# That Random Coin Toss? Not So Random Afterall…

### from the *a-weaker-man-might-be-moved-to-reexamine-his-faith* dept

One of my all-time favorite scenes in a play and movie, is the scene in Tom Stoppard’s *Rosencrantz & Guildenstern Are Dead* where every coin toss comes up heads, leading to a bit of a philosophical discussion on probability. Of course, the randomness of the coin toss is the quintessential example of a random event and is used regularly for a variety of situations in which randomness is required, let alone expected. Except… it turns out the common wisdom may be wrong. Paul Kedrosky has the news of a test that showed that if you ask people to try flip a coin and get more heads than tails, they will, and not by a small margin either. In the test, 13 people were asked to flip a coin 300 times, trying to get as many heads as possible. *All 13 participants* got more heads than tails. Seven out of the thirteen had statistically significant margins of heads over tails (meaning almost certainly not a matter of chance). The highest was one individual had 68% of the coin flips land heads. In other words, a coin toss isn’t particularly random.

## Comments on “That Random Coin Toss? Not So Random Afterall…”

## Ok this is weird, but

I’ve known for a couple of decades now what the trick is to a coin toss. But you have to do it one certain way. If you do the “Traditional” coin toss, where you flip it with your thumb, catch it in palm of hand, then smack it over onto the back of your other hand, you can get better than 90% right. It will come up opposite (I think, its been a while) of whatever it was when it was facing up before the flip. Dont know why, it just does, if you flip-catch-slap it right. You can win a lot of bets with this method. Dont know if other methodologies work this way for coin tosses, but this one is consistent. Just dont EVER bet the farm when someone else flips, as they might not do it “right”, always try to be the flipper yourself to control how it works.

## Re: Ok this is weird, but

That’s why you call it in the air.

Also, I seem to remember a study where one side just came up slightly more. Might have been heads.

## Re: Ok this is weird, but

Wow, I was surprised how well this worked. I got tails 8 out of 10 times just by starting with heads up, and doing flip-catch-slap you described.

## Ok this is weird, but 2

“That’s why you call it in the air.”

But that doesnt matter if you see what it was face-up before it was flipped. It still applies, though again, if someone else is doing the flipping, your odds arent as good. Still, I always call it opposite when its flipped, and am right more than wrong.

## Re: Ok this is weird, but 2

@RD:

You call it in the air to prevent the way the flip is performed. If you call it while it’s on the thumb, then the flipper can aim for 3 flips versus 4 flips. 3 would produce the same side (provided you “flip-catch-smack”) while 4 would produce the opposite. If you “call it in the air” the flip has been performed and the flipper can no longer influence the result. (Actually the advantage would go the “caller” as he now has a split second to determine height and flip speed.)

-CF

I suspect the results would be different if you didn’t give the flipper the results on the go. Knowing what got them a “heads” result, they will try to duplicate that action exactly. While they cannot always do the same, they can hone down the variables and attempt to do the same thing over and over.

Don’t let them see the results, and I suspect they would end up pretty much 50/50 again.

This is “tech” how, anyway? Perhaps this is just a stupid friday blog post that we all have to look at until Monday because Mike hasn’t figured out how to release posts over the weekend. The internet is a 5 day a week business!

## Re: Re:

Real randomness is one of the holy grails of information science.

## Re: Re:

When someone says that the whims of the RNG god aren’t related to Tech, it is a fair sign that person doesn’t know anything about Tech.

## Old news

There have been better studies on this already.

## Methodology

I have to question the methodology of this study. They gave people a goal of influencing the outcome of a “random” event where it seems possible to do so.

In my opinion a coin toss is random if the coin falls to the ground and bounces because it is possible to know the rate of spin and time your catch to always get heads. I would be very difficult to get that every time, but 300 tosses is plenty of time to practice.

Ditto anonymous coward:

http://comptop.stanford.edu/preprints/heads.pdf

Is a coins weight evenly spread out over the coin, or could the weight be more to one side than the other? If I flip my water bottle; it always lads “heavy side” down.

## Re: I can imagine...

…that a quarter is heads-side heavy. If the front and back are both raised up the same amount, the head covers more area than an eagle, or a detailed image of the state, etc. But, that would mean that you would get tails more often, since the heads side is heavier.

