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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.
can I call it as whatever I started on after I flip it? ;-)
Programming is simply the application of logic to creativity
rock-paper-scissors to settle the disputes of mankind. And drunken boxing.
-fren
"Where are we going, and why am I in this handbasket?"
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.'
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
Except in Madden 2004. Then it's the opposite.
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
So does this affect the deviation from the expected outcome for a large number of trials? Is flipping a coin (the epitomee of probability experiments) no longer a memoryless trial? Ugh, Markov chains... **shudder**
-- n
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.
Back to One Potato, Two Potato. Well all know that is more accurate anyway.
Surely coins randomness in values and the reason they make the best 1 out of 2 decision as it were, is because of these small variables, not many of which are under human control, to bring out a "good" result. This study has also been done by a statistician. Personally, a statistician talking about the requirement of Super-human strength to do a task, does not convince me as much as, say a Biologist. If we wanted to know really, we would need an expert panel from many fields. But then again, who cares?
tim
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
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...
i'll finally be able to to be CT first in de_aztec :)
Wait.. that's how SCO is deciding who there gonna sue.
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.
My coin has heads on both sides. Of course it lands the same face it starts on. Duh
Free XBox, PS2
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.
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.
... and see if they nearly always end up with the side you flicked face up.
Seems to work at least 7 times out of 10. Makes for a fun bet on the unsuspecting ;)
I've been demonstrating this stchick coin toss hoax for years. I would flip a coin and make it land heads 100 times in a row. It was a stupid trick but I would perform it when people say that coin tosses are fair. I had fond memories of upsetting two brainiacs back in HS with this.
I never can catch the damn thing because I'm too clumsy, so it rolls around the floor a few times before resting on a side. Do that, and guaranteed random results. Especially if you have uneven hardwood floors like me!
Bored? Why not join a decent mess
I guess thats why I always loose at coin tosses. And I always thought the coin just hated me or something.
Whenever I flip a coin, it tends to land on the side it did not start on. Without the after flip-on-to-the-arm that is.
at least when I was flipping. Fortunately, most people I know don't know how to flip a coin properly, or never have quarters on them.
I bet Rosencrantz is pissed to find this out!
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
...how on earth did they quantify that "10,000 tosses" number? Methinks they might have pulled that number out of thin air.
What does this mean for...any number of things? If the coin toss is no longer a theoretically valid randomizer (or at least a completely unbiased one), what's going to happen to, for instance, the NFL? That whole initial coin toss thing kinda goes out the window, I guess.
But don't ask me, I'm not a football guy.
I have discovered a truly marvelous
"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.
You may toss.
Heads: I win.
Tails: You lose.
Nice and simple.
We suffer more in our imagination than in reality. - Seneca
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.
:-(
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.
Who flipped the same penny a million times or something and found out that due to the physical nature of the penny, it is more likely to land on Heads?
Or is that story even real?
Should I stop regurgitating stories that I heard when I was 12?
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.
Yes because with RSP we can determine which side the coin should start out on! It doesn't get any more fair than this!
Enig? Det alt for hot det smor!
Worth listening to, if for nothing else than the very cartoony sound of the coing flipping machine... Link.
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..
Only for the wealthy, but is dropping a banknote end on and letting it "fall" to the floor biased? (it could flop either way). I suppose this may have the disadvantage of being tracked by the government or exploding though, if you use a $20 anyway.
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.
Does the difference between 50 and 51% really matter? Especially if it only becomes apparent after 10,000 flips. I would say it is close enough to "even" as to not matter. Especially given the situations most people use the coin toss for. "Wendy's or BK?"
IMHO I think the results show less of a bias for actual coins and more of a bias for human motor skills involved in flipping the coin.
Maybe rather than spending you time coming up with droll little cleverisms to pick up a few +1 funnies you can perform a public service and tell me how I can apply this to roulette during my trip to Reno this weekend. Should I go and start betting on whatever color was on the wheel when I arrived? And what exactly counts as arriving? when I walk into the casino? when I first spot the table? when I first place the bet? It's going to be nice to be filthy, filthy, filthy rich.
...and who are you going to believe? A few crackpot 'scientists', or the millions of 5th grade Science Fair projects which have already conclusively shown that the odds are split 50/50, right down the middle? I tell you, ten million grade schoolers can't be wrong!
There goes my "randomly" generated PGP key. @%*&!
I also reply below your current threshold.
drop the coin edge first. It won't stop on the edge and should take a number of random(?) bounces.
Here's the excellent NPR piece, with pics of the gadget they flipped the coins with: NPR.
"During World War II, South African mathematician John Kerrich carried out 10,000 coin tosses while interned in a German prison camp. However, he didn't record which side the coin started on, so he couldn't have discovered the kind of bias the new analysis brings out."
I wonder how many geeks they put in jail to come up with the results in this paper...
Let the teams choose heads or tails. Then put the coin on the referee's hand and flip it. Since neither of the teams know, which side it started on, the result will be completely random to them.
Basically, to take advantage of this coin toss, either side would have to know if, beginning the flip, heads or tails was down. If they don't the bias isn't relevant.
At least that's what I would think. IANAM (I Am Not A Mathematician.)
I let my Magic 8-Ball make my decisions.
It it more useful than a coin toss?
"Yes Definitely"
See?
The problem with socialism is that they always run out of other people's money. - Margaret Thatcher
Great, at this moment, a half million geeks are sitting at their desks flipping quarters nonstop to check it out.
Articles like this are planted by MS into /. to preoccupy our minds and divert our attention.
Now if I can just get the theme from 'My Favorite Martian' that hit me from the previous article out of my head. Then I'd be able to concentrate on stopping flipping this quarter.
I used to have a good sig...
It's interesting to hear other cultures do coin flips whereas their coins have different sides.
Some have hand and flag.
Some have queen and king.
Some have religous symbols and the pope.
Some have head and saddam.
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.
