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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.""
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
this is not a fascinating new discovery in probability theory, though they make it sound that way. of course when you flip a coin it can be biased if you can influence the number of spins. But after a certain number of spins, it might as well be random since you have less control over it.
move along, move along.
"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.
What they are reporting is that your hand is a biased way to toss the coin. Nothing inherently biased in the coin, but rather in the hand that tosses it. Not that surprising.
I somehow doubt it's that bad to reach 51%, it looks like it's in statistical variation. After all, an early opening chance streak of even 60/40 heads/tails (quite possible) would already skew numbers +20 out of the necessary +100 difference in 10,000 flips they performed. Standard deviation here is 50, so 100 off is well within "natural variation" at 3 sigma.
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.
Doing the Right Thing should not be preempted by making a buck.
Here's the excellent NPR piece, with pics of the gadget they flipped the coins with: NPR.
or, failing that, we have rock-paper-scissors-spock-lizard
"I would say that 99 per cent of what my father has written about his own life is false." - L. Ron Hubbard Jr.
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).
Magicians and charlatans may take advantage of this illusion.
As it happens, Persi Diaconis, one of the statisticians interviewed in this article and presumably one of the discoverers, was a magician.
For example see this brief bio.
Their preliminary data suggest that a coin will land the same way it started about 51 percent of the time. It would take about 10,000 tosses before a casual observer would become aware of such a small bias
;)
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
"I don't know that Atheists should be considered as citizens, nor should they be considered patriots." -George H.W. Bush
I noticed the same thing years ago when I was younger ... if you take a hair brush, you can toss it in the air and watch the revolutions to see why it might work on a mathematical level (obviously it's harder to see coin flips :))
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 original state.
The article also states that the spin can be controlled increasing the odds.
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?
This article was discussed on All Things Considered on NPR last week sometime (probably Wednesday, because it was the night it was pouring in LA).
Given the distances involved, I doubt the weight difference is significant enough. This could be easily verified by using a coin with a larger difference like a Peace dollar or the "Una and the Lion" gold 5. Then a coin with and incused design, like a $5 half eagle could be used as a control coin.
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 on it to make it come up heads or tails fairly consistently.
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.
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...
No, it has nothing to do with weight or center of gravity due to the bread. You can repeat the experiment by marking one side of the bread with a magic marker.
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).
--Xandu
Here's my trick: Flip the coin with a low rate of rotation. It'll take a few hours of practice, but soon you'll be able to catch the coin at a certain height and guarantee (with about 90%) certainty that the side you want is up. The trick is not that it doesn't rotate at all, but that you can determine the height at which the heads or tails will be on top. Try it! It's easier than it sounds.
The other person calls it in the air, that way the tosser can't favor the odds and the caller doesn't see which side it started on.
Drunks. They tip better.
Jiminy Christmas. He's not redundant. It's a failed correction:
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.
There are no trails. There are no trees out here.
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.
Calling 9 out of 10 coins correctly is improbable, but not impossible. To "beat the statistical odds" you would need to run a series of 10 coin runs, and compare it in a chi-square analysis which looks for differences between expected(.5) and actual (.9 in your first trial) outcomes.
imagine your hand was in a sock puppet... like that
"I would say that 99 per cent of what my father has written about his own life is false." - L. Ron Hubbard Jr.
Methinks Galileo said it best :)
There is no single effect in Nature
not even the least that exists,
such that the most ingenious theorists
can ever arrive at a complete understanding of it.
This vain presumption of understanding everything
can have no other basis than never understanding anything.
Perci Diaconis, the main researcher cited in the study, is one of the most respected combinatorialists in math. In fact, in the domain of combinatorics of cards, he is the most prominent researcher in the field. I once heard him introduced as "When you play cards with Perci, technically you're not gambling."
This is not some quack. He's brilliant (and a very entertaining lecturer to boot). You get your PhD in math from Harvard in three years and then you can make fun of him.
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.
This has to do with "moment of inertia". Basically, the mass distribution of an object determines how a spinning motion precesses (the spin axis itself rotates around a different axis - you might think of this as "wobble", like a spinning top does over time).
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 from the front cover to the back (the short axis), or a line from the top center to the bottom center (the long axis). You CANNOT get a stable spin around the middle axis - in the case of a book, this would be the left-to-right axis.
