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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
Who gets the funds to study these projects? I want a grant to study something like this. I can probably come up with a hypothesis like, hmmm, do strippers like drunks or sober people more. Wheres's my money !!!
Stay tuned for new sig...
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%
step one: go to vegas
step two: bet on coin flipping
step three: PROFIT!
wait, that makes too much sense.
dang
Jack the sound barrier. Bring the noise.
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!"
maybe the folks over at SCO could help test this theory... they're all a bunch of tossers ;) ...I'll get my coat..
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.
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.
If you start 50% of the tosses on heads and 50% of them on tails, that will remove the bias. The fact that you would like do so without even thinking about it, explains why the bias isn't normally seen (that and it is a small bias).
You would only add memory to the system if you always started a flip on the side that it last landed on (or always on the opposite side). If you always start on a predetermined side regardless of how the coin landed last, the outcome would in no way be dependent on the previous outcome (although depending on how you predetermined the side, and how you are using the data you may have to adjust for the bias).
Most Interesting Part of the Article:
:-)
This slight bias pales when compared with that of spinning a coin on its edge. A spinning penny will land as tails about
80 percent of the time, Diaconis says, because the extra material on the head side shifts the center of mass slightly.
Is it time to start making some bets with some friends?
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
I only flip it to the other hand if it doesn't land on the side I want.
paintball
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?
Considering a football game and the grass/turf on the ground, the coin doesn't really get much of a chance to add much randomness due to the amount of energy absorbed - in fact, usually, it falls and lies there - hardly any bounce back. A fairer way would be to have the coin fall on a glass plate so it bounces back more, thereby inserting much more randomness into the toss.
While we're still on the subject, what about using a roulette wheel to decide? Pick red or black and let the ball decide. You can have a nice transparent glass ball (so that you can see that there's no metal inside it to bias it in any way) hitting a metal roulette wheel and glass and metal collisions have among the highest bounce co-efficients.
Find a job you like and you will never work a day in your life.
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
tasks(723) drafts(105) languages(484) examples(29106)
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 $
This is just a result of standard statistics. This has been known in Gambling for some time. If a game has a 50/50 chance, and you start losing, you are most likely to keep on losing. You are starting the next game that has a 50/50 chance of winning, however, *YOU ARE ALREADY LOSING*. The same goes on the flip side. If you are already winning, and you continue a game where you have a 50/50 chance of winning, *YOU ARE ALREADY WINNING*
Think about this. The coin first lands on tails. On the next two throws, it's 50/50 chance of tails or heads. Thus, if it landed once on tails, and once on heads, you have 2/3 tosses tails, and 1/3 toss heads.
However, statistics also says, the more you play the game, the more the overall outcome will get close to 50/50. However, if you start out losing, you are more likely to stay losing. You will just get closer and closer to 50/50 even if you don't win overall.
This is one of the number one myths of gambling. Just because you've been losing, doesn't mean your "luck" will change and you can start winning. In fact, you are more likely to stay a loser overall.
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. --
It would very useful to learn how to flip a coin (into the air), but not have it actually flip (end-over-end) as per the article. They implied that if the coin is oscillating or wobbling, people would not notice that it's not actually flipping. This could win me a lot of root beers!
The Russians have won. They have made the world a cesspool of distrust, greed, fear and hate.
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.
from my understanding (which could be wrong) in all instances of a 'random generator', the numbers will never be random, as proven in programming.
True, a finite state machine with no continuous input can generate only repeating sequences. However, there do exist sources of entropy; the most common is the least significant bits of an ADC wired to a reasonably unpredictable analog process, such as an FM receiver, a microphone, or even a moving trackball. If your random number generator is based on hashing an entropy source, then the numbers will not follow a repeating sequence. And even in mobile devices that don't have an analog input, it's possible to use a long-period PRNG such as Mersenne Twister and re-seed it with entropy whenever you dock it.
> Ever seen the movie "Black Hawk Down"? Bill did that.
Bill produces movies ?
25% Funny, 25% Insightful, 25% Informative, 25% Troll
There is a rather simple way of generating a "fair" event (i.e. probability 1/2) using an unfair coin. Instead of calling on a single toss, you call on a sequence of 2 tosses (H on first, T on second OR the other way around). You toss the coin twice - and reject the pair of tosses if you observe both H or both T. Even if the coin is biased - the probability of HT versus TH are equal. (This of course does not address the question of "Does the starting side have a greater probability of showing up finally?" - but that is now irrelevant. You always start with the same side showing up since the fact that the toss is biased is no longer of any consequence.
This is a very common idea in statistics - the "order" HT versus TH is what is called an "ancillary statistic".
Actually, they turned out a profit by selling their research meterials on ebay:
For Sale: Unique Gambling Penny
Scientifically proven to land on tails 59.439% of the time!*
(*Special throwing instructions included.)
Quoth the Penguin, "pipe grep more!"
>> And at least Bill never sent a troop into battle who didn't come home to his or her family.
> Is that true?
It is. There were a number of casualties in Somalia. But remember, Bush Sr. sent those troops in, not Bill Clinton.
25% Funny, 25% Insightful, 25% Informative, 25% Troll
Deficit is not the same as debt. Debt is how much you're in the hole. Deficit is the rate at which you're going deeper into the hole.
Carpe Cerevisi - Seize the Beer
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.
What I do is write comments on slashdot that look plausible but are actually completely false. I like to use pseudo-science and obscure jargon to back up my arguments and convince the unsuspecting spectator. Sometimes I just make unverifiable claims with an air of authority and that's enough to convince people to give me karma.
Doesn't it make you feel good to know that our freedoms are protected by politicans, lawyers and journalists.
"if the person who calls the toss never sees the face of the coin upon the toss,"
Then the coin was showing both heads and tails until you resolved it by looking at it.