An old-style 10p piece would land on the opposite side from where it started about 90% of the time, if it was caught in the hand, rather than dropped on the floor.
:)
I won a large number of coin tosses based on that fact
did you have to say "new math"? I have three oranges, and you take two away. How many do I have now? Three, because you better gimme back my damn oranges.
Lycestra
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.
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.
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?
IIUC, there's more "stuff" on the heads side of a coin. (The head is a large surface, the tails usually have more of the coin "removed" so to speak.) So if you were to draw a line down the middle, the heads side would have more material, and is thus heavier, ending face down slightly more often.
You cannot apply a technological solution to a sociological problem. (Edwards' Law)
Any mathematical theory that attempts to predict such behaviour is guesswork at best and will inevitably be rendered useless by a butterfly flapping its wings in China.
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
What if it lands on it's edge?
Hate me!
using the massive parallelism of /., we can test this.
tuck your thumb under your index finger, place a quarter on your thumb heads up, and flip the coin into the air. be sure to get the initial conditions right (quarter, heads up). let it land on the floor.
message me with an H or T indicating whether it landed heads or tails. i'll tally as many msgs as i can and will post the results in a day or so.
As an interesting aside, there is a very strong statistician by the name Persi Diaconis, formerly a circus performer and magician, who got tired of it and went to get a degree at Harvard (!!) instead.
He's very interested in this kind of work and spends a lot of time debunking psychics and "ESP research", as well as analysing games of so-called chance.
Anyway, the subpoint is that he can usually manage to flip a coin 10 times in sequence in his favor! That is, heads or tails or whatever he wants. The point then is that we are asking, mathematically, "how hard is this?"; i.e., how much can the initial conditions influence the outcome of a coin toss. This is interesting to me, at least.
And to all of the nay-sayers out there, this seems to be a very interesting problem in dynamics. "How hard is it to control the outcome of a coin flip?" isn't all that different from "How hard is it to land (x) on the surface of (y)?" Except that it's easier to study and, thus, gain insight from. Recall, the field of probability theory began in the 1600s (?) with LaPlace et al. studying games of chance. In around three centuries, it became the basis for at least two "paradigm shifts" in physics.
Further, if you stop to think about why the coin lands _on the same side it starts on_, as opposed to, say, usually landing on heads (the heavier side), you'll have a bit of a hard time answering that question convincingly. At least I do.
You don't get the benefit of this if you can't see what face the coin started on. Coin toss win/lose ratio: still 50/50. Pick the right coin face.
Now if someone did some research about how many times a coin was pulled from someone's pocket coming up heads, now THAT's where the money (!) is. Sorry for the bad pun.
-- Having a Creationist Museum is like having an Atheist place of worship
How do they explain it in other universes when, for example, it always lands on heads? (Insert Futurama references here). Or a universe where the coin always lands on its edge, but everything else is just like our universe?
As info, I agree with others who said it's the tosser who's bias is showing here, not the coin (who's heavier heads side may impact it slightly).
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I slept with your wife.
I only flip it to the other hand if it doesn't land on the side I want.
paintball
One more crippling bombshell hit the already beleaguered Coin Tossing community when Science News confirmed that Coin Tossing reliability has dropped yet again, now down to less than a fraction of 1 percent reliability out of all random number generations. Coming on the heels of over 100,000 coin tossings which plainly state that Coin Tossing has lost reliability, this news serves to reinforce what we've known all along. Coin Tossing is collapsing in complete disarray, as fittingly exemplified by failing dead last in the recent random number generation competition and pole vault.
You need to be a mathemetician to predict Coin Tossing's future. The hand writing is on the wall: Coin Tossing faces a bleak future. In fact there won't be any future at all for Coin Tossing because Coin Tossing is dying. Things are looking very bad for Coin Tossing. As many of us are already aware, Coin Tossing continues to lose reliability. Spare change flows like a river of blood.
Football Coin Tossing is the most endangered of them all, having lost 93% of its core supporters, including the Miami Dolphins and the Greenbay Packers. The sudden and unpleasant departures of long time coin tossers only serve to underscore the point more clearly. There can no longer be any doubt: Football Coin Tossing is dying.
Let's keep to the facts and look at the numbers.
Coin Tossing proponent Bob states that there are 70000000 users of Coin Tossing, and that 35000001 come out heads the majority of the time. How many users of /dev/rand are there? Let's see. The number of Coin Tossing versus /dev/rand posts on Usenet is roughly in ratio of 2000 to 1. Therefore there are about 70000000/2000 = 35000 /dev/rand users. Coin Tossing posts on Usenet are about a millionth of the volume of computer-related random number generation posts. Still, there are about 70000000 users of Coin Tossing. A recent article put quarters at about 80 percent of the Coin Tossing market. Therefore there are 60000000 quarter users. This is inconsistent with the number of quarter tossing Usenet posts, so we assume that coin tossing is way overexaggerated. Studies also show that an astounding 35% of all coin tosses come out undecided, usually from dropping the coin. 2% of all coins tossed are lost and never found again.
Due to the troubles of spare change, abysmal toss-failures and so on, quarter tossing went out of business and was taken over by nickel tossing, which sells another troubled method of random number generation. Now nickel tossing is also dead, its corpse turned over to yet another charnel house.
All major surveys show that Coin Tossing has steadily declined in reliability. Coin Tossing is very sick and its long term survival prospects are very dim. If Coin Tossing is to survive at all it will be among Coin Tossing dilettante dabblers. Coin Tossing continues to decay. Nothing short of a miracle could save it at this point in time. For all practical purposes, Coin Tossing is dead.
Fact: Coin Tossing is dying
(1) look ay coin
(2) place bet
(3) flip coin
(4) not applicable
(5) profit
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.
Maybe it depends on which coin you are flipping? Did they compare the behaviour of US coins, Canadian coins and European coins, for example? I didn't see anything like that in the article.
