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Science of the coin-toss: Bias in Heads-or-Tails
MrSharkey writes " An interesting
article published in Science
News puts a new scientific spin on the outcome of the venerable
coin-toss. "A new mathematical
analysis suggests that coin tossing is inherently
biased: A coin is more likely to land on the same face it started out
on.""
heads they're wrong.
tails they're right.
rock-paper-scissors to settle the disputes of mankind. And drunken boxing.
-fren
"Where are we going, and why am I in this handbasket?"
And the society shaking ramifications of this are what? We will stop tossing coins before football games and instead have a pocket sized random number generator and the teams pick a number?
Even if I knew that tomorrow the world would go to pieces, I would still plant my apple tree. -Martin Luther
Their preliminary data suggest that a coin will land the same way it started about 51 percent of the time.
I wonder what their margin of error was.
If you've ever watched a football game, you'll notice that the coin always hits the ground. This is done for at least one reason, to prevent tampering by the tosser.
It seems that it would also be good given the results of this study, as it could add more randomness (through the act of hitting the ground), thereby countering the "same side down" effect.
libertarianswag.com
Perhaps related, bread more often falls butter-side down because it usually only has time to complete half a rotation in the distance it falls from your countertop.
Yeah, whatever. You were lucky. 51% is the stated bias. in 13 tosses, that would possibly bias it one count and even then it is statistically more likely it wouldn't.
I do not fear computers. I fear the lack of them. Isaac Asimov (1920 - 1992)
A coin is more likely to land on the same face it started out on.
If this is true, we would still want to call the opposite face since we after it lands, we always flip it onto the other hand. That is, if we start with heads facing up, and it lands more frequently with heads facing up on our palms, by the time we slap it onto the back of our opposite hands, tails is facing up!
Yeah, guys, 51% is really biased there... especially when you can completely solve this by the simple expedient of not looking at the coin before you toss it. (or by having one person pass the coin over, and the other person call it)
pb Reply or e-mail; don't vaguely moderate.
I just don't want to think about it!
Bias:
Heads 49.9%
Tails 49.9%
Coin becomes
Self-aware 00.2%
I bet Rosencrantz is pissed to find this out!
"didn't-gildenstern-prove-that-already dept"
Wow, Taco, about 7 Slashdot readers will even get that. +1, Obscure!
That was a pretty funny book, actually.
I want to delete my account but Slashdot doesn't allow it.
An interesting alternative is to flip the coin so that it lands on a smooth floor, spinning on a vertical axis. Then the uneven distribution of mass between the head-side and the tail-side will cause a bias.
It is my experience that dimes and quarters are nearly unbiased for this test, whereas nickels are heavily biased (pun intended) toward tails . [In a past life, I taught a statistics class for which I assigned daily homework, deciding whether or not to take it up on the basis of a coin flip at the end of class. On days for which I really didn't want to spend all evening grading papers, I would use a nickel; I'd use a much-fairer quarter on other days. And none of the class caught on... ]
"My opinions are my own, and I've got *lots* of them!"
First - the experiment they used to "prove" this involves creating a mechanical device that will flip a coin for you. After some tweaking, they got it to flip and land consistently with heads up.
Of course you can flip a coin (or any other object) and get it to land the same way every time. All it means is that you've eliminated the random factors of human interaction, air, friction, etc. There's nothing inherently random about a coin - it's the random factor in the action.
Here's the excellent NPR piece, with pics of the gadget they flipped the coins with: NPR.
Who gets the funds to study these projects? I want a grant to study something like this.
I think this is what you study after your grant proposal has been refused and the only thing left in the department treasury is a quarter.
This was on NPR the other day. There are a number of issues one of which is that when we flip a coin it actually has a fairly high probability of never actually "flipping" end-over-end. You can test this by attaching a ribbon to the coin and to, say, the table, flipping the coin and then counting the number of twists in the ribbon. It isn't a question of trying to flip it more or less times so much as the physics of the flip. As mentioned in other posts, letting the coin bounce on the ground does make things better since in that case the coin's motion is less predictable.
I'm a magician, and a "mentalist". That means, I pretend to have psychich powers (which I don't, but I don't explain that until after I've convinced the spectator that I have).
One of my tricks is to predict the outcome of a cointoss. I start out with pseudo science explanation, and then, as I continue to be correct, continue on to a supernatural explanation.
The explanation given in this article, as to why a coin is biased, can be boiled down to this (quote from the article): For a wide range of possible spins, the coin never flips at all, the team proved. . That is - the extra bias is towards the side that was up from before the toss, and is a result of the coin not spinning at all. If that's their big scoop, I'm dissapointed, because if the coin doesn't spin, it's not within my definition of a coin toss.
The article actually mentions magicians: Magicians and charlatans may take advantage of this illusion. Keller observes, "Some people can throw the coin up so that it just wobbles but looks to the observer as if it is turning over."
He has obviously seen a magician to the same trick I do. Of course I wont reveal the secret, but I can tell you this: he's wrong. The dirty work does not happen in the toss. The coin actually do spin, and the secret move is done at an offbeat moment.
