choice to stay with their original answer or switch, the ones that stayed with their answer (37,391) were correct in 47.18 % of the time and the ones who elected to change (41,860) were correct in 52.81% of the time. I have no idea where they get their 33% &amp; 66% calculations.

Doomsday Machine
08-08-2002, 05:29 PM
If you are saying that by changing your original pick that you will be correct 90% (9 out of 10) of the time then you missed a few too many math classes when you were in school !!!

Voodoo Daddy
08-08-2002, 05:41 PM
Voodoo walks up to NH_Steve and gives him a high 5 yelling, "One Pocket Rules"...HAHAHAHAHA

SpiderMan
08-08-2002, 05:45 PM
Doomsday,

I think, though the percentages are skewed, that the results do support Ross's contention that it is an advantage to switch. The only stat that is odd was the 25% of first-time right choices, I agree it should have been 33%. But, of the ones who had chosen wrong, it makes sense that about half of them won and half lost, because about half chose to switch.

If you just look at the ones who switched (assuming half did switch), then half of 25% hurt their outcome and half of 75% improved their outcome.

If the initial guesses had been right 33% of the time, still twice as many would have improved their position as hurt it. Since you don't know which group you are in initially, it's best to assume you are in the "wrong" group since that is most likely.

SpiderMan

NH_Steve
08-08-2002, 05:54 PM
Apparently I'm not smart enough to get this. The way I see it, since you haven't been told whether your first guess is right or wrong, doesn't revealing the 3rd -- obviously incorrect -- door simply increase your odds of winning whether you switch or not equally???

Kato
08-08-2002, 07:12 PM
Kato walks up and tells Voodoo and NH Steve to play some one pocket because I haven't had a good nights sleep in 3 weeks./ccboard/images/icons/tongue.gif

Kato~~~Overlord of One Pocket

NH_Steve
08-08-2002, 07:32 PM
LOL, but no, I don't go for the Nick Varner wedge style of game /ccboard/images/icons/smile.gif /ccboard/images/icons/smile.gif

NH_Steve
08-08-2002, 08:06 PM
<blockquote><font class="small">Quote: Ross:</font><hr>
Here is the most direct explanation I have found:

If your original guess was correct and you switch, you lose.
If your original guess was wrong and you switch, you win.
Since your original guess would be wrong two out of three times, if you switch you'll win two out of three times.
<hr></blockquote>Ross, I still don't see it that way (somehow, you're not surprised, since you've seen this go all weekend! /ccboard/images/icons/smile.gif ). Where I think your explanation falters in it's logic is this: since you have not been informed whether your first pick is right or wrong, and you change it, then your first pick is meaningless statistically -- a red herring -- your true chances are simply 50% at that point (having improved from 33% when the host opened one of the other doors to find a loser -- unless of course the host opened the winning door [33% of the time!] -- in which case it's time for you to write home for more $$$)

Unless you wish to factor in some kind of subtle reading of the game host's demeanor (if he knows which door is right, that is).

Bottom line, taken from start to finish as a whole, if both your picks and the host's are totally blind, it does not matter who opens the doors, or whether you switch your pick or not, your chances are 1:3. IMHO, them's the fax, even if I ain't no genius!

('Course I don't claim to be a genius -- and maybe this post proves that!)

NH_Steve
08-08-2002, 08:14 PM
Ross, I just did their 'test' (http://cartalk.cars.com/Tools/monty.pl) about eight times, and not once did 'Bugsy' pick the winner -- if that is a condition of the puzzle, no wonder the numbers are skewed!! Bugsy knows too much!

cheesemouse
08-08-2002, 09:58 PM
All I want to know is: if at the beginning of a pool game when the guy flips the coin in the air and I say "heads, NO, tails" will I win 2/3 of the time? Heehehehhhhehhheeee.....

Patrick
08-08-2002, 10:44 PM
If there are a million doors, you pick a door, and the host picks a door. The host knows which door is right. Would you pick his door or yours? It is one in a million chance that your door is right.

Patrick

bluewolf
08-09-2002, 06:05 AM
<blockquote><font class="small">Quote: cheesemouse:</font><hr> All I want to know is: if at the beginning of a pool game when the guy flips the coin in the air and I say "heads, NO, tails" will I win 2/3 of the time? Heehehehhhhehhheeee..... <hr></blockquote>

How to win 100% on the coin toss

"heads I win, tails you lose" &lt;G&gt;

bluewolf

rackmup
08-09-2002, 06:32 AM
I don't know any names but I am willing to bet it is someone that lives on Everest in the Himalayas (Nepal/Tibet) at an altitude of 29,035 feet. That's a high IQ.

Glad to help and resolve any controversy.

Regards,

Ken

SPetty
08-09-2002, 07:19 AM
After mulling on this on my incredibly hellacious commute, I think I've figured out where you guys are coming from. Although I still don't fully get parts of your explanations, I'm so much closer than I've ever been before! /ccboard/images/icons/smile.gif

Let's see how this rephrasing of the situation goes over:
If I consider that I don't care if you open the other doors to show the losers or not, then I can fully comprehend this scenario and these contentions. I think, for me anyway, it boils down like this:

Ten dots/doors/numbers/whatevers - I pick one, you get the other nine. If given a choice, would I switch with you? That is, you get my single dot and I get your nine dots. Would I switch? Absolutely, every time. Trading a 1/10 chance for a 9/10 chance is always a good choice.

Does that answer change just because you show me that eight of your dots/doors/numbers/whatevers aren't winners? No, probably not. &lt;--(The *key* for me...)

Thanks, guys, for sticking with it. This is one of those that's been bugging me literally for years. /ccboard/images/icons/smile.gif

TomBrooklyn
08-09-2002, 07:22 AM
I read all of the above posts, but some of them require taking some time to think about, which I didn't have available yet, but this is what I'm thinking now. Steve and Ross's point work if you start with more than three choices. If you start with only three choices, however, there is no benefit in the odds to changing your choice after one door is eliminated.

This doesn't seem to conform to Ross's 3Card Monte challenge, so I'm going to go back and think and that for a while later. Once we get this straightened out, we should contact Marylyn Von Savant and tell her of our findings.