The Tao of math: The numbers you can count are not the real numbers.
as in, if you have it in your palm, heads up, and then flip, it will usually land heads up?
Strictly speaking, you don't even need to flip it if you use this technique.
Patrick Doyle
I mod down every jackass who puts his moderation policy in his sig. Oh, wait a sec....
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?
To see what I'm talking about take a racket, hold it flat by the handle, and just flip it up and catch it by the handle. You'll see at one point it's vertical. Try to get it flip while remaining horizontal. I was never able to do this. It always went straight up, turned what appeared to be 180 degrees, and then came right back down.
Any physics geek care to explain?
My Linux Command of the Day site : LCOD
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.
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...
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).
Hmmm. Hell I figured that out in an "i am curious" experiment when I was 12. How much money did they spend on the study? I should apply for a few science grants.
Besides the fact that neither college is government funded in any significant way, the last thing I would think we should cut is education spending to save the deficit.
And I know I shouldn't feed the trolls.
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)
...my girlfriend is most likely to return to the same face she started on during an orgy?
Due to the nature of thihgs, you can toss a coin till end of time and never get 50/50, but I bet if they kept repeating this experiment they would see their numbers change and swing to the other side.
Another example of wasted government grants.
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'd post a longer comment but I'm heading to Vegas
an ill wind that blows no good
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
This knowledge has been around a lot longer than most people realize. I remember hearing about this effect as a kid in the 1960s and it was "old knowledge" then. If you did a coin toss, you shook the coin in your hands before flipping it such that which side was up when you initially flipped the coin was random and the trick was to not disclose which side was up at the time it was flipped.
Also, you were actually lucky that it worked as well as it did with a quarter. One of the other things that can effect the outcome is whether the coin is serrated on the edge or not. Dimes, quarters, half-dollars, etc. are serrated and the effect isn't as pronounced. Pennies and nickels are not serrated and will more frequently follow the how it starts is how it ends up bias.
They that can give up essential liberty to obtain a little temporary safety deserve neither safety nor liberty.
Ben
Somehow I doubt this was the most expensive experiment ever...
Research materials budget - 0.01 $
I actually did a paper on this for my grade school math class. I was a bit of a smartass, and I insisted that because of the physics of it, one side was more likely to come up than the other ;)
From what I read about it, there's good scientific basis for this. Apparently having more weight facing down stabalizes the rotation of the coin, slowing it down, making it a bit more possible that it'll come up on one side. Now it's not much different, maybe 5% if that...
It also depends on if you catch and flip or let it hit the ground. From what I can tell, if you let it hit the ground it has more effect than catching and flipping. (The slower you allow the rotation to get the more the weight difference has an effect it seems).
At my school? They stopped talking about probability as it comes to coins, and took other random factors.
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.
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.
I read about the coin toss not being 1:1 years ago.
It shouldn't be shocking... The concept of a coin toss was always a mathematical idealization. Of course when contextualized in physical space it has a bias. It's the reason that there is such a thing as history. Anyone who thought a coin toss had equal odds was making a category mistake.
After you flip the coin and it lands in your palm, glance briefly at the coin. It helps if you hold up your fingers to block your opponent's view of the coin.
If the coin in your hand favors your opponent's call, continue to slap the coin on your other hand's wrist, so when you reveal the coin you win.
If the coin favors your call, open your hand and show your opponent you just won, without the wrist-slap to flip over the coin.
...because these scientists are useless tossers.
Since only two stanford researchers tossed the coin their experiment is intrinsically biased. Unbiased statistical analysis would require hundreds of stanford statistitians to toss the coin...
>
I don't know wether the article or the researcher is talking nonsense. But this makes no sense.
The article starts out stating:
A new mathematical analysis suggests that coin tossing is inherently biased
And somewhere later it states:
In experiments, the researchers were surprised...
So what is it? Mathematical or experimental proof?
The hand waiving explanation in paragrahs 6 through seven is not very convincing, one could also argue that the tilting of the axis is an inherent part of the randomness of the toss.
I'm gonna clean up now at the coin-toss tables!
Unless they start implementing covering the coin-toss dealer's hand before flipping.
I think downtown Vegas has total view coin-toss tables though along with the 3 deck Blackjack shoes.
"Music is everybody's possession. It's only publishers who think that people own it." - John Lennon.
Did they get their quarter at a discount? Where I am from a quarter costs $0.25.
Butter the bottom! That way when it falls it's 1/2 rotation..oh nevermind.
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
Now I have to go regenerate my PGP passphrase. Anybody have a 16-sided die?
TZ
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. --
http://noosphere.princeton.edu/terror.html Kind of spooky.
What people are missing out on here is that you can reintroduce randomness by not knowing what state the coin was flipped from. Assuming you pulled the coin out of a chaotic place like your pocket (and not out of something organized like a roll of coins fresh off the mint), the state is already randomized.
But then... why are you even flipping it?
Does anyone know if there is a bias to horizontal spin. Spinning the coin with its side on a flat surface works more-or-less as well as a coin-flip, and it's probably fairly random as to which side it finally settles on when it loses momentum.
And the second amazing thing is that, so far, in the first hour after this story was posted, there were over 225 posts. (Posting this observation was the ONLY way I could think of as having anything to say. Relatively, anyway.) Was that research led by a guy named Shroedinger?
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....
Of course, the solution to this is simple.
Flip the coin, but don't look at it. As it hasn't been observed, the probability function has not collapsed, and thus the upper face is BOTH Heads AND Tails.
Better still, tie the coin to a cat and flip the cat into a box containing poisonous gas. You still won't know what the outcome is, but at least there will be one less cat in the world.
Norman Cook's Ode to Sl
Let the damn coin fall! The chaos of the ground below will result in perfect randomness. The coin may flip or it may not, and if it does it will flip with different speeds along a random axis.
If I wanted easy I wouldnt be an engineer or a patriot.
CAn'T CompreHend SARcaSm?
Looks like I'll have to find a new way to make those all-important, life-changing decisions.
