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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.""
Yup, I figured this out awhile ago with quarters. My younger sister bet me that I couldn't call quarter tosses. I conveniently neglected to tell her about this random effect here, and called 9 outta 13 tosses; 7 straight :D
Moral Of The Story: don't bet on quarters.
'If you're flammable and have legs, you are never blocking a fire exit.'
I was expecting this article to say something about the subtle differences in weight between the Eagle and the Washington bust. I wonder if there's any consistant bias in this sense that might expose itself after several rounds of a million tosses?
Moderation: +1 pwnage
I knew this when I was in school (in india). I had often won such head-tail tosses based on this.
Just thought I would enlighten you people before any so-called "mathematician" claimed this "discovery".
I am not trolling, im dead serious. You can ask any indian you know and you will get the same answer.
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.
What if you pick the coin up randomly, let it roll aroudn in your pocket, call before the coin is then removed and flip it without checking
which side the coin is on to start with..
and for those who are wondering,
the bias is at 51% starting side.
You have 5 Moderator Points!
Which Helpless Linux zealot/MS basher do you want to mod down today?
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.
As they say about statistics: lies, big lies and statistics. As for the "bias", how much is it anyway? If the probability is 0.50000000000000000000000000000000000000000001 then I really can't get that excited.
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!"
In football games they let the coin hit the ground and bounce around before coming to a stop. That introduces complexities that the scientific study did not address.
It may very well turn out that the odds of getting heads/tails after letting the coin fall on the ground are still 50-50.
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.
It doesn't seem to me like that would nullify the effect described in the article. If the effect of hitting the ground has a 50% chance of favoring either side, the initial bias would still show through in the final result.
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.
Yeah right. All you need to do for a fair coin toss is hook your index finger, balance the coin on it, and use your thumb to flick up at the side of it. This sends the coin into the air spinning quickly end-over-end on an axis as horizontal as your hand was - and at a vertical angle perpendicular to it. You can measure your horizontal-ness by how far to the left or right your coin goes. And believe me, it's not at all difficult to get a perfect vertical toss.
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?
Wow, Taco, about 7 Slashdot readers will even get that. +1, Obscure!
That was a pretty funny book, actually.
Except that it was also a movie that more than a few people have seen. Not really that obscure.
This contributes to the theory that nothing is truely random, but the laws of physics are so complicated that there are things that we just can't understand and appear to be random.
The tosser of a coin is giving it a certain ammount of force that is going to cause it to rotate while it travels up in the air and down to the ground. Given knowledge of the force and angle at which it's applied, and the distance from the thrower's hand to the ground, it might be possible to solve for the result of the toss. However, since it's not so easy to measure that force and run those numbers while the coin is in the air, that's not going to be useful in calling the coin in most situations. Likewise, it's hard to control the throwing motion to make sure there will be a heads or tails result without making the toss look clearly unfair.
Talk about research into the useless...
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
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.
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.
No, you simply failed to understand the study. It wasn't a test of whether a coin could be flipped reproducibly. Yes, they came up with a device to flip a coin reproducibly, but then they looked at the effect of varying the flip parameters like force and angle. The question of whether the coin is biased then boils down to whether the set of values that cause the coin to land same side up is greater than the set that cause it to land same side down.
I'm guessing Persi Diaconis (a Havard educated statistician who has appearantly published a lot of work in statistics [I'm estimating from his site he's published 150 papers on the subject, and no I'm obviously not a statistician]), his wife Susan Holmes, and Richard Montgomery probably had a conversation over a couple of beers at a conference.
They probably didn't get any funding. They're statisticians and probably used to it.
What do you mean my sig is repetitive? What do you mean my sig is repetitive? What do you mean....
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 studied magic, and you can get good at making the coin land on the desired side after a while. You start flipping the coin exactly the same way the same number of rotations. They should have gone to the streets and had randome people flip the coins for them and see if most people's flips have an even number of rotations. They have found a statistical anomoly based on thier own flipping tendencies.
There is a big difference between the deficit and the debt. You do need to cut back spending until the deficit is zero. This does not mean you will stop spending money or even that you will have no debt when your deficit is 0. The deficit is the year-to-year shortage. The debt is the accumulated deficit. You mortgage is like the debt. The deficit is how much money you have to borrow each week to be able to buy everything you want and still afford to buy food.
