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Kellon
12-09-2004, 03:21 PM
I hope you won't consider this too out of place, but I'm trying to recall a book my son had a few years ago by Noam Chomsky, in which he (Chomsky) laid out a "proof" for flipping a heads 100 times in a row. I may be totally mis-recalling the whole thing. It seems like it was in a lengthy footnote or something. I asked my son, but he couldn't remember the title, since it was one of those "for class" things that get forgotten as soon as the assignment is completed. There was something about it that bugged me then and still bugs me every once in a while now. I must have looked at a couple hundred web pages over the past month trying to find a hint of it, to no avail.

Any of you probability experts read Chomsky?

gaming_mouse
12-09-2004, 03:42 PM
Kellon,

What do you mean by a "proof" of flipping a coin 100 times in row? I can't even imagine what that could mean. The odds of that happening, of course, are (.5)^100, and astronomically small number.

gm

rybones
12-09-2004, 03:53 PM
I actually learned this trick because of reading something about this when I was in school and it always stuck with me. Anyway I do not know if what I read was Chomsky or not, but what I read had to do with analyzing true randomness. The deal is that you can learn to flip a coin so that it lands on whichever side you wish it to land. The principal is the same a juggling bowling pins. You need to toss them in the air with precission so that you always catch the narrow end. Alas, this stuck with me I decided to play with it in my college days. Since then, if I flip a quarter in the air and let it land in my hand I can make it land heads up 80 out of 100 times or so. It is a pretty cool bar trick and has won me more than a fair amount of money.

I don't know if this is what you meant or not, but I hope it was intersting.

Ryan

gaming_mouse
12-09-2004, 04:06 PM
Ryan,

This is a cool trick. Hard to believe, actually. I mean, how many rotations does you quarter do. I know that when I flip a coin it's spinning so fast that there is just no way anyone could count the number of flips or anything and control how it landed. Do you flip it more slowly? Even so, still cool.

gm

Kellon
12-09-2004, 04:12 PM
"Proof" was a really poor choice of words, which is why I put it in quotes. A better word wasn't occurring to me when I wrote the question.

What little I recall was something about having 50 pairs of people (might even have been more) each flip a coin and the person (or persons?) who flipped heads then were repaired and flipped again, etc. At the end, according to the discussion, you would end up with a person who flipped a heads 100x in a row. One of the things that bothered me then and now was that it didn't seem to allow for nobody in the pairs flipping heads.

Chomsky apparently is also a mathemetician at some level, I believe, for whatever that's worth.

I could be pretty far off in my recollection, but I do think I've got the jist of it. I hate to say more or ask questions about it without having it in front of me, which is why I'm trying to find it.

rybones
12-09-2004, 04:28 PM
I have never been able to count as you are right it flips too fast. However take a quarter out -- or better still for learning I big ol silver dollar -- and start by trying to just flip it twice. It is actually really hard for the first 2 or 3 days/6 gazillion times. I found beer really helpful in the beginning (ah college). Soon you will find that you just have a feel for the coin and you will be flipping more revolutions than you can count. However, you will also have this sense of: "ok too fast that time, slow it a bit."

Good luck,

Ryan

quix0tic
12-09-2004, 05:53 PM
I read chomsky's politics and hugely respect him. The example you allude to may be from some of his linguistic work with which I am less familiar. I do remember some example where he suggested taking a stadium full of people and letting them each stand and flip coins, sitting down when they got tails. At the end of even 11 or 12 flips, you will still have people standing up (2^12= about one person in 4k). Point seemed to be that events which can be seen as highly improbable individually are in fact very likely. Don't know if that is what you were looking for but just throwing it out there.

ZeeBee
12-09-2004, 07:49 PM
Trying to get a coin to land on the right side repetitively is very, very difficult.

But doing it by the usual coin-flip method of catching it and slapping it onto the back of your hand is actually fairly easy.

With a little practice you can learn to tell one side of most coins from the other by rubbing your thumb over it as you turn you hand to slap it on the back of your other hand. All you have to do then is get the coin to turn over as you slap it down if it's facing the wrong way - pretty easy too.

A few minutes practice and you should have it.

ZB

MortalWombatDotCom
12-09-2004, 08:39 PM
[ QUOTE ]
I read chomsky's politics and hugely respect him. The example you allude to may be from some of his linguistic work with which I am less familiar. I do remember some example where he suggested taking a stadium full of people and letting them each stand and flip coins, sitting down when they got tails. At the end of even 11 or 12 flips, you will still have people standing up (2^12= about one person in 4k). Point seemed to be that events which can be seen as highly improbable individually are in fact very likely. Don't know if that is what you were looking for but just throwing it out there.

[/ QUOTE ]

i've heard about similar "experiments" where, for example, you fill a dump truck with dimes, dump it out, pick up every dime that comes up heads, put those back in the truck, and repeat. eventually you wind up with a dime that has come up heads a disturbing number of times in sequence. also a scheme with stock picks, where you send an emails to each of a thousand people, recommending to half of them to buy a particular stock issue, and to the other half, to short sell. you repeat 9 more times, changing around your recommendations so that you don't send the same set of recommendations to any two recipients. after 10 letters, one person thinks you can predict with 100% accuracy the short term behavior of certain stocks, and another 10 people think you have a track record of 9 and 1. offer those 11 people a subscription to your stock recommendation service, or shares in your mutual fund, or whatever.

neither of these things has anything to do with chomsky, but i like the sound of my own keyboard clicks.