Once a coin is flipped and then covered so that the outcome is not revealed the coin is in both states*. Heads or tails.
Of course I 'll leave it up to the astute reader to determine if heads means the cat dies or if tails does.
-- Robert
* of course if you are standing on the border facing north between California and Nevada it also depends if you are left or right handed to determine which state it lands.
Bet this
then catch. The coin is then turned onto the back of the other hand. I would always call oposite to what was showing before it was initially flipped. I seemed to win more than lose.
photosMy Photostream
shit. now how am I supposed to choose my response reliably to a slashdot poll?
Depends on the coin. I believe with US coinage there is a slight edge to the tails side, as the heads side is heavier. So, if you frequently bet money on coin tosses, consistantly calling tails will earn you a little money.
common sense: noun
What those who are ignorant of the subject matter think; usually wrong.
"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"
In other words: don't run off to Vegas and bet your life savings on coin tossing.
SIG: TAKE OFF EVERY 'CAPTAIN'!!
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.
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.
In football games (at least in the NFL), they call it in the air.
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"
-nod- Clinton had a few misadventures in bombing to his name, this is true. I don't necessarily think any of his were on the same scale as Bush's Iraq adventure, though. And at least Bill never sent a troop into battle who didn't come home to his or her family.
25% Funny, 25% Insightful, 25% Informative, 25% Troll
Thousands of children die every day, yet things like faster semiconductors are getting funded. Riiiiight.
Unlimited growth == Cancer.
No mechanical random number generator is perfectly uniform.
Vote for Pedro
BULLSHIT!!!
Well, any science that changes the outcome of our sports events....
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.
During World War II, South African mathematician John Kerrich carried out 10,000 coin tosses while interned in a German prison camp. However, he didn't record which side the coin started on, so he couldn't have discovered the kind of bias the new analysis brings out.
Ever seen the movie "Black Hawk Down"? Bill did that.
Start it on the other one then. Of course, that will only work in the northern hemisphere.
Confucius say, "Find worm in apple - bad. Find half a worm - worse."
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.
Open a casino.
Rank Presidents by th
You are incorrect on this statement. Bush does not use a coin on complex decisions of this gravity. It show a total lack of politcal acumen to even suggest such a thing. First he must have his advisors input, by viture of this the EINY, MEINY or Rock, Paper, Scissors methodology of the forgien policy decision making tree. For example, The Iraq War had three proponents. Chaney, Rumsfeld, and Powell. In studing each persons initial, mind you initial, public position, it is obvious the EINY, MEINY method was used as Powell was out goes Y O U. So please give our government its due for having a more educated matrix of decision making.
in deed.
> Ever seen the movie "Black Hawk Down"? Bill did that.
Bill produces movies ?
25% Funny, 25% Insightful, 25% Informative, 25% Troll
people are starting to forget that IN A BATTLE, PEOPLE DIE. That's how it works. Some soldiers do not come home and that's just how it works. It is plain stupid to expect that everyone or nearly everyone will come out of it ok.
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.
Buttered toast plus cat is something that the Ed-boys might think up. But in our universe, the cat would win purely on account of more mass.
And at least Bill never sent a troop into battle who didn't come home to his or her family.
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...
Working toward a usable PDA environment in the spirit of Newton OS: Dynapad
Now let's see the data. And then the independent replication. Is there a National Institute of Stochastic Processes where I can apply for a grant? Yes, I know what that means to my chances of getting it; I think most places award grants based on some randomized process.
"I may be synthetic, but I'm not stupid." -- Bishop 341-B
wow. This kind of research will surely result in his tenure. What's next for this guy? Simply amazing.
It's insane. Apparently it's okay for one guy to use the U.S. Military for his personal prestige, but not to improve national (and global) security. Idiots!
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.
Need a website host? Try out http://WebQualityHost.net
I'd like to see the Superbowl start off with a spirited R-P-S, with close-up camera catching the action.
It's only funny until someone gets hurt. Then, it's hilarious.
What are the chances that tossing a coin 100 times would give 50% heads?
I remember in primary school we were asked to conduct this "experiment" (I put experiment in quotes because I suspect it was just a way of keeping us busy for a while, like most other things you're asked to do at primary school). We included any throws where we failed to catch the coin and had it accidentally land on the floor. Astonishingly the results were exactly 50 times heads and 50 times tails. Our teacher didn't believe us.
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.
Long time ago, a friend and I did a coin toss to determine what movie to get. Heads and tails were both movies I wanted to see; edge was his choice. (He wasn't very assertive.) Flipped the coin, it hit the ground and rolled up against the bottom of the shelf, on its edge.
I then called best 2 out of 3.
What are the odds of two consecutive front-page Slashdot stories each reporting research by one of two different scientists, both named "Keller"?
--
make install -not war
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".
My high school statistics class flipped 100,000 coins and we discovered no statistically significant variance from an hypothesis of even probabilities. We should have easily seen an effect as large as this.
I have discovered a truly marvelous sig, unfortunately the sig limit is too small to contain i
Well, as much as I agree with you (and I do) I think the parent still has a point. Semiconductors actually have a meaning and a use. If you stop building semiconductors, a whole part of the economy is going to die, and not a small one. Flip-coin toss analysis on the other hand, has a very minimal added value, to say the least.
Write boring code, not shiny code!
Tech support guy: Heads, we give him a real answer, tails, we make up something.
Tech support gal: Why bother flipping a coin. We Indians can influence a coin toss at will.
Tech support guy: Oh yeah... screw it then, lets give him the made up answer.
Well duh! I've been using this method to win bets for over a decade!
The ref will simply state, "I am thinking of a number between 1 and 10, please guess a number."
This will eliminate all potential unfairness of the coin toss.
In other news, I'm thinking of becoming a coin toss referee... I believe I stand to make a good deal of money with the new legislation.