Imagine every week you had to borrow $100 on your credit card to be able to afford everything you bought. At the end of the year you'd have your mortgage still, and an additional $5200 debt. If you continue to borrow at a greater rate than you earn money you will never get out of debt and your deficit will continue to grow.
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No, that doesnt matter either, I can tell the difference between the head and tail sides of a coin before I take it out of my pocket. I can also flip a coin so that it lands the same way up almost every time.
The easiest way to learn this is to use a "lucky" coin to make simple decisions such as "should I clean the bathroom today ?" you will quickly learn to cheat, even if only subconciously.
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, it would still be 51%-49% one way or the other, because any variance in the consistency of the ground is random.
This is not a sig.
Who said it was government funded?
Lot's of cheap research has been and continues to be done on the researchers own tab, as long as the costs are low enough. If they are genuinely interested in the outcome, who is to say that it's not worthwhile?
Read, L
And because there's always time for 'one more useless fact'...
One might think that the purpose of 'tosser' as an insult is to imply that the person referred to as 'tosser' in fact throws up at a regular basis and therefore either is a pregnant woman or an incompetent drinker.
One could not be farther from the truth... Like most subtle insults in the english language, this particular abuse of the term 'tosser' originates from the east side of the Atlantic Ocean and in fact refers to someone dealing (tossing cards). This movement resembles the act of masturbation, which in the UK apparently is as bad an insult as 'fucker' is in the US.
That has huge impications for one of Austrlia's favourite gambling games, two-up, which is tradionally played (illegally) on Anzac day, and is an game you can legally play in our Casino's casinos.
"We've got a deficit over a half-trillion and things like this are getting funded. Riiiiight."
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I think you might be missing the point here, nobody will right a grant request to determine if a coin flip is fair or not. What is being funded is research into how the geometry of an object changes its motion. Nice toy problems like the coin flip give people an insight into modern mathematics research without requiring a lot of background.
If you think about the coin in terms of first year physics then you just have a point mass moving which is not terribly interesting. By taking into account the shape of the coin you can determine more accuratly the motion of the coin, so accuratly that you can discover it is not totally random. If you use your imagination a little you can see that in a few years these same methods will be used in robotics projects and the space program.
If you use your imagination a lot you might see that they have been used in the past to determine the motion of a falling cat:
http://www.math.ucsc.edu/Faculty/Montgomery
I had a math professor in college who was demonstrating coin-toss probabilities to the class.
He flipped a nickel onto the floor, and it landed... ON ITS EDGE. (There's a classful of witnesses to back him up.) He was known for practicing magic tricks as a hobby, but swears up and down this was pure chance.
I wonder what the probability of this is, and whether it figured into the researchers' coin-flipping calculations?
Weeks of coding saves hours of planning.
Don't you guys do the final flip? Here in .au you flip the coin in the air, catch it, then slap it on the back of your other hand, turning it over in the process... Unless of course it's the cricket, in which case it's too important, and you simply let it fall on the pitch.
Send lawyers, guns, and money!
I've seen magicians who can catch it, determine which side is up in their hand, and choose the result as they slap it on the other hand. Any tossed coin should come to a stop without human intervention, and be called while it's still in the air, by someone who can't see it. (you need a third person to make sure it's actually thrown properly, of course)
you're a fucking moron. ask anyone in the military if they prefer Bill 'draft-dodger' Clinton, or George W. who has given the military pay raise after pay raise since he went into office?
When was the last time you WENT to a fucking funeral? Don't tell me about soldier's funerals. I was at one a few months ago for a friend of mine who was killed in Iraq. Was I sad? Yes. Do I think he died for no reason? Hell no. And neither did he. He knew what he was getting into, and he loved his job. PERIOD.
Believe me, his family is absolutely getting taken care of and I'm joining the Air Force to defend this country, so morons like you can voice your opinions.
Mod me down for being off topic, but these goddamn bleeding heart liberals thing they know everything about everything, when really they just want to stir up trouble.
-jg