## Re: Re: I can imagine...

“that a quarter is heads-side heavy.”

Really? There seems to be a lot more detail on tails, seems like it would be tails heavy.

## Re: Re: Re: I can imagine...

‘Detail’ on a coin is either cut away from the highest point or raised from the lowest point. So claiming detail as the cause of the weight really doesn’t mean anything.

## Re: Re: Re:

^{2}I can imagine...I recall from a few years ago that tails IS marginally heavier on the quarter…I believe that it is also the only coin that such a statement is true of (all the other coins are heads heavy, I believe)…Can someone confirm or deny this with some evidence?

## Re: Re: Re:

^{3}I can imagine...I would need a physicist and a statistician to do exacting calculations before I believed that weight distribution even mattered.

This is not a shuttlecock with a feathered tail and one end highly weighted far away from the tail. The embossed characters on either side are opposed only on the shortest axis if a basically flat object. The torque a heavier side would exert on the flipping coin is trivial.

The bias thus introduced would probably be less than the confidence interval of the statistical analysis.

I would guess that a more important weight consideration would be “top heavy” or “bottom heavy” (like heavy near the top of the head), but that probably is insignificant, too.

## Re: Re:

Exactly, that’s why I always contended that heads has a slightly better chance of winning, because there seems to be slightly more weight on tails just by the curvatures, though it’s a very very slight difference. If you flipped the coin, without trying to influence it, the chances of getting heads vs tails maybe almost 50/50 but if you flipped the coin many many times it may show a bias.

This is why in statistics they always say, “if you flipped an unbiased coin” or “if you rolled an unbiased die” they have to add that word unbiased.

In fact, I knew people that used to be able to manipulate how the dice rolled and they seemed very good at getting it to roll however they wanted. They made money just making bets with others on how the dice will land as well. Of course no one would ever admit that they were manipulating the dice but these people were very coordinated and after watching them for a while it becomes somewhat obvious. Then again, they only played for a few dollars, it wasn’t worth making an issue about.

They should be getting more tails than heads. The heads side is slightly heavier.

## Really?

This isn’t something I would expect to read on Techdirt, and the quality of the post shocks me. It’s not unknown that the heads-side of an American coin is heavier. It’s the case with every coin in production. I would have expected this to be researched before the post was published.

## Re: Really?

Really? You were “shocked”? Like, “where were you on 9/11?” That kind? So you’ll be saying “where were you when Mike blogged about the coin study?”

Hey Aaron. How about next time, you don’t be a d-bag, and just say, “I thought it was well known heads is heavier.”

## Re: Really?

Well, if heads is heavier, it should have come up less, because the coin should land heads-down. So, I guess now you can be even more “shocked.” Like, hands-on-your-cheeks, wide-eyed, slack-jawed shocked.

## Ok this is weird, but 3

“In my opinion a coin toss is random if the coin falls to the ground and bounces because it is possible to know the rate of spin and time your catch to always get heads. I would be very difficult to get that every time, but 300 tosses is plenty of time to practice.”

With the method I described above, I have never even attempted to “time” the flip. It doesnt matter. This is for the flip-catch-slap method. Fall to the ground, and I think its a lot more random.

ill assume since they didnt meantion a handflip after catching, this means heads being heavier doesnt matter with the results.

## Idealized coin flip.

Sure, in reality coins are not all the same, nor is each one perfectly evenly weighted. And sure, people can have steady flipping techniques to influence the outcome.

Probability doesn’t really care about that, since we use a “idealized coin toss” in all discussions on the topic. Pr{H}=Pr{T}=0.5

Those are even odds.

## call in the air, and let it fall

If you catch then slap, you are able to catch at the right moment/position, and even correct during the slap. I think it is more of a case of the mind sometimes working faster than we realize.

My parents and another couple were camping and a coin flip was used to see who would have to do the dishes — the men or women. Halfway through the dishes, the women folk realized “heads I win, tails you loose” was a trick. They were not happy.

Two important aspects of tossing a coin are missing.

1. The one who tosses is not the one who is calling.

2. The caller calls after the coin is flipped. (as a lot of folks have pointed out.)

Give any bloke a coin for a month to practice he can obviously get hold of how to get a head more number of times.

C’mon Mike, is it a slow news day or what?