"You should always go to other people's funerals; otherwise, they won't come to yours." -- Yogi Berra
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." To see whether the predicted bias shows up in actual coin tosses, the team made movies of tossed coins and then calculated the axes of spin.
Ok, I admit it. When I was 10, I noticed that I could toss a coin in such a way to always have it land the same side up (and then I would flip it over onto my hand, thus it would be the opposite side showing). I've used this trick for years to win coin tosses, but never really knew that the coin wasn't flipping (it really looks like it does, so I thought I was just flipping it right so that it spun the same numebr of dice).
You can also place a single die in your palm and roll them so that if a 5 or 6 is nearly guaranteed (which 6 more likely, 5 if you screw up). Doesn't help in craps (where you have to toss them far), but helpful in table top RPGs.
-no broken link
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!"
OH yes, bombing Iraq did wonders for our security. Idiot! But then again, you ARE and AC.
with different currency? (IIRC the Euro is notoriously bias for one of the two outcomes). It would also be interesting to see the study applied to other seemingly "random" processes. There's a great scene in an episode of TNG where Data is playing craps, and is able to roll 11 every time. (Or something to that effect... I'm sure there's a /. reader who can point out my lack of TNG knowledge).
>> 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
Well. obviously, but only if the caller is just as likely to call heads as tails.
I've wondered about this. I just don't know which side is heavier but you would think that would affect the outcome. I've heard the same thing of dice. The sides with more numbers, ie 4,5, 6 etc. have a slightly higher chance of rolling because there is more die on them and it changes the outcome a wee bit. Leave it to a bunch of D & D nerds to wonder about this kind of stuff.
Hold up, wait a minute, let me put some pimpin in it
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
Perfect bias boundary condition is defined as (Assuming no qunatum effects, which is ying-n-yang in nutshell.),
Heads I win.
Tails you lose.
That's not quite right either, is it? I don't believe the govn't has defaulted on any of it's "payments" on the loans which cover its deficit spending. Likewise, many people buy houses that cost more than their salary. In any case, a house has value and is not just an expense,so it's probably not the best analogy anyway.
Maybe this guy should RTFA. Then he would know that the article talks about spinning coins landing tail about 80% of the time.
But then, maybe the grandparent should have specified what he was refering to.
And could anyone tell me why the article brings up someone flipping 10000 coins and NOT recording the results?
I have misplaced my pants.
Come to think of it, aren't there three players? What are they using, some magical 3-sided coin? Something fishy is going on at the Wheel. I never trusted that show since they gave up the shopping sprees after you guessed the correct puzzle. Ah, the days when you only had $100 bucks to spend at the end of your spree and you were force to buy a ceramic dalmation.
----
Spam subject of the moment: Offshore account secrets -nashville disrupt
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.
So if the govt job is better, the plan worked!
Say it really fast and throw the coin in the air before they have time to think:
"Heads I win tails you lose."
eTrade SUCKS
Technically speaking, you're in debt pretty major with a mortgage payment... so it's a great deal like a budget deficit works.
:)
You couldn't pay for your whole house so you got a mortgage..
The govt can't pay for everything it does so it releases t-bonds/t-bills/etc... mortgaging the country, in essence... and paying the intrest (most often) to big banks that buy them (or your grandmother who got them for you when you were born)
I suspect it depends more on what the coin was last read as saying.
If picking up the coin and flipping again is a routine'd behavior by the flipper, then the coin can be expected to have a position directly related to its position when it was last shown.
The heavy face of the coin really only makes a difference when the coin is dead-on-edge, or is close enough to being so that the center of mass pulls it over.
tasks(723) drafts(105) languages(484) examples(29106)
will your dignity be the same before the salad toss?
Or maybe the Balkans (including numerous helicopter crashes there due to poor planning)?
Oh well, I guess I can be a hypocrit too.
Which was fully refundable.
Bill was just a political strategist, not a military one. Somalia
Actually it was gamblers who figured that one out. That's why if you go to a casino you'll find their die pits are all filled.
You could easily cure your ignorance by learning to read. The 51% number was calculated from a theoretical model. The purpose of the mechanical coin flipper was to test the predictions of the model. The 10,000 number wasn't an experiment used to compute the bias: it was an offhand estimate of the number of coin flips that would be necessary to produce a statistically noticeable deviation with such a small predicted bias.
I don't know how this estimate was produced, but I can guess. A binomial distribution, such as coin toss, approaches a gaussian as N grows large. The drift of a gaussian grows like N, but the volatility grows like root N, so that the relative contribution of drift grows as N increases. 10,000 happens to be the crossing point in this case: 100 = sqrt(10,000) = 51% x 10,000 - 50% x 10,000.
"The good reader is a rarer swan than the good writer."
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
Agreed. I've noticed the likliness of getting one side based on the orientation of the coin since I was seven years old or so... just from watching a _few_ (I never sat around flipping coins). Is this really that new to everyone else out there? But then, the only fair decisions based on coin tosses I ever see are computer simulation examples where fairness is assumed.
"Lets flip on it." *looks at the coin before toss and prepares to call it in the air*
But alternatively, if they flip it and put it on the back of the hand, and you don't know about that before hand, it's somewhat of a gamble.
-DrkShadow
That's your defense. Nice.
Army Rangers is a lightly armed mobile force doing commando-type raids. Last I heard, heavy armor isn't part of the equation in those type of operations.
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.
When I read your comment, I saw it applying so well to another school of thought that is popular here on Slashdot. With your permission, I have modified a few of your words and am "redistributing" here.
"Who said it was [corporately] funded? Lot's of cheap [software] has been and continues to be done on the [programmer's] own tab, as long as the costs are low enough. If they are genuinely interested in the [product], who is to say that it's not worthwhile?"
We may experience some slight turbulence and then...explode. -Capt. Mal Reynolds
is to XOR together a power of two pseudo-random bits. Math at
http://irresponsiblecybernetics.com/phorum/read
It's Christmas everyday with BitTorrent.