08-09-2002, 07:36 AM
Well, I may have missed a few math classes, Doomsday, but I assure you this math is correct.

Let's go over the details of the Guess The Number game:

1) I pick a number (the "magic" number).
2) You guess one number.

Now, at this point, your guess is 1 in 10. Do you agree with this?

Now, again at this point, regardless of the number you choose, and the number I chose, I can list 8 numbers that were not right. Do you agree with this?

At this point, do you also agree that your guess is still the original 1 in 10 to win? That nothing at all has changed?

Now, let's go over the probabilities:

The odds that your original number (which I will call "Y")was right: 1 in 10.
The odds that it was ANY OTHER NUMBER (which I will call "X"): 9 in 10.

Now, do you understand that I can always leave "X" and "Y" as the last two numbers? "X", whatever it is, will be the right number 9 out of 10 - BECAUSE THE ONLY TIME IT IS NOT RIGHT IS WHEN YOU ORIGINALLY GUESSED CORRECTLY. Every other time, "X" is the correct number. Every other time.

And that is where I came up with the 9 out of 10 to switch, and that is why it's right.

- Steve

08-09-2002, 07:45 AM
Tom, the three choice thing works. Here's another way to describe it:

Let's say you always pick Door 1, that you always switch, and that the prize is randomly distributed behind any of the three doors.

If the prize is behind Door 1, you lose (1/3). Easy enough.

If the prize is behind Door 2, I MUST expose Door 3 to you, right? I can't show you Door 1 (your pick) or Door 2 (the one with the prize). And if the prize is behind Door 3, I MUST expose Door 2 for the same reasoning, correct?

In effect, do you see that by switching, regardless of which of the last two doors the prize is behind, you are guaranteed to get it?

By staying, you are only winning the 1 in 3 when it's behind Door 1. But by switching, if the prize is behind Door 2, you win, and if it's behind Door 3, you also win. That is a 2 out of 3 chance.

The key point is that switching yields the winner whenever your original choice was not correct, which as we have established, was a 1 in 3.

- Steve

bluewolf
08-09-2002, 08:16 AM
The host shows the bum door. In the two remaining, one has the grand prize and one has a kool prize. So you win either way.

bluewolf

TomBrooklyn
08-09-2002, 08:36 AM
I clearly saw it if there is more than three choices. Now that I think about it, it should be true for three choices also. It is better to switch your choice. If you do your odds are 1 in 2. When you made the first pick, your odds were 1 in 3.

So what was the outcome of the Marilyn Vos Savant hub-bub?

Ken
08-09-2002, 08:53 AM
That is a good way to look at it and I agree that it is best to get the remaining 9 choices rather than stick with your original choice. You will certainly win more often.

The difference here is that the original example involves three doors and you get only one chance. If each incoming player switches then Monty will lose more often but you get only ONE chance to play the game. Initially after you have made your choice the prize is behind either your door or one of Monty's two doors. Monty has a 100% chance of having at least one bad door. He also has a 1:3 chance of having the prize door, the same odds that you have. Why switch to a door with the same probability as yours? I think as soon as he shows you which of his doors is the dud you lose the advantage to switching to his two doors. If you know that one of the duds will be revealed I think you both change to a 1:2 chance.

It still doesn't make sense to me. It certainly makes sense when you go to higher numbers of doors such as picking one or getting all the remaining nine but maybe three is a special case.

All the explanations involve playing the game many times. That misstates the fact that you have ONLY ONE chance.
KenCT~~still not convinced

08-09-2002, 09:02 AM
<blockquote><font class="small">Quote: TomBrooklyn:</font><hr> It is better to switch your choice. If you do your odds are 1 in 2.<hr></blockquote>

Tom, I made this mistake too. If you switch, your odds don't go to 1 in 2. They go to 2 in 3. This is because if you switch, it doesn't matter which of the last two doors it's behind, you will win. So by switching, you get the benefit of two doors, whereas by staying, you only get the benefit of your original door.

When you switch, your odds are n-1 in n, where n is the number of doors/cards/lottery tickets.

- Steve

08-09-2002, 09:06 AM
<blockquote><font class="small">Quote: Ken:</font><hr> [Monty] also has a 1:3 chance of having the prize door, the same odds that you have. <hr></blockquote>

Ken, Monty actually has a 2:3 chance of having the prize door, since he has 2 doors. And when you switch, you are basically taking both of his doors, in exchange for your one.

The fact that one of his doors must necessarily be a dud does not reduce the importance of his having two doors at the outset.

- Steve

Ross
08-09-2002, 09:35 AM
<blockquote><font class="small">Quote: NH_Steve:</font><hr> Ross, I just did their 'test' (http://cartalk.cars.com/Tools/monty.pl) about eight times, and not once did 'Bugsy' pick the winner -- if that is a condition of the puzzle, no wonder the numbers are skewed!! Bugsy knows too much! <hr></blockquote>
Yeah, that is the set-up. Monty (Bugsy at cartalk) knows which door is the winner and always shows you the dud from the two you didn't pick. There is another simulator at http://www.stat.uiuc.edu/~stat100/java/Monty.html. It also has several links to other simulators. If you don't trust any of the simulators you can always get a friend/significant other to play Monty using 3 cards as the doors, with one of them being the prize. Play at least 20 times or so for the odds to start to show up clearly.

heater451
08-09-2002, 09:51 AM
<blockquote><font class="small">Quote: Ken:</font><hr> . . .All the explanations involve playing the game many times. That misstates the fact that you have ONLY ONE chance.
KenCT~~still not convinced <hr></blockquote>The reason the explanations involve more than one chance is so that that the following should be more apparent:

Given that, if you were playing the game multiple times, then you would win more often, if you were to switch doors. But, since you only have one shot, then you should switch, because you would still have the benefit of the "more often" situation. Does that make sense?


~~BTW, Ken, how is traveling these days?

==================

Rod
08-09-2002, 09:56 AM
Actually Steve I've never given this much thought. I think your right though. Now I have to ask myself, when will I ever be on a game show. Self says, probably never!

