Science of the coin-toss: Bias in Heads-or-Tails 559
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.""
well... one way to solve it (Score:5, Funny)
tails they're right.
Re:well... one way to solve it (Score:5, Funny)
Re:well... one way to solve it (Score:3, Funny)
Re:Tax dollars at work, one coin at a time (Score:5, Funny)
Re:Tax dollars at work, one coin at a time (Score:5, Funny)
> 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 !
Re:Tax dollars at work, one coin at a time (Score:5, Funny)
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"
Re:Tax dollars at work, one coin at a time (Score:3, Insightful)
Is that true?
Or do you include coming home dead as coming home?
I mean, I would take Bill of any Bush any year, but I find it a little unlikely that no soldier died during duty during Clinton's stretch...
Re:Tax dollars at work, one coin at a time (Score:5, Insightful)
Re:Tax dollars at work, one coin at a time (Score:5, Funny)
Bill produces movies ?
Re:Tax dollars at work, one coin at a time (Score:4, Insightful)
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
Re:Tax dollars at work, one coin at a time (Score:5, Insightful)
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?
Re:Tax dollars at work, one coin at a time (Score:3, Interesting)
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.
Re:Tax dollars at work, one coin at a time (Score:4, Funny)
Then the coin was showing both heads and tails until you resolved it by looking at it.
Re:Tax dollars at work, one coin at a time (Score:5, Funny)
Research materials budget - 0.01 $
Re:Tax dollars at work, one coin at a time (Score:4, Funny)
For Sale: Unique Gambling Penny
Scientifically proven to land on tails 59.439% of the time!*
(*Special throwing instructions included.)
Re:Tax dollars at work, one coin at a time (Score:5, Insightful)
Thousands of children die every day, yet things like faster semiconductors are getting funded. Riiiiight.
Re:Tax dollars at work, one coin at a time (Score:5, Funny)
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.
Re:Tax dollars at work, one coin at a time (Score:3, Interesting)
Imagine every week you had to borrow $100 o
Re:well... one way to solve it (Score:3, Funny)
Heads their right.
Tails you're wrong.
Re:well... one way to solve it (Score:3, Informative)
Neither of you can get the damn joke right?
Heads I win.
Tails you lose.
If I call that, way no matter what the toss is, I win. Ok, ok maybe "joke" is an overstatement.
Re:well... one way to solve it (Score:5, Funny)
Heads: Gonna get me some head
Tails: Gonna get me some tail
So either way you win. I don't get it, though, since everytime I try this, the coin lands on its edge. Seriously, what are the odds of that?
Re:well... one way to solve it (Score:5, Informative)
Nope. You missed two points, one made in the article, another about statistics.
1) Their argument is not about differential face/tail weight. Their argument is about the likelihood of the coin to flip at all. They make the point that over a surprisingly large RANGE of initial flipping forces, the coin fails to flip...even though it appears to flip in the air to the casual observer. It's actually precessing. This means that, given a flip force chosen randomly from the set of flip forces a person can apply, there's a slight bias that the coin will not actually flip.
2) It doesn't matter that even over many, many trials the count is not exactly 50-50. As you point out, you don't actually expect that even with a fair a coin you will get exactly 50-50 results on a single run. However, you do expect that the variance from 50-50 is normal and unbiased, and dependent on the number of trials you have. You can use inferential statistics to determine if the distribution of non-50/50 results you get after repeated experiments is more or less than the variance predicted by chance. I won't get into how, but apparently their measured bias is reliable.
Thank God we still have (Score:5, Funny)
-fren
Re:Thank God we still have (Score:5, Funny)
Re:Thank God we still have (Score:5, Funny)
Re:Thank God we still have (Score:4, Funny)
Re:Thank God we still have (Score:5, Informative)
Re:Thank God we still have (Score:3, Informative)
Re:Thank God we still have (Score:3, Funny)
Oh Darn... (Score:5, Funny)
Re:Oh Darn... (Score:3, Funny)
Re:Penny Arcade (Score:3, Funny)
Re:Oh Darn... (Score:5, Interesting)
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.