Since when does the flipper and the caller get to be the same person in a fair toss?
We hope your rules and wisdom choke you / Now we are one in everlasting peace
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.
From a graduate level algorithms course:
Puzzle: Suppose you have a coin that is not 'fair' - it lands heads greater than 50% of the time, but all you know about Probability(heads) is that it is somewhere between 50 and 75%. How can you emulate a 'fair' 50/50 coin with this coin? (eBay'ing the coin and flipping the proceeds does not count)
Solution: Flip the coin twice. If both flips are heads, or both flips are tails throw away the result and repeat: {H,H}->Repeat, {T,T}-> Repeat. If the flips are different, then use the result of the first flip: {H,T}-> H, {T,H}->T.
__ Someday, but not this morning, I'll finally learn to use the preview button.
I will gauchely reply to myself to add that, as the article implies, it's not simply the range of applied flip force. It's an interaction between applied flip force and leverage point, angle, etc. of the flip--more specifically, the axis of rotation conferred onto the coin due to all these factors--which determines if it will actually flip. So, you can't simply decide you will flip the coin "harder" to get fairer results.
No, it is actually worse than that. Clinton and Aspen specifically removed the Bradleys and M1's from the country because it didn't "foster a sense of trust". This was over the strong objections of military commanders. Then he ordered them to arrest Aidid, for which commanders requested Bradley's and other such equipment. Denied! So in went the troups without proper support, and many good men died. The only reason was to preserve appearances on a humanitarian mission.
The article says that the coin lands matching the top face 51% of the time. There is a 2% greater possibility of same-face landing. I'm willing to live with that when deciding who has to get the beer.
If that's not good enough for you, throw the coin at a wall or a cluttered tabletop - that should give you enough interference to truly randomize the decision. Sounds more fun to me, actually...
Your brain is not a computer.
"...while interned in a German prison camp"
thats an interesting way of putting it
I tried 2 quarters, spun them 25 times each. Both came up 14 heads 11 tails. At this point I seriously doubt the 80% tail figure. Sorry, didn't try other coins.
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.
Roll the coin along your index finger with your thumb as you launch it. Give it a little upward flip with the thumb at the end. It will precess and look as if it's flipping. This is why 'call it in the air' is a necessity.
- None can love freedom heartily, but good men; the rest love not freedom, but license. -- John Milton
I always thought rock papaer scissors is always fairer. With a coin toss, someone makes a decision and the other tosses (erm...yeah). I don't think the call and the toss have an equal representation of fairness. Rock paper scissors however each person makes an equally important decision. Not only that but more people can participate where as if there are more than two people in a coin toss, it needs to go to a systems of "rounds" or "heats", and there are many ways that rounds can be . Sure there are problems with synchronisation in the rock paper scissors system more often than not, but the system works, and is fairer.
"I just can't sit while people are saying nonsense in a meeting without saying it's nonsense" J Watson, Sci Am 288:(4)51
It doesn't even say they did it once !!
it says that perlininary results show that the bias is 51%,
which would imply you need more than 10000 tosses.
It doesn't say how many trials accounted for the 51% , but if they rely on the fact that "many tosses do not flip at all" and factor that in, then this really starts to smell.
or to quote R.P.Feynman (lectures on physics volume 1, IIRC)
The neatness in which all these lines converge simultaniously at a far away point are proof that this is the result of work done by a mathematician, and which does not represnt real data.
-- Avishalom is usually vish
Actually, I have always ended up with the opposite results. It has ussually been that if I flip it from the heads side, it ends up on the tails side.
I personally think it has almost everything to do with flip height and speed. But, I'm sure it's subconciouse for me.
From a dimly recalled stats class: probability theory depends (in part) on the assumption that in an infinite number of fair coin tosses, the heads/tails outcomes are equal in frequency. If in a finite number of fair coin tosses the outcomes are skewed by starting conditions (the side you select as "up" at the start of the toss), that sort of undermines the assumption, doesn't it? If the assumption is wrong, can the conclusions that depend on the assumption be right? Maybe this is why when my kid says "I'll probably be home by midnight", well, never mind.
My other machine is a lever.
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.
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.
the scary part is that attempting to cause 50/50 H/T has nothing to do with fixing the bias in same as starting side/diff from starting side.
The message on the other side of this sig is false.
But where do you buy money?
With a different side facing up each time. And instead of having one person call what it will land on, have them call the side that it will land on exactly 1 time.
If the coin happends to land on the same side zero or both times, then start over and do two more tosses.
regardless of the fact that the coin *may* land on the same side it started on, if the side-chooser doesn't know where it's starting and the flipper is impartial, the effect of the called coin toss would be the same.
Those who can, do. Those who can't, simulate.
As in most scientific experiments that defy logic, I would call into question the controls used in this experiment:
Were the coins used for testing weighted on one half or the other? Even a sample of 10,000 coins assumes that a perfect coin (or the average coin) is weighted perfectly. With different designs on either half, one half has an advantage of landing down (or up).
Flipping slugs (a coin before an impression is made) would be better, although most coins today are composites, and not one type of metal (again, throwing off the weight).
The other day/week NPR ran a simlar story regarding a device which would always allow the coin to land heads or tails (and they discovered the same thing - about a 51% chance; in fact, this might be the same guy). This seemed absolutely absurd, as the scientist basically went about the hard way to measure exactly how hard a coin is flipped, the calculate the exact distance to make sure the coin landed the same way, every time.
Winners tell stories while losers yell deal.
"Random: Having no specific pattern, purpose, or objective: random movements." BS! There is no such thing that is truly random event to begin with! It's all a matter of properties, math, and conditions. The flipping of a coin is no more random then the law of gravity being carried out on a ball that you dropped out of your hand, it's just that the measurements are too small to make and the exact environment is to complex to properly reproduce. If you flipped a coin the exact way two times it would have the same exact outcome! Assuming the conditions are "exactly" the same, but there are way to many variables(most of which we are not even aware of without years and years of thought on the subject, because all the measurements would have to be on a sub subatomic level with 100% accuracy and perfect precision). Bottom line...Random just means the math problem to formulate the outcome is too complex or time consuming to apply to any given event.