Ross
08-09-2002, 03:12 PM
<blockquote><font class="small">Quote: Doomsday Machine:</font><hr> In the website you are offering for "proof" they have made several mistakes !! If you take that 27,161 people have picked the correct door on their first choice you see that the percentage of the first picks that are correct are 25.52% (which seems somewhat low considering that 33% would be expected). For the remaining 79,251 that picked the wrong door and then had the choice to stay with their original answer or switch, the ones that stayed with their answer (37,391) were correct in 47.18 % of the time and the ones who elected to change (41,860) were correct in 52.81% of the time. I have no idea where they get their 33% &amp; 66% calculations. <hr></blockquote>
Doomsday, I just checked and the percentages are correct. The 79,251 you quote is the total number of times the game has been played (it's labeled "total number of trials"), not the number of times a wrong door was picked. 27,161/79,251 = .3427 or 34.27%.

Ross
08-09-2002, 03:26 PM
<blockquote><font class="small">Quote: TomBrooklyn:</font><hr> So what was the outcome of the Marilyn Vos Savant hub-bub? <hr></blockquote>

Tom, see http://www.dartmouth.edu/~chance/course/topics/Monty_Hall.html for a New York Times article on the history of the the Monty Hall/Marilyn uproar.

Doomsday Machine
08-09-2002, 03:55 PM
Ross, please get your calculator out and try to follow this simple explanation. On the website they are showing the total trials currently at 79,306 which is MYSTERIOUSLY the exact amount of "Stickers" 37,408 added to "Switchers" which is 41,898. The purpose of this website is to prove this crazy theory, which apparently you also subscribe to, that is you have a much higher probability of picking the correct door by changing your initial wrong pick to the door left over AFTER being shown that the third door does not contain the "big deal". You have to take the people who initially picked the correct door (27,179) and add this amount to the total trials (amount of people given the chance to change their initial incorrect pick) and you get a total number which is 106,485 with the percentages broken down as follows:

Total number of ALL choices= 106,485
Initially correct 27,179 = 25.52%
Keeping their choice and correct 37,408= 35.13%
Changing their choice and correct 41,898 = 39.34%

Now, to the theory they are trying to prove:

Total of incorrect original choices (Trials)= 79,306
Keeping their choice &amp; correct 37,408 = 47.17%
Changing their choice &amp; correct 41,898 = 52.83%

It is misleading and wrong to state that if you change your initial selection after seeing that the third door does NOT contain the big deal that you will have a 66% success rate of picking the correct door and by sticking you will be correct only 34% of the time. They are showing by their own results a 47% &amp; 53% success rate respectfully based on 79,251 attempts (which I find difficult to believe). So the advantage of switching is 6% (53% - 47%)according to their figures and NOT 32% (66% - 34%) that you and they claim !! If you LOGICALLY do the calculations you will see that I am correct.

08-09-2002, 04:16 PM
Doomsday, I agree, those numbers are totally out of whack.

Still, that is unquestionably a problem solely with the counter on the site. It is not a problem with the theory, or with the practice of the theory.

- Steve

08-09-2002, 05:55 PM
The numbers are OK, the stickers+switchers=total number of trials. The times the correct door was selected has nothing to do with whether the picker stuck with his original door or switched. The layout could be done better. Line 2 is the stickers and they won the cruise approximately 33% of the time. Line 3 is the switchers and they were right approximately 66% of the time. The layout doesn't tell us the number of times the stickers were right and the number of times the switchers were right. You can only get those numbers by multiplying the percentages by the number of stickers or switchers.

08-10-2002, 05:42 AM
alright,

Lets take a look at the mathematical proof . . .

check this

http://www.math.uah.edu/stat/games/games6.html

And if you can't understand that, then you probably can't break the 80 barrier on the previously mentioned IQ test either. Go back to school. Its like math for dumbies. And it should once and for all put this dead horse to rest. Poor thing don't have no skin left its been beaten so hard. Flies buzzen all over the place. Its getten pretty growse, lets just let it go huh?



Poolchamp

p.s. I don't agree with steve's logic . . . only his result. A better way of looking at the game is this . . . Your first choice matters little. Lets say you choose door 1, the host chooses door three. At this point, you are given the option to change your door. Look at it different, you simply make a second decision. You can either choose door one again, based on either 1 or 2 is correct. Or you can now choose door 2. All it is is you simply make another selection. Its not a matter of making a new selection or not, both doors would have a 1 in 2 chance at this point. Your first choice doesn't matter one bit. Hope you can understand it that way steve. As for the real logic, check that site, you should understand it no problem. Its like barney style.

p.p.s. One more thing, the name of this imfamous inigma is The Monty Hall Problem.

Harold Acosta
08-10-2002, 10:06 AM
&lt;blockquote&gt;&lt;font class="small"&gt;Quote: nAz:&lt;/font&gt;&lt;hr&gt; the average iq is 100, so 1/2 of the population is over 100, and 1/2 is under 100.

84-116 is normal, and anything above and below are obvious. anything under 70 is mental retardation. (70 is the average IQ of most pool players i met... im sure you will agree with that lol)

in the standardized stanford/binet intel' test, 68.2% score normal, and 15.9% score in each direction. though the WAIS test is the most widely used, i only have info on the stanford-binet test, but you get the general idea.

also note that online tests are always wacked out to give you a score you probably don't deserve, so don't break out the champaigne yet. This particular online test is probably one of the more accurate ones though.

Tom try out this IQ test its pretty good. I scored 127 /ccboard/images/icons/frown.gif Not bad for a grade scool drop out

<a target="_blank" href=http://www.emode.com/tests/uiq/authorize/register.jsp?url=/tests/uiq/index.jsp>http://www.emode.com/tests/uiq/authorize/register.jsp?url=/tests/uiq/index.jsp</a> &lt;hr&gt;&lt;/blockquote&gt;

nAZ, took the test and scored 127, a "Facts Curator" under their terms. College dropout I might add.

Note: This score is normal I believe...