Some level of added insurance would be provided by simply not allowing those selecting a landing side to see the side on which the coin begins. If the flip is being done by a third party, of course, there's the danger that there's collusion between the third party and one of the participants prior to the toss, even for a 1% better chance in the throw, but we still have a better chance of non-tampering and non-bias as a result. And regardless, even in the worst case scenario, where the participants know the side on which the flip is beginning, we only have a 1% statistical advantage to the one side. Furthermore, a non-level, somwhat randomly varied surface onto which the coin is tossed, rather than a plane, will add another randomising factor.
I thought about it for a second, and given the odds of throwing 9 heads in a row AND doing it right as you were using it as an example were astronomically high - stood up and said 'that's a two headed coin'
Teacher smiled and proceeded to show the class the two headed quarter
So they did the experirment and got 51%. This is wholly compatible with the notion that the coin is random.
And by the way, ONE trial of 10000 does not prove anything. Show me 51% for ALL trials of 10000 and then lets' talk.
Analyzing the motion of a disc which rotates about both an axis through the side (flipping) and an axis through the face simultaneously is a straightforward physics problem that decades of physics undergrads and grad students have had to solve as part of classical mechanics classes. The problems are typically phrased in "relevant to coin-tossing" form, as well. In my mechanics class, the problem was phrased something like "what ratio of angular velocities (around the two rotational axes) is necessary to have the coin have a 2/3 chance of landing with the same side facing up as that which started?"
New scientific spin?
Seeing as it's the way Bush determines his foreign policy choices, I think it's very important to study the coin toss.
Actually, I see this as very important.
Everyone I personally know assumes that coin tosses is a fair, random decision. And that's a fairly fundamental assumption.
This shows that you can assume some things, and you can't assume others. And the list of things you can and can't assume is always changing.
And, just to make your head explode, I'll point out that that means that, over the long term, you can't assume anything.
Think of this research as a sort of lesson in appropriate behavior
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Another case of duh. I observed this in High School in the late 1980s when my friends and I used to play various quarter games for money. It greatly increased my chances when spinning a quarter for money during lunch.
I also used it to increase my chances when playing same/different with another player. Each person spins a quarter, and both players stop their respective quarters wihtout letting the other see the results. The person can look at their own results, and one person guesses whether the quarters are they same or different. If the person guesses correctly, then they take the money. Otherwise, the other person takes the money. Other amounts of money oculd be bet, but only quarters were used to spin in the game. You can really gain a psychological advantage over a person when you win a few without looking at your results and winning each one!
At the next eco-hypocrisy-meeting, count the private jets used to get to the meeting. Should be interesting to see that
There is a neat trick for dealing with a biased coin in a coin toss:
- Flip twice.
- Discard the pair of throws if it's both heads (HH) or both tails (TT).
- Count HT as heads, and TH as tails.
(I think this idea was from John von Neumann.)
Applied to the current situation: Flip twice, once starting H down, once with T down.
I remember my middle school science teacher would have a "coin tossing" lab each year with students, students would keep track and submit the totals. It was all a lesson in probability. He had everyone use pennies dated after 1982 (when they changed the alloy). Heads up was almost 51% of the time. His theory was that heads was "rounder" than tails and that accounted for the difference. Course, 7th grade students don't exactly make the best objective testers
> Seeing as it's the way Bush determines his foreign policy choices,
> I think it's very important to study the coin toss.
Eek ! Somebody please hand him the coin with the "don't bomb" face showing next time !
25% Funny, 25% Insightful, 25% Informative, 25% Troll
You'll get 7 or better out of 10 correct about 17.2% of the time just by chance if there's no bias at all...
Somehow I doubt this was the most expensive experiment ever...
Research materials budget - 0.01 $
that coin tosses is a fair, random decision
if the person who calls the toss never sees the face of the coin upon the toss, and doesn't call it until its in the air, is it not still random, and fair?
We're like rats, in some experiment! -- George Costanza
Of course one could also just flip a coin to see which side to start up before performing a coin toss (begin infinite loop regression)....
-- I'm not a pessimist, I'm a realist. It's not my fault that life sucks so much. --
I'm a geek, so I don't toss coins: I roll a d20 instead. 1-10 I win, 11-20 you lose!
Eek ! Somebody please hand him the coin with the "don't bomb" face showing next time !
Thats not how it works in this white house. His coin says "Bomb Iraq" and "Bomb Syria"
Thousands of children die every day, yet things like faster semiconductors are getting funded. Riiiiight.
Unlimited growth == Cancer.
If you have a mortgage, but your salary more than covers your mortgage payments, you do not have a deficit.
However, if you already can't pay your mortgage and your solution is to move to a bigger house in the hope that by stimulating the housing market it might get you a better-paying job, the US goverment would probably like to hire you as a financial adviser.
> Ever seen the movie "Black Hawk Down"? Bill did that.
Bill produces movies ?
25% Funny, 25% Insightful, 25% Informative, 25% Troll
You're right, of course. I think the difference really is that Bill Clinton actually attended the funerals of those who were killed in action. Bush not only doesn't attend, he doesn't even allow the funerals to be mentioned by the media. Oh, and he also cuts the benefits to any soldier that does survive. A true patriot.