Re:Oh Darn... (Score:3, Funny)
True random number generators (Score:3, Informative)
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
From the article (Score:5, Funny)
I wonder what their margin of error was.
Re:From the article (Score:4, Funny)
("What does that even mean?" "Quiet, brain.")
Let it hit the ground... (Score:5, Informative)
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.
Re:Let it hit the ground... (Score:5, Funny)
Re:Let it hit the ground... (Score:4, Funny)
I don't think that helps (Score:3, Interesting)
Re:I don't think that helps (Score:3, Insightful)
Re:Let it hit the ground... (Score:5, Funny)
Look, referees have a hard enough time as it is, without you throwing in needless insults.
Don't know if that actually works though.... (Score:4, Insightful)
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.
Re: Making a fair toss with unfair coins (Score:3, Interesting)
Interesting, but .... (Score:3, Funny)
Re:Interesting, but .... (Score:5, Funny)
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.
Butter-side down (Score:5, Interesting)
Re:Butter-side down (Score:3, Funny)
Re:Butter-side down (Score:3, Funny)
You must be rather singy with the butter. I can drop it from any height, and it'll land butter side down. ;)
Re:Butter-side down (Score:4, Informative)
The reason bread usually lands butter side down has to do with how it falls off a counter. People don't drop bread, it slides off the counter (or plate, or what have you) and people usually have their bread butter side up on the countertop. As it slides off, it rotates, as half of the slice doesn't have a countertop holding it up. Given standard countertop heights and standard bread thickness, the bread has time to rotate 1/2 turn before it hits the ground. Raise or lower the countertop (below about 1' it won't even make 1/2 rotation or above about 10' it'll do a whole rotation) or get thiner or thicker bread (really thin bread, like extra thin rye, or super thick bread, like about a whole loaf).
Re:Butter-side down (Score:5, Interesting)
Scientific American actually crunched the numbers on this issue a couple years ago for a piece on Murphy's Law. Turns out the universe is out to get you.
Considering the case of a slice of bread slipping off the counter top, it will begin to rotate at that point the center of gravity is off of the counter. Presuming a fall from rest and you're not spiking your bread, the rate of fall and rotation are determined by gravity.
Your main variable is this case is the height of the counter top. Although it turns out this height is constrained to a narrow range of comfort determined by human physiology.
Now take this argument to the general case of an arbitrary bipedal on an arbitrary planet. The most probable height of humanoid-type life is a function of gravity on the home world. Planets with weaker gravity make it easier to grow taller people; conversely planets with stronger gravity will tend to produce shorter people.
The taller beings have higher counter tops, but the weaker gravity will cause their bread to rotate slower than our earth-bound bread. Turns out their counter tops will also be at a height destined to produce butter-down drops.
Same for the munchkins on the planet with stronger than earth gravity. Their bread will rotate fast enough to make it around to butter-side-down when falling from their munchkin-height counter tops.
So yes, the fundamental laws governing the universe are designed to ruin your breakfast. Look on the bright side, it's not just you--the universe is out to get everyone.
This is interesting... (Score:5, Interesting)
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!
What do you mean always? (Score:4, Funny)
OMG! (Score:5, Interesting)
80,000 geeks tossing at home now! (Score:4, Funny)
Of course there's a bias (Score:5, Funny)
Heads 49.9%
Tails 49.9%
Coin becomes
Self-aware 00.2%
Re:Of course there's a bias (Score:3, Funny)
> Self-aware 00.2%
Dammit, please don't make my next game of Galaga into a Prime Directive issue.
yay! (Score:3, Funny)
step two: bet on coin flipping
step three: PROFIT!
wait, that makes too much sense.
dang
Heads Again! (Score:5, Funny)
Nice Department, Taco (Score:5, Informative)
Wow, Taco, about 7 Slashdot readers will even get that. +1, Obscure!
That was a pretty funny book, actually.
Re:Nice Department, Taco (Score:4, Informative)
Re:Nice Department, Taco (Score:4, Interesting)
That was a pretty funny book, actually.
