Noam Chomsky Flips Heads 100x in a Row

[slickpoppa]

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]

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]

[ 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]

[ 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]

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]

[ 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]

Don't you need one million pennies for this?

[LockLow34]

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]

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]

[ 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