Kellon
12-09-2004, 08:57 PM
You could be on the right track. Next time I see my son I'm going to have to lean on him to think harder about what the book was about, if not the title.

Thanks for your help, everyone. And -- good luck with learning to control your coin flips. /images/graemlins/laugh.gif

slickpoppa
12-09-2004, 11:44 PM
I remember reading a story on an internet site a couple of years ago about Ken Uston (famous BJ card counter) losing a lot of money betting against some guy with similar coinflipping abilities. I think the guy offered 2:1 odds and let Uston call the coin in the air. I guess he was somehow able to time his catch to get whatever side he wanted to come up.

magiluke
12-10-2004, 04:08 AM
It's not hard to believe, actually. There is no such thing as a random coin flip. There have been machines built that will flip a coin the same exact way every time. The thing that makes it "random" in human imperfection. We do it slightly differently every time. If you can temper the way you do it into something with little varience, you can flip it the way you want it (although not perfectly).

LockLow34
12-10-2004, 04:57 PM
[ QUOTE ]
I hope you won't consider this too out of place, but I'm trying to recall a book my son had a few years ago by Noam Chomsky, in which he (Chomsky) laid out a "proof" for flipping a heads 100 times in a row. I may be totally mis-recalling the whole thing. It seems like it was in a lengthy footnote or something. I asked my son, but he couldn't remember the title, since it was one of those "for class" things that get forgotten as soon as the assignment is completed. There was something about it that bugged me then and still bugs me every once in a while now. I must have looked at a couple hundred web pages over the past month trying to find a hint of it, to no avail.

Any of you probability experts read Chomsky?

[/ QUOTE ]

Little party trick:

Bet someone \$10 you can flip a penny and have it land heads up 20 times in a row.

Pull out 50 pennies and flip each one, discarding the ones that land tails up.

Repeat.
Repeat.

...

eventually you'll have one that landed heads up 20 times in a row.

"I said 'A' penny...not a specific one."

gaming_mouse
12-10-2004, 05:13 PM
[ QUOTE ]

"I said 'A' penny...not a specific one."

[/ QUOTE ]

Yes, when I feel like the sh*t (deservedly) beat out of me, I will be sure to try this out.

gm

Kellon
12-10-2004, 06:01 PM
I don't feel I can articulate it sufficiently to carry much weight, but I have the same basic problem with this that I did with the Chomsky proposal. Why is there any assurance that even 10 sets of flips, let alone 20, starting with your 50, will have a heads remaining? Let's assume for the moment that you get a 50-50 split every set of flips. I'll give you the heads wherever it can't be split evenly. You're down to 1 coin after just 6 sets of flips. Or am I totally misunderstanding?

MortalWombatDotCom
12-10-2004, 07:09 PM
[ QUOTE ]
I don't feel I can articulate it sufficiently to carry much weight, but I have the same basic problem with this that I did with the Chomsky proposal. Why is there any assurance that even 10 sets of flips, let alone 20, starting with your 50, will have a heads remaining? Let's assume for the moment that you get a 50-50 split every set of flips. I'll give you the heads wherever it can't be split evenly. You're down to 1 coin after just 6 sets of flips. Or am I totally misunderstanding?

[/ QUOTE ]

your incredulity is well founded. if you started with 1024 coins and performed this "trick", you would expect the number of coins that survived the first 10 flips to be 1. sometimes you'll get more, sometimes less.

assuming 4 coins survived the first 10 flips, the chance that you'll have any left after you flip each of them up to ten times more is close to 1 in 256.

starting with only 50 coins and attempting to get one to come up heads 20 times in a row, you'll be saying "wait, hold on, i'll get it to work this time" long after everyone else has gone home. or maybe you'll get beaten up and have your \$10 taken before that happens.

felson
12-13-2004, 03:15 PM
Don't you need one million pennies for this?

LockLow34
12-14-2004, 10:09 AM
Yes, you'd need 2^20 pennies for that. Was pulling the idea out of my nether region so hadn't really thought it through until later.

beckham9
12-16-2004, 02:30 PM
Assuming a 50% heads/ tails ratio, dont you need way more than 50 pennies to get one that flips heads 20 X in a row?

you need like 2^(19) pennies, which is a lot. or am i just thinking wrongly

dtbog
12-23-2004, 05:42 PM
[ QUOTE ]
I can make it land heads up 80 out of 100 times or so.

[/ QUOTE ]

Does this mean you can make your AK beat 22 80% of the time too?

Now THAT's a useful bar trick.

-DB

Photoc
12-27-2004, 04:15 PM
[ QUOTE ]
Little party trick:

Bet someone \$10 you can flip a penny and have it land heads up 20 times in a row.

Pull out 50 pennies and flip each one, discarding the ones that land tails up.

Repeat.
Repeat.

[/ QUOTE ]

With my luck, they'll all land tails up and I'll be F'd.