08-10-2002, 10:16 AM
Poolchamp, I went to the site and grabbed this:

<blockquote><font class="small">Quote:</font><hr>The mathematical formulation we have used is just about the most complete one possible. However, if we just want to solve Marilyn's problem, there is a much simpler analysis (which you may have discovered yourself). Suppose that the host always opens a door with a goat. If the player's first door is incorrect (contains a goat), then the host has no choice and must open the other door with a goat. Then, if the player switches, she wins. On the other hand, if the player's first door is correct and she switches, then of course she loses. Thus, we see that if the player always switches, then she wins if and only if her first choice is incorrect, an event that obviously has probability 2/3. If the player never switches, then she wins if and only if her first choice is correct, an event with probability 1/3.<hr></blockquote>

I'm not certain why you mentioned you don't agree with my logic, when it is exactly mentioned in the above paragraph. For most people, myself included, this analysis is a helluva lot easier than the complex mathematical proof you seem to think a vegetable could understand.

As to the host's strategy, I mentioned this as well. As long as the host is NOT opening his door at random, the player's odds will always go to n-1/n by switching. If he is opening doors at random, and the player's original choice makes it down to the last two, the player will always have a 1 in 2 chance.

- Steve

bluewolf
08-10-2002, 11:22 AM
.

=also note that online tests are always wacked out to give you a score you probably don't deserve, so don't break out the champaigne yet. This particular online test is probably one of the more accurate ones though.

Tom try out this IQ test its pretty good. I scored 127 /ccboard/images/icons/frown.gif Not bad for a grade scool drop out

<a target="_blank" href=http://www.emode.com/tests/uiq/authorize/register.jsp?url=/tests/uiq/index.jsp>http://www.emode.com/tests/uiq/authorize/register.jsp?url=/tests/uiq/index.jsp</a> &lt;hr&gt;&lt;/blockquote&gt;

nAZ, took the test and scored 127, a "Facts Curator" under their terms. College dropout I might add.

Note: This score is normal I believe... <hr></blockquote>

I got 124 and most of the ones i got right were in spatial/math. now that is a joke. those are my worse area. the others were more vocabulary and i am not good at the kind of definitions they gave.

bluewolf

Ross
08-10-2002, 12:06 PM
<blockquote><font class="small">Quote: Doomsday Machine:</font><hr> Ross, please get your calculator out and try to follow this simple explanation. On the website they are showing the total trials currently at 79,306 which is MYSTERIOUSLY the exact amount of "Stickers" 37,408 added to "Switchers" which is 41,898. <hr></blockquote>
No mystery involved. The 79,306 is clearly labeled "Total number of trials." which by definition is the sum of those who stick and those who switch (since every player must do one or the other). In your math, you add the number who were initially correct to the total number of trials, which counts the initially correct players twice. This incorrect total gives you funny numbers for the rest of your calculations.
<blockquote><font class="small">Quote: Doomsday Machine:</font><hr>The purpose of this website is to prove this crazy theory, which apparently you also subscribe to, that is you have a much higher probability of picking the correct door by changing your initial wrong pick to the door left over AFTER being shown that the third door does not contain the "big deal". <hr></blockquote>
Far from being a crazy theory, it is a theory that is easily tested. Just grab a friend, take three cards and simulate the set-up and you can find out for yourself. Why, even Monty Hall himself agrees with this "crazy theory" (not that this proves anything)- see the NYT article I linked in another post.

08-10-2002, 12:49 PM
Sorry to say Bill Clintons IQ was as high as the two Bush presidents combined. I really don't think honesty has anything to do with being President, try thinking of an honest President besides Jimmy Carter. They are all lying about something.####

08-10-2002, 04:17 PM
lets dig it up for one more beating steve.

The paragraph that took from the end of that mathematical proof of two possible host strategies merely displays the end result of the logic. In that paragraph, based on two strategies, Marilyn was correct given the "standard strategy" (the host must pick a goat door). The probabily would be 2/3 (66%) that you would win if you changed your door. Not 1/2 that you mentioned.

And by the mere result, we can see that you and Marilyn are using different logic to come to a similiar conclusion. That conclusion being that you increase your odds by changing you door.

Poolchamp

08-10-2002, 04:29 PM
Poolchamp, can you just describe with which of my posts you're faulting the logic?

Obviously, as far as I'm concerned, I think my analysis is absolutely foolproof. But I'm not above admitting I'm wrong, as I did earlier in this thread when I showed that switching doors resulted in n-1/n, rather than my initial contention that it was 1/2.

So... I'm very much interested in finding which of my analyses you have a problem with.

- Steve

08-10-2002, 05:48 PM
Ok Steve,

I understand where your logic about the 1/2 comes from. Rather than dispute that, I will make my best attemp to explain the logic given in the site that posted previously. Exercise 8 i think is the key to look at here.

First read it, ill explain it, im not retyping it. Looking at like A first:

it says l,k,j are distinct, meaning that they cannot equal each other at all. The first selections is different from the hosts selection, also the second selection is different from the hosts selection. In other words, the player changes doors if line A is true or p = 1.

Line B is a little more tricky to understand i suppose. Read the line carefully, then my explination as follows:

if we have l=j and l=Y and j=X then Y=X (player does not change)

therefore line b = 1-p(1)= 0 or in other words, line b is not true. if p were equal to 0, then line a would not be true and line b would be true.

The question is, what determines p. p is your probability, figured mainly by running the experiment. See exercise 15-18. Also, when they are defining the strategies of blind and standard, and easier way of defining it is, blind the host does not have preknowlegde of the position of car, standard he does have that preknowledge and must choose a goat. A previous post does provide a link to a web site that can run the standard simulations for you. http://cartalk.cars.com/Tools/monty.pl

As for blind, you will have to do that with someone else. Don't spend all day running 1000 simulations, just do 30 or so should be enuf. And, your p must be equal to 0 or 1, not in between. Therefore, round to the nearest number.

As far as the rest of the logic problem, im not going to try and explain it, there was a teacher with a previous post who posted the afore mention site. Ask him, if you don't comprehend the terminolgy used in the analisys, you can click on the hyperlinks for a detailed definition of each as well.