Except that it was also a movie [imdb.com] that more than a few people have seen. Not really that obscure.
Re:Nice Department, Taco (Score:5, Informative)
Um. Wasn't it a play?
Expressing my doubts (Score:3, Informative)
Well, if it all comes down to it, the impact of a coin on the ground should provide enough random bounce to negate all systemic bias.
Depends upon the coin... (Score:5, Interesting)
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... ]
Needs more testing... (Score:4, Funny)
Crap science (Score:5, Insightful)
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.
Re:Crap science (Score:3, Interesting)
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
NPR (Score:5, Informative)
Comments from someone who's been studying this (Score:5, Interesting)
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.
Re:Comments from someone who's been studying this (Score:4, Insightful)
Re:Comments from someone who's been studying this (Score:4, Informative)
When you catch the coin, feel it with your finger. If it is right-side-up, just open your hand. Otherwise, slam it down on your opposite wrist, which flips it over. Takes some practice to become smooth at it, but it works very well, especially if you can keep your audience's attention on your face while you're doing it.
Re:Comments from someone who's been studying this (Score:3, Interesting)
And then pendersempai foolishly responded:
pendersempai, I think those are Templar Knights knocking at your door...
--Rob
I'm also a kind of magician/charlatan (Score:4, Funny)
Additionally (Score:5, Interesting)
Most Interesting Part of the Article (Score:3, Interesting)
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?
Law School (Score:5, Funny)
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 say bollocks (Score:5, Insightful)
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.
This is supposed to be some amazing new result? (Score:5, Informative)
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?
Is anything truely random? (Score:3, Interesting)
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...
Re:Is anything truely random? (Score:3, Insightful)
1) No pattern, purpose or objective.
A coin flip is NOT random, modern physics can describe it down to the quantum level.
2) Described by a probability curve.
A coin flip IS random, i.e. 51/49 probability dictribution.
3) All outcomes equally likely.
A coin flip is NOT random, as it's not exactly 50/50
I think that people use the word "random" a lot, when they mean "unpredictable". Specifi
Avoiding bias (Score:5, Interesting)
- 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.
Re:Avoiding bias (Score:5, Informative)
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.
Um, no. If you want to use von Neumann's procedure, you should flip it twice under the same conditions. Your suggestion would bias the sequence towards TH, which counts as tails.
Vegas (Score:3, Funny)
I'd post a longer comment but I'm heading to Vegas
2,000,000 flips says... (Score:4, Interesting)
Gambling (Score:3, Interesting)
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.
Start on the side? (Score:4, Insightful)
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)....
A useful skill (Score:4, Interesting)
geeks don't toss coins (Score:4, Funny)
Re:so... (Score:3, Funny)
Re:so... (Score:5, Interesting)
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!
Re:Mmm-hmm. (Score:4, Insightful)
Re:Mmm-hmm. (Score:3, Informative)
Toss by the handle, catch by the handle. If you give it the right flick of the wrist, the handle lands right in your hand. Subconsciously, the way we flip and catch the coin may influence the outcome by causing us to catch it at the exact point in the arc that it returns to its o
Re:Mmm-hmm. (Score:5, Informative)
Re:rubbish (Score:4, Interesting)
Re:Large number of trials... (Score:3, Informative)
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
Re:The most interesting question is.... (Score:3, Informative)
What they mean is probably that you have to do 10000 tosses before the bias manifests itself into something that is statistically significant...
I'm pretty confident that a casual observer would fall asleep long before 10,000 tosses without noticing anything
Re:subtle weight difference (Score:3, Informative)
To remove the human bias, a machanical device that puts a consistent amount of spin on each flip could be used. This is important; with enough practice a person can flip a coin with the right number of spins
Re:tennis racket (Score:3, Informative)
Try it with a rectangular block of wood. You'll find the following simple fact to be true: you can create a sustained, non-wobbling rotation ONLY about the longest and the shortest axis. For a book shaped object, this would be either around a line thru