Creative Demolition
That's why intelligent people tend to avoid such battles in the first place...
hmm.. I don't get this Microsoft joke...
I haven't mastered the art of the flip per se, but with the protocol of "flip, catch, then place on the back of your other hand", I can control the outcome by the feel of the coin (furtively flipping or not flipping as I place it on the back of my other hand).
This gleaned after an hour feeling up a coin and realizing that one side is smooth and the other is rough.
There's a reasonable discussion of coin tossing in section 10.3 of Ed Jayne's book "Probability Theory: The Language of Science" published by CUP.
Like the article in Science News Jaynes makes it clear that the manner in which the coin is tossed is important. To accentuate the effect of bias---and to make the experiment easier to do---he reports how he tossed the 'metal lid of a small pickle jar' in three different ways: in the first he can control whether he gets heads or tails; in the second he always gets tails; in the last he gets 54 heads from 100 trials.
Leave it to a bunch of D & D nerds to wonder about this kind of stuff.
I would imagine it would interest Craps players more than D & D nerds.
I don't believe there would be enough of a significant advanvtage to earn a person any extra money though (maybe if you had the time and bankroll to sit through billions of rolls it would)
Have you tried Linux yet?
"We've got a deficit over a half-trillion and things like this are getting funded. Riiiiight."
. html
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
True, but as long as you have enough credit to get to another country, establish a new identity and basically start over, then you are golden.
US government can always just make (literally) more money. And yes I understand this causes all sorts of other problems. I didn't say it was a smart move. But then again, check out current (and previous) administrations activities. Neither really shines as acting intelligently.
Our founding fathers removed the guys in charge. Be American. Vote incumbents out.
Slashdot is great!! I just love seeing this shit in every fucking thread on this site. Your mother sows socks in hell - moron.
Prof. Farnsworth - "Oh a lesson in not changing history from Mr I'm-My-Own-Grandpa!"
It would take about 10,000 tosses before a casual observer would become aware of such a small bias...
_
I can't wait until Super Bowl X !!!!!
Stupid straw argument. Studying randomness in coin tosses *is* trivial to the point of absurdity if it costs the taxpayer even one cent.
"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.
Anybody notice that it was an Anonymous Coward who takes a verbal cheap shot at the President in a completely unrelated article?
Yeah, and Osama bin Laden is a prime example...
Oh my, that absolves Bush completely! I'll go vote for him next time.
No, Bush Sr did that. That is, Bush Sr committed the troops to Somalia. Clinton inherited this shitty situation from Bush and made it worse by doing nothing, but it's simplistic to place all the blame at Bill's feet.
or george w.
Well it's not a good analogy for operational spending, but what about spending on infrastructure like transportation. The Federal Government does spend a not insignificant portion of money on transit and military capital expenditures. This could constitute an investment rather than an expense, as opposed to the operational budget, where you really would be burdening future generations to pay for the consumption of their parents.
----- Question authority, but not ours. Hate the man, but we're not him.
I personally think it has almost everything to do with flip height and speed.
Natch. People confuse randomness with unpredictability. Just because we cannot predict the result of something doesn't make it random.
Of course, I'm a determinist (compatiblist, actually), so to me, everything is a coin toss (ie: not random, though often unpredictable).
Sorry, this war against the US started years ago. 9/11 just woke us up to reality. Bush didn't start it, but he's cognizant of the fact that anything less than a total victory against the many terrorist groups who want us dead, and the removal of the conditions that breed terrorists will only result in our children, and our children's children in having this problem, or a worse one on their hands. It's best we grow up and face up to the responsibility.
Actually, even if you know the face of the coin, it is still random, it is simply not "fair" (At least according to these guys). But, considering the fact that the numbers they got were very close to 50-50 (they said 49-51), it is entirely possible that they are wrong. Random variation tells us that some time, somewhere, there will be one million heads in a row, on a fair coin toss. Don't try calculating it, but here is the equation:
P(X=N) = ((1-p)^(n-1))p
Where little p is the probability of success (aka heads). This gives us the probability of flipping a coin and getting heads one million times in a row.
With the fact that this is possible in mind, it is also entirely possible that they got these results through random variation alone. I would like to see them run some significance tests on their results, and release them so others can do the same.
I have a special set of ivory dice with very deep hollows for the numbers.
They certainly do favour the higher numbers. I keep this set especially for adult games, not D&D.
eating out,
having more than seven sets of clothes
(laundry once a week)
I don't know what site redirected you here but you are posting on slashdot.
Who said that we need to stop spending money until the defecit is zero? Oh, that's right, you did.
Probably been said... but, you know what they say about when you assume. = )
All your heads are belong to us.
...Rewrite all my coin toss programs.
It's called a coin flip for a reason.
As long as the coin flips, you don't have this problem!
Any idiot can tell you that if you don't flip the coin, it's going to be biased.
Is this the death of two up ?
So does Anonymous Coward have good karma?
I usually find that if I toss with my right hand, it's much quicker than when I flog, ah, I mean toss, with my left.
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
Still using one of Clinton's old coins, is he?
I think the difference really is that Bill Clinton actually attended the funerals of those who were killed in action.
He didn't attend the funerals of those killed in action in Somalia.
Bush not only doesn't attend, he doesn't even allow the funerals to be mentioned by the media.
False.
The biggest laugh I've ever seen at a technical talk was at last year's AAAI (American Association of Artificial Intelligence) conference in Acapulco, Mexico. A young Japanese researcher described his new robot that played rock-paper-scissors with a human. At the end of the talk, someone in the audience pointed out that the robot had just a sphere for a hand - perhaps he'd missed a detail in the point in the talk, but how did the robot indicate which state he was playing? Ah, explained the presenter, the robot always plays 'rock'. Big yuks in the crowd.