As far as your logic is concerned, it would help me understand where you are coming from if you would define n.

Poolchamp

p.s. I only scored a 135 on that iq test. If I can graspe this concept, I would think that you would as well. And this post is some hainous typing, i didn't exactly proof it.

08-11-2002, 12:01 AM
see what you started here tom? this is why we don't ask open ended questions.

poolchamp

TomBrooklyn
08-11-2002, 04:47 AM
Well, it has been most educational.

08-11-2002, 11:22 AM
<blockquote><font class="small">Quote: poolchamp:</font><hr> As far as your logic is concerned, it would help me understand where you are coming from if you would define n.

Poolchamp<hr></blockquote>

Poolchamp, in earlier posts I had mentioned that n would be the number of doors/cards/lottery tickets/numbers/etc. My impression now is that you didn't read at least part of this thread (I don't blame you; it's pretty long). To sum it up, I was using various examples to convey the concept to the doubters. You can look back at some of those posts to see all the different explanations.

Anyway, when the host is NOT opening randomly (a fact I brought up in almost every post), switching will always yield a probability of (n-1)/n (so, 3 doors, 2/3).

My "logic" was always that - whenever you switch - you in effect get every other door. When you stay, you only get yours. In my opinion, this is much more intuitively understandable than the proof.

Anyway, we should let this one lie. As you mentioned before, it's been beaten to death.

- Steve

bluewolf
08-11-2002, 04:48 PM
pick a door. any door. who cares?

bluewolf

bluewolf
08-11-2002, 05:02 PM
I dont know about a reliable source but it goes like this:

dolphins
hump back whales
wolves
alaskan malamutes and siberian huskies
vulcans
smart humans
dumb humans
all other life in rediculous order

bluewolf

bluewolf
08-12-2002, 10:52 AM
what good is a high iq if you dont have common sense? my father had both and was very successful. my son had a high iq but not common sense. so he screwed up over and over for years until he finally learned from his mistakes. at 28, he is just now getting his life together.

bluewolf

10-19-2002, 05:26 PM
<blockquote><font class="small">Quote: nAz:</font><hr> the average iq is 100, so 1/2 of the population is over 100, and 1/2 is under 100.

84-116 is normal, and anything above and below are obvious. anything under 70 is mental retardation. (70 is the average IQ of most pool players i met... im sure you will agree with that lol)

in the standardized stanford/binet intel' test, 68.2% score normal, and 15.9% score in each direction. though the WAIS test is the most widely used, i only have info on the stanford-binet test, but you get the general idea.

also note that online tests are always wacked out to give you a score you probably don't deserve, so don't break out the champaigne yet. This particular online test is probably one of the more accurate ones though.

Tom try out this IQ test its pretty good. I scored 127 /ccboard/images/icons/frown.gif Not bad for a grade scool drop out

<a target="_blank" href=http://www.emode.com/tests/uiq/authorize/register.jsp?url=/tests/uiq/index.jsp>http://www.emode.com/tests/uiq/authorize/register.jsp?url=/tests/uiq/index.jsp</a> <hr></blockquote>


Yeah, I got 122. And I guess I'm a "word warrior" according to the test.. I can really wing the words out. cool.

TomBrooklyn
10-19-2002, 06:40 PM
<blockquote><font class="small">Quote: bluewolf:</font><hr> what good is a high iq if you dont have common sense? <hr></blockquote>Is it true that geniuses are more likely than average to go insane?

John F. Nash, the Princeton University math professor who won a Nobel Prize was and still is insane. Bobby Fischer, the chess player, seems mentally unstable.

BillPorter
10-20-2002, 03:59 PM
Hey, SpiderMan, congratulations on having the character and intelligence to see the logic of the other side of the argument and agree with it! It is rare to see such rationality on this or any other board, so I thought it deserved a compliment. And compliments as well to those who persisted in trying to understand what seems to me to be a very slippery probability problem. I'll admit, I was dead wrong when I first encountered this one and it took me a lot of thought to "see the light."

10-21-2002, 05:44 PM
Spiderman your being to hard on Bill Clinton. Most of the above mentioned people would have gone to jail for crimes committed while in Office but until Clinton we have let them escape the Office without proscuting them. People regard Reagan as a God but when questioned about Iran Contra he couldn't remember anything. He didn't lie he just lied about not remembering. Truman and Carter were the honest Pres except where Harrys daughter Margret piano playing was concerned.####

ted harris
10-21-2002, 07:41 PM
<blockquote><font class="small">Quote:</font><hr>the average iq is 100, so 1/2 of the population is over 100, and 1/2 is under 100.<hr></blockquote>
So how many are at 100?
Just to clear things up, there are 3 billion people on earth with an IQ of 100 or less. Holy cow!

ted harris
10-21-2002, 08:21 PM
How can he have a low IQ? Yeah right, with an IQ of 91 he graduated from Harvard with an MBA? Horse pucky he has the lowest IQ! Below is a link for all you dummies out there that bought this story!
<a target="_blank" href=http://www.museumofhoaxes.com/lovenstein.html>http://www.museumofhoaxes.com/lovenstein.html</a>
Your story is nothing more than a hoax! Why don't you think about what you write, or do you believe everything you read and/or hear?!!!

PQQLK9
10-21-2002, 08:57 PM
<blockquote><font class="small">Quote: ted harris:</font><hr> How can he have a low IQ? Yeah right, with an IQ of 91 he graduated from Harvard with an MBA? Horse pucky he has the lowest IQ! Below is a link for all you dummies out there that bought this story!
<a target="_blank" href=http://www.museumofhoaxes.com/lovenstein.html>http://www.museumofhoaxes.com/lovenstein.html</a>
Your story is nothing more than a hoax! Why don't you think about what you write, or do you believe everything you read and/or hear?!!! <hr></blockquote>
Feel better? /ccboard/images/icons/smile.gif

ted harris
10-22-2002, 09:56 AM
Much, and thank you.

10-22-2002, 02:34 PM
Patrick wrote: "A child with 200 IQ is not smarter than an adult with less IQ."