The same holds true for any object - the tennis racket has a long axis (handle thru the tip) which you can spin it about easily, and a short axis (a flat-plate spin), but the middle axis, which is trying to flip it like a pancake-griddle-flip motion, simply WILL NOT STAY STABLE, no matter what you do.
Notice that a bullet (with an obvious long axis) stays pointed in the right direction even though it may spin millions of times before hitting its target. That's why.
The reasons have to do with the mass distribution, so if you have an object with uneven mass it won't be so simple. And it's easist to see with an object with three distinctly different dimensions, like a book or a block of wood. It's not so obvious at first glance with your tennis racket. And it's even more interesting when you get to a cube, where extremely small weight differences are not apparent to the naked eye - try spinning a die (dice) about its face... You'll discover that the "long axis" is really from corner to corner, so you can easily spin a die on a corner, but if you toss it in the air you won't be able to spin it about a face.
I don't recall the details offhand, as it has to do with rotational inertia and momentum and so forth, but essentially, when you try to flip something about the middle axis, the weight at the ends of the long axis wants to move outwards, and this disrupts the stable spin. This is easily and 100% repeatably demonstrated. Just another good science fact to get your kids interested in the natural world.
--Brandon / Split Infinity Music
you can't know for sure what yours is or his so looking at yours gives you enough of a advantage that it might help
But looking at yours doesn't change what his is, so looking doesn't give you any advantage at all.
I have misplaced my pants.
>> 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
We have another variant we play, although mostly under the influence of alcohol.
:)).
rock-paper-scissors-satan-penis
Satan is the typical heavy-metal "beast" sign. And penis is index finger pointed slurpishly downwards (as opposed to being erect
Because:
Nothing beats the Satan, except unerect penis.
Penis is always wrong, but whoops Satan.
Rock, paper and scissors follow the usual set of rules.
I admit, it's not the most clever enhancement for rps, atleast not at first glance, but as I said, it's a barrel of laughs under the influence and has solved many disputes over the years.
Moreover, this aswell as the usual RPS is best played with 3 or 4 players and with both hands. Before the game you pick the amount of losses it takes to loose the entire game. Say 10ish or more for 3 guys with both hands. Then you count the losses for each hand separately. Great game!
1 Earth is warming, 2 It's us, 3 it's royally bad, 4 we need to take action NOW
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 call that boiling it down? I consider this idiotic, how the hell do they from first principles come up with a statistical distribution of the starting "set of parameters" for human coin flipping that in any way is defensible?
The claimed conclusion is that, based on both a mathematical analysis and an experimental test is that most values favor the face that is up to begin with. As to the details of the statistical distributions they assumed, you aren't going to find that in a general report in the popular media--you'll probably need to delve into the details of their mathematical and experimental models. But it is certainly a plausible claim. Simply from the fact that people commonly flip coins to make randomized decisions, one already knows that parameters that result in "heads" vs. "tails" outcome have to densely interleaved. This means that the result is very likely to be independent of the details of the statistical distribution that you assume for things like the magnitude, angle, and timing of the initial vector of force applied to the coin.
Even a study of 100,000 flips. It will not come out 50/50 of course. Some people...... Anyone agree with me here?
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.
Insightful? You mods must all be American. This is why the US cannot manage it's economy.
Debt is how much you owe. A deficit is the amount each period (year) you are going further into debt.
If you have a mortgage you have a debt. But since you are paying off the mortgage each month you are getting a little bit less in debt. So you do not have any kind of deficit. It will take you a long time to pay off that mortgage, but it's entirely possible to pay it off without changing your spending habits.
If you have a deficit, like many first world countries do today you are completely screwed. The debt is already huge but get this: EVERY YEAR WE MAKE IT BIGGER. Without a serious change in spending habits these countries will NEVER be able to pay off their debts, let alone reduce them.
Do you understand the difference? If you don't, try running for office. The US needs can always use a few more politicians who don't understand why this is bad.
Be happy. Nothing else matters.
Bush not only doesn't attend, he doesn't even allow the funerals to be mentioned by the media.
1. If he did attend a funeral, I am damn sure he would be accused of grandstanding.
2. Your second point is B.S. You may be thinking of the rules developed during the Clinton administration regarding limiting press access to off-loaded caskets. This has nothing to do with funerals being "mentioned by the media," nor does it preclude families from inviting the press to a funeral if they so desire.
Evil is the money of root.