What's on the other side, then?
Ydco co
I though every schoolkid knows how to throw a coin: place it on the index finger so that the edge hangs over, place the thumb under the edge and snap the thumb forcefully up. This will make the coin fly up and at the same time spin rapidly around a horizontal axis. When I read the title I thought they found a bias in this, correct way which would have been extremely unlikely.
Bill 'draft-dodger' Clinton, or George W.
Shouldn't that be George 'draft-dodger' W.?
Or being in the champagne unit counts as being drafted nowadays?
I've heard the same thing of dice. The sides with more numbers, ie 4,5, 6 etc. have a slightly higher chance of rolling because there is more die on them and it changes the outcome a wee bit.
Depends on the dice. Your typical, rounded-edge drugstore dice are full of bias. Casino dice, on the other hand, are made with an exacting process to ensure that bias is minimized, and the spots are made of a material that is of the same density as the rest of the die.
Persi Diaconis used to be a magician before he became a statistician.
I'm a Backgammon nerd, but here goes...
Are you a grammar Nazi? I'm trying to improve my English; please correct my errors!
1. Bush hasn't attended a single funeral, and he hasn't even attended a single homecoming of the deceased. Not only that, but it's his administration that's banned the media from filming or photographing the returning coffins: you might chose to blame Bill Clinton, but he's not the President any more, so quit trying to pass the buck onto him.
I'm sure Bush is really busy and just can't find the time to attend a single funeral yet alone all 550+ of them. All that holiday time (he took 28 days off last year, compared to 13 for the average American) and all those fund raisers (he and Dick Cheney attended over 100 of those last year) must really cut into a big chunk of his schedule.
Isn't it funny how he doesn't mind creating widows and orphans but he doesn't like been seen with them?
"Accept that some days you are the pigeon, and some days you are the statue." - David Brent, Wernham Hogg
I would have thought that was obvious....tails and heads!
There is no coin. It is only in your mind.
to say nothing of Cheney, Perle, Ashcroft and the rest who are PROUD of being draft dodgers.
But by paying your mortgage, your debt is decreasing. A decrease in debt is the same as a profit (=surplus). A deficit means your debt is increasing, as the other poster pointed out.
(And yes, I did an accounting course at school)
Not only that, but it's his administration that's banned the media from filming or photographing the returning coffins: you might chose to blame Bill Clinton, but he's not the President any more, so quit trying to pass the buck onto him.
I'm not blaming anyone. It was a rule passed during the Clinton administration. George Bush is enforcing that rule, and I have no problem with that. If families want to arrange some sort of press coverage for the return of their dead loved-one, they are free to do so.
Again, I point out that if Bush were to go to a funeral, I guaran-friggin-tee you that he would be accused of grandstanding.
I was in the military until just before Bush was elected, and I have good friends fighting in both of the theaters now. I hold no grudge against Clinton, but I guarantee you that professional soldiers and Marines prefer this administration to the last.
I notice that your major points revolve around cameras and public displays of grieving families. You want to judge the President's level of caring by how much time he spends on camera and how public a spectacle he can make of it. I think that's a bit self-serving.
Evil is the money of root.
No, I would rather a President who doesn't hesitate to wage unneccessary wars was around for more than glorious "Mission Accomplished" showboating.
Paying your respects to the dead isn't grandstanding, and accusations of grandstanding aren't why he doesn't do it: being associated with even the slightest whiff of failure is why he doesn't do it.
"Accept that some days you are the pigeon, and some days you are the statue." - David Brent, Wernham Hogg
And yes, deposing the Taliban and Hussein have dramatically improved the security of this country and the world. Or have some airliners flown into buildings these last couple of years, and I just missed hearing about it? Even if you can't (or won't) understand global politics, you ought to be able to understand that flewer terrorists attack == greater security.
1. I really doubt he'd be accused of grandstanding. His approval ratings and the media bias are positive enough that while there may be a very small group of people who didn't like it, most folks would find it touching.
Of course, after the fact, it may come out that he only went to *one* funeral, disregarding everyone else. If he did that, and had his folks make a huge deal of it, like he was doing something ultra-signifigant, then sure, maybe he'd be accused of grandstanding and rightly so.
2. Good thing Bushie cut their bennies though, eh?
Working toward a usable PDA environment in the spirit of Newton OS: Dynapad
to say nothing of Cheney, Perle, Ashcroft and the rest who are PROUD of being draft dodgers.
Well, duh. They are far to important to have been exposes to any danger. Rich people don't deserve that kind of treatment!
Working toward a usable PDA environment in the spirit of Newton OS: Dynapad
So the Air National Guard is just a bitch job, for people who don't want to be in the military? So all the Guard troops in Iraq are "avoiding" service? Bush is a pilot. He flew jets. What do you do?
-jg
A crappy defense, yes. Yup, Bill fucked up a few times. That is expected, though everytime it happens it's a scandal. But at least he didn't make it his policy to fuck up as much as possible like W.
Working toward a usable PDA environment in the spirit of Newton OS: Dynapad
So all the Guard troops in Iraq are "avoiding" service?
Of course not. They are in Iraq, not in Texas, as Bush was. AFAIK, National Guard was never deployed in Vietnam. Guarding Texas against invasion sure sounds like avoiding military, when the alternative was going head to head with the vietnamese. Not many chances of getting killed serving in Texas, is there? Except maybe, for flying a plane while drunk, but that's another story...
Bush is a pilot. He flew jets.
He flew jets over Texas. Until he got his licence revoked, for not passing his physical (apparently, he didn't feel the need to take it). Doesn't quite compare with flying combat missions over Vietnam, does it?
What do you do?
Software developer. In Croatia. Served in the military, if that's what you're asking.
What did I do to rate foe status?
Thanks!
You suggested that some people have a god given right to a job. I found that so retarded that i don't want to read any more of your posts.