You're confusing IQ with knowledge. IQ measures one's ability in critical thinking. Thus, an adult may know more facts about a given topic than a child does, but the adult's ability to use that knowledge to apply critical thinking skills may be less than the child.

Aldewey....(sorry for anon post, but won't let me change it.)

10-22-2002, 02:43 PM
Steve wrote: "You pick a door. The host then reveals ANOTHER door that is NOT the grand prize. He then asks you if you'd like to change your guess to the last door.
Believe it or not, you should. Your original guess was based on a 1 in 3, whereas now you are increasing your odds to 1 in 2."

Not true. Yes, the contestant selected his door when there were 3 doors to choose from, so at that time his odds were 1 in 3. After the third door is exposed, though, there are only 2 doors left to choose from. The odds are 1 in 2 if he changes his door or if he doesn't change it.

aldewey

10-22-2002, 02:49 PM
Steve wrote: "your guess is STILL a 1 in 3 if you don't switch. It's still a 1 in 3 because your guess was made with the same information you now have (there were 2 duds)... now they're just showing you one of the duds. If you do switch, your guess has improved to a 1 in 2, because you're basing your guess on new information."

That would only be true if the contestant weren't allowed the option to change doors after the non-winning door was exposed. However, once it is exposed, there are only two potentially winning doors remaining, and choosing either one at that point is a 50/50 proposition.

aldewey

10-22-2002, 03:12 PM
Steve wrote: "You pick one door. I open 999,998 doors, all revealing duds. (Keep in mind, I am NOT doing this randomly - I know which door has the prize in it)."

That's right....you know which door has the prize in it...so it's not random. BUT, if I've ALREADY picked the door with the prize in it, you'd still reveal only 999,998 doors and leave one closed. The fact that you as the host are choosing WHICH doors to open doesn't mean that the door you choose not to open is automatically a winner---you HAVE to leave one door closed in order to leave me with a choice. All it means is that you know that the doors you are opening are NOT winners.

AFTER the 999,998 doors are open, I know the same thing you do....that 999,998 doors are losers, and one of the two remaining doors is the winner.

Simply put, the fact that you as the host choose to leave the 999,999th door open doesn't mean it is the winner. It means that you have to leave one door closed in addition to the one I chose.

At that point, armed with that information, I now have a choice between only 2 doors....the one I picked, or the one I didn't. That's a 50/50 proposition.

aldewey

10-22-2002, 03:25 PM
"In Marilyn's example, the host KNOWS which has the grand prize."

Yes, he does know which door holds the grand prize, but if I've PICKED the door with the grand prize, the host is STILL going to leave another unwinning door closed and try to entice me to change my guess.

(In fact, if subterfuge on the part of the host was a factor, I'd imagine he'd try even harder to get me to switch if he knew I had picked the winning prize so the show didn't have to pay out to me).

Perhaps this will help:

Scenario 1: I pick a losing door. The host opens all the other doors except the winning door. I then have to choose between my door and the remaining door.

Scenario 2: I pick the winning door. The host opens all the other doors except one other non-winning door. I then have to choose between my door and the remaining door.

In either case, once I'm down to 2 doors, and I can choose one or the other, my odds now become 1 in 2. When I first selected the doors, my chances weren't as great. But if I select to stay with my door, my chances at that point are 1 in 2. The fact that the host KNOWS which door wins doesn't mean that the door he leaves closed MUST be the winner. His knowing which door wins only lets him successfully reveal all non-winning doors. But he has to leave 2 doors closed...one that wins and one that doesn't. It's a 50/50 prospect, either way.

aldewey

10-22-2002, 03:37 PM
Ross wrote: "Here is the most direct explanation I have found:

If your original guess was correct and you switch, you lose.
If your original guess was wrong and you switch, you win."

How is that different from this:

If the door I didn't pick was the winner and I switched, I'd win.
If the door I didn't pick wasn't the winner and I switched, I'd lose.

Ross wrote: "Since your original guess would be wrong two out of three times, if you switch you'll win two out of three times."

You're missing this: The door I picked would be wrong two out of three times only WHEN there are 3 possible winners. The door I didn't pick would ALSO be wrong two out of there times WHEN there are 3 possible winners.

However, once the third door is opened, we are NO longer talking about 3 possible winning doors. AT THAT MOMENT, only one of two doors can win, and at that moment, the odds are 1 in 2 that either door will win.

aldewey

SpiderMan
10-22-2002, 03:45 PM
<blockquote><font class="small">Quote: Anonymous:</font><hr> Spiderman your being to hard on Bill Clinton. Most of the above mentioned people would have gone to jail for crimes committed while in Office but until Clinton we have let them escape the Office without proscuting them. People regard Reagan as a God but when questioned about Iran Contra he couldn't remember anything. He didn't lie he just lied about not remembering. Truman and Carter were the honest Pres except where Harrys daughter Margret piano playing was concerned.#### <hr></blockquote>

Yeah, I guess being hard on Bubba was easy since I didn't like his politics. Can't be objective about everything, especially if you think you're right /ccboard/images/icons/wink.gif

SpiderMan

MikeM
10-22-2002, 05:34 PM
Exactly Al, and before it was a 1 in 3, so changing gives you better odds. Read Ross' explanation and it makes sense.

MM...this has given me a headache

MikeM
10-22-2002, 05:52 PM
<blockquote><font class="small">Quote: Anonymous:</font><hr> Ross wrote: "Here is the most direct explanation I have found:

If your original guess was correct and you switch, you lose.
If your original guess was wrong and you switch, you win."

How is that different from this:

If the door I didn't pick was the winner and I switched, I'd win.
If the door I didn't pick wasn't the winner and I switched, I'd lose.

Ross wrote: "Since your original guess would be wrong two out of three times, if you switch you'll win two out of three times."

You're missing this: The door I picked would be wrong two out of three times only WHEN there are 3 possible winners. The door I didn't pick would ALSO be wrong two out of there times WHEN there are 3 possible winners.

However, once the third door is opened, we are NO longer talking about 3 possible winning doors. AT THAT MOMENT, only one of two doors can win, and at that moment, the odds are 1 in 2 that either door will win.

aldewey
<hr></blockquote>

Al,

If you boil it down to a 50/50 proposition you are ignoring the fact that your original choice was based on 1/3 and ignoring the statiscal probability information available to you.

Don't look at it as being asked "Which of these two doors are correct?"

Look at it as "Do you wish to switch your choice based on new information available to you?"

"Statiscally speaking" switching is the only way to go.

MM

BillPorter
10-22-2002, 07:18 PM
<blockquote><font class="small">Quote: Anonymous:</font><hr> Steve wrote: "You pick one door. I open 999,998 doors, all revealing duds. (Keep in mind, I am NOT doing this randomly - I know which door has the prize in it)."

That's right....you know which door has the prize in it...so it's not random. BUT, if I've ALREADY picked the door with the prize in it, you'd still reveal only 999,998 doors and leave one closed.

aldewey, If you did this each morning and always stayed with your original choice, it would take years before it would be likely that you would have the right door. On the other hand, how many mornings would it take to get the right door by switching? I started out with the wrong view of this problem myself and I was in good company because quite a few Ph.D. mathematicians got it wrong originally. It absolutely goes against what seems to be common sense, but, in the end, I think you will figure out that Marilyn was right on this one. Hope so!

BillPorter
10-22-2002, 07:28 PM
MM, after reading all Al's posts, I think he has just dug himself into a position and no longer is really trying to understand the problem. By continuing to say that it's a "50/50 proposition" he is actually implying the patently false proposition that if he did the game again and again, and never switched, he would win 50% of the time! How can you argue with a person who thinks chosing one of three doors will lead to a win 50% of the time just because a host opens one of the two remaining doors!!!????

MikeM
10-22-2002, 08:41 PM
Bill,

I can empathize with Al because I did the same thing with my statistics professor in college. He posed a similar question, something to the effect of If a woman has a boy what are the statistical chances of her second child being a boy? I don't really remember, but I believe the correct answer was 1 in 3. I dug my heels in the same way Al has because I reasoned that it had to be 50/50. I was wrong. I thought maybe I could come up with an explanation that would turn Al. Longshot I know and now I've probably opened a new Pandora's box that will shoot this thread to No.1 !!!!!.

MM

Patrick
10-22-2002, 09:53 PM
What I mean is, if you have 200 IQ as a child, you will have less when you are an adult. Maybe 170-180 IQ. Child IQ scores measure too high.

Patrick

Barry
10-22-2002, 09:57 PM
Probably, In pool was Burton Spain, Who was a member of Mensa.

Patrick
10-22-2002, 10:02 PM
You call them insane because you don't understand.

TomBrooklyn
10-22-2002, 10:48 PM
<blockquote><font class="small">Quote: MikeM:</font><hr>...my statistics professor in college posed a similar question: If a woman has a boy what are the statistical chances of her second child being a boy? I don't really remember, but I believe the correct answer was 1 in 3. I reasoned that it had to be 50/50. I was wrong. <hr></blockquote> Mike: That question is similar in that it has to do with probabilities, but the similarity ends there. I'm going to go out on a limb here, but I don't really think I am, and say with certainty that for the question as you remember it, the chances are 50/50, or 1 in 2!!! I was wrong at first about the three door problem, and I understand the reasoning now, but I am SURE of this! Lol, =TB=

TomBrooklyn
10-22-2002, 10:54 PM
<blockquote><font class="small">Quote: Patrick:</font><hr> You call them insane because you don't understand. <hr></blockquote>Well, Bobby Fischer is not insane for sure, but he has certainly been exhibiting weird anti-social behavior. There is a website somewhere, I don't have the link handy, that has some recent audio interviews with him from somewhere in the South Pacific where he is living in exile as a fugitive.

I think a lot of genius have trouble relating to people because very few people understand them or things that they can understand easily. But John Nash was certifiably insane. Ask him, or see the movie, American Beauty. =TB=

BillPorter
10-23-2002, 06:42 AM
Mike,

I found the problem you refer to in your post. I think it goes as follows:

"If a family has two children, and the older child is a boy, there is a 50 percent chance the family will have two boys. However, in a family with two children, if all we know is that one child is a boy (no age specified) there is a 1/3 chance of that family having two male children. "

I'll bet that the same people who had trouble with the door problem will stumble on this one. Let's see.

BillPorter
10-23-2002, 06:46 AM
Tom,

Speaking as someone who has taught this stuff for over 35 years, I can tell you that the standard textbook answer to the question of the relationship of genius to insanity is that higher IQ people actually have better mental health, ON AVERAGE, than people with average IQ's.

BillPorter
10-23-2002, 06:53 AM
Tom, I have to agree with you on this one. But check this out:

"If a family has two children, and the older child is a boy, there is a 50 percent chance the family will have two boys. However, in a family with two children, if all we now is that one child is a boy (no age specified) there is a 1/3 chance of that family having two male children."

I think this is the problem he was trying to remember. And strange as it seems, it works out.

MikeM
10-23-2002, 08:15 AM
I believe that's the one. Maybe Ross can weigh in on this one, him being a statistics professor. Maybe he's tortured his students with this one as well.

MM...this thread at No. 2 with a bullet!

BillPorter
10-23-2002, 12:46 PM
Mike,

After wading through a couple of hours of comments about this problem on the Internet, I have decided that it isn't worth any more of my time. For an example of how complex the arguments on this one can become, see these links:

http://www.wiskit.com/marilyn/boys.html
http://mathforum.org/library/drmath/view/55640.html
http://www.icdc.com/~samba/marlright/children.htm

It goes on and on. The nub of the problem seems to be that there is a lack of clarity regarding the sample space from which the family is chosen. Me, I'm going to go play some pool!

10-23-2002, 01:28 PM
Quote TB:

"But John Nash was certifiably insane. Ask him, or see the movie, American Beauty."

I think you meant to write "A Beautiful Mind."

Babs

TomBrooklyn
10-23-2002, 01:48 PM
Oh yea, thats right, Babs. I was close, both titles are composed of letters. What I really meant was, ask him, and then go see American Beauty.

I had a kind of strange feeling when I saw 'A Beautiful Mind'. I didn't like it that much when I watched it, but I liked it more the next day when I thought about it. It won four Academy Awards also. I've found some movies that win a lot of Academy Awards are kind of obscure like I thought ABM was. (Remember multi-award winner Chariots Of Fire? What was that about?) Maybe it makes the Academy members think they have a high IQ to be able to figure it out.

Thanks for the clarification, I'll edit the prior post later.

=TB=

SPetty
10-23-2002, 04:50 PM
<blockquote><font class="small">Quote: Babs:</font><hr>
I think you meant to write "A Beautiful Mind."
Babs <hr></blockquote>Hi Babs,

Welcome to the board! I am really looking forward to reading your future posts!

/ccboard/images/icons/laugh.gif /ccboard/images/icons/wink.gif

10-24-2002, 12:37 AM

Patrick
10-24-2002, 12:37 PM
If you know the first one is a boy, it is 1 in 2 chance to be another boy.

If you know one of the 2 children is a boy, then it is 1 in 3 chance for the other one to be a boy.

Patrick

10-24-2002, 01:09 PM
<blockquote><font class="small">Quote: rackmup:</font><hr> I don't know any names but I am willing to bet it is someone that lives on Everest in the Himalayas (Nepal/Tibet) at an altitude of 29,035 feet. That's a high IQ.

Glad to help and resolve any controversy.

Regards,

Ken <hr></blockquote>

Uh.. I think that is AQ.. (altitude quotient)

10-24-2002, 02:25 PM
<blockquote><font class="small">Quote: finnegan:</font><hr> I would say your asking what pool player has the highest iq i would say johnny everlino he made a living out of pool for about 50 years <hr></blockquote>Without getting too particular about being exact, say you made three groups: below average, average, and above average intellegence. Where would most top pool players fall into, or is there any pattern at all? I'd guess probably not too many are in the below average group, but I could be wrong about that. Between average and above average, is this a factor for playing at the best level?
SlimJimmy

10-25-2002, 08:59 AM

10-26-2002, 10:30 PM
29029

10-28-2002, 09:26 PM
Tom, I think at this point, a good question to ask would be who has the highest emotional IQ? The hostility and in-fighting on the CCB has gotten so out of hand it's scary. Maybe BD should shut down the forum for about a week to give everyone a chance to cool off.

Yours Truly,

An anon poster who won't participate in the fighting.

TomBrooklyn
10-28-2002, 11:02 PM
Good question about emotional IQ. You can tell a lot about a person by reading what they write and and how they express it.

But shut the forum down? Nah, the stuff of late is lightweight banter. Something has to fill in the slow times in between active pool topics. Thats when the off-topic stuff starts picking up. Then some folks start complaining about the off-topic stuff. The standard response is that that comment is off-topic. Then comes the 'what have you contributed thats on-topic lately anyway' comment. Then the ball gets rolling. Then come the calls for bans, censors, alternate forums, moderators and registration proceedures. It's happens like a formula. Get a few good pool topics going, and everyone forgets about the problems. As surely as the tide rolls in and out.

Some people don't know how to dispute or criticise statements without criticising or insulting the person who made them. Big difference. That's when things can really heat up, it can get major stupid and hateful. You won't see me getting in the middle of that stuff much. Interesting to read, though. But a lot of it's not pretty.

Then there's the blatent super-insulting troll. Only had one of them, and he got banned.

=Tom=

Ludba
10-29-2002, 12:14 PM
It's hard to believe this oft-beat late equestrian has anything left to flog. Harder still to think anyone still holds on to the thin hope that the three-door scenario is a 50/50 chance.

But anyway, let me get my kicks in. The most interesting thing about this problem is not the riddle itself, but its psychological implications. The reason people claw so desperately to the 50/50 answer instead of the obviously (more on the use of 'obviously' later) correct 1-in-3 answer is twofold: 1) as someone said above, our brains are not wired to handle probability; and 2) choosing the correct answer is like betting against ourselves.

You choose door number one. The host opens door number two. Do you want to switch? No, of course not. I picked door number one, because I thought it was right. Why would I change my answer if I thought I was right? I'd be betting that I was wrong, which is inconceivable to me because then I would have to rethink something I already thought to be true.

The problem is YOU WERE PROBABLY WRONG to begin with. That is a statistical fact AND it follows common sense. If you have a one-in-three chance of winning, you will most likely lose. But then you encounter a second, more novel situation: the host opens another door and gives you the switch choice. But the voice in our heads (common sense) says,"Stick to your guns. What if you were right to begin with?" You probably weren't. And it's smarter to bet against yourself in something you know little about (By 'little' I mean the 30 minutes we spent in our 7th grade math class studying probability). Scientific fact and common sense part ways in the most difficult questions and more often than not science/reason/logic is right.

Now to why the answer is 'obviously' correct even if you don't follow Steve's valiant efforts at explanation (Steve, you must have the patience of Job). The reason we should change our door is the same reason we should change our belief about the answer to the problem: OUR FIRST ANSWER IS PROBABLY WRONG. Common sense tells us that the switch/stay question is a 50/50 chance. But in math and especially probability, common sense is usually wrong to begin with.

I would argue further that in most everything common sense is wrong to begin with (I just want to go on record as the first person to chastise those with common sense and little intelligence). This is because common sense is developed through the trial-and-error method. The first few times you encounter a situation (e.g. probability problem), your answer is wrong. This is why the trial-and-error method is not very effective in handling novel situations. Ask any lab rat that's been zapped with a few volts of electricity for picking the wrong cheese.

The advantage of math (or any other branch of science) is that if I wanted to add 537 plus 100, I could arrive at 637 without breaking a sweat or opening up the calculator on my desktop, although I have never added those two numbers together. But the most non-commonsensical stuff comes in when I start adding imaginary numbers or finding cosines.

My point here is that if you start from the premise that you're initially wrong in most things, you might give yourself an ulcer, but you'll probably be the first scientist on your block to discover relativity or develop a cure for cancer. Think outside the box.