## Re: Re:

“C’mon Mike, is it a slow news day or what?”

You’re just jealous because you don’t have a successful blog and nobody listens to you. Poor industry shill.

if the same action is applied to the toss, catch and flip of the coinage it will always be the same. it’s all in the wrist sorta speak but, actually in this case it’s all in the thumbage.

if the same action is applied to the toss, catch and flip of the coinage it will always be the same. it’s all in the wrist sorta speak but, actually in this case it’s all in the thumbage.

als I’d like to refer to an experiment done by derren brown, http://www.youtube.com/watch?v=X1uJD1O3L08

he tosses a coin 10 times and gets 10 heads, he went and flipped a coin for 8 hours and eventually gets 10 heads, because of the random nature it’s quet unlikely to get 50/50 ratio every ratio has some possebilety and a sample of 13 where only slightly over 50% had more heads then tails is not a very good basis

## Re: Re:

Not to mention most people get heads most of the time on their own. This study is worthless, just reiterating old knowledge. But, it would have meant something if they told people to try and get tails and they actually could get tails more often. It would be more interesting to see that a coin flip is not random because of the desire of the person doing the flipping, not because of science.

I just flipped a coin a few times to further investigate my trends and I got all heads. I honestly cannot remember the last time a coin I flipped was tails. At least not a quarter. I think I flipped a penny a little over a year ago that was tails, it was a shock at the time, but it was probably some demonic penny mischief.

http://www.npr.org/templates/story/story.php?storyId=1697475

If a human flips a coin starting on heads, it tends to come up heads.

http://www.cbc.ca/technology/story/2009/12/07/tech-coin-toss.html

A key fact that is left out of the TechDirt post is that the UBC researchers instructed participants on how to manipulate the toss. Therefore, it is misleading to simply say, “if you ask people to try flip a coin and get more heads than tails, they will.” Simply “trying” is not enough.

http://robert.accettura.com/blog/2009/08/24/coin-tosses-not-totally-random/

Finally, coins themselves are not inherently fair.

## Did anyone think....

Did anyone think to try it the other way around? That is, to try and get more tails with the same coin?

## But imagine a jar full of pennies

What are the chances of life? I use pennies to illustrate:

“The creationist/IDers (Intelligent Design advocates) love to say “Life is too complex to have been created by chance”. The problem is that they are looking at the end results and then computing the probability that it got there – rather than computing the probability for any life.

To demonstrate what I mean I would like you to do a little experiment. You will need two things – a jar of pennies (the more pennies the better), and a 5×4 foot (or larger) unobstructed clean flat spot on the floor – preferably with out any carpet – the larger the area the better…..”

http://blog.chronofish.com/?p=47

## Mike, wtf mate!?

The results are random unless you try to alter them. That stands with anything, even throwing dice…

## coin Tossers

Although I have a day job as a Network Administrator, I have been a professional magician for over 25 years. Repetitive coin tosses WILL have a strong bias to either heads or tails. Once the person tossing, gets into a familiar rythm for tossing the coin they will replicate their actions with surprising accuracy. The strength of the toss, the height of the toss etc etc all being very very similar each time will result in the coin landing back in the hand the same way a great number of times. I learned to control the toss of a coin at an early age in my magic career. A better control would be to have 300 people toss a coin and allow it to land on the ground, the result being noted by an independant observer. I believe this would result in a more even spread of heads and tails.

“In other words, a coin toss isn’t particularly random.”

NONSENSE! One can add BIAS to a coin toss (in fact, a university study showed that if you hold a coin a certain way (with some practice) you can almost guarantee that it will come up heads or tails).

But all that demonstrates is that “figures never lie, but liars figure”.

Coin tosses are random, coin tossers are not.

## Re: Re:

“a university study showed that if you hold a coin a certain way (with some practice) you can almost guarantee that it will come up heads or tails”No matter how I hold the coin I can guarantee that it will come up heads or tails. Since there’s only two sides to coins it has to come up heads or tails! 🙂

This is not a proper statistical analysis. The sample sizes were not nearly big enough to have anything worth looking at. Not only did they have an insufficient number of coin flips, they only used thirteen people. This should not be taken seriously since it was a poorly conceived experiment.

– Engineering Student

In reality there are no “random” results; only causes and effects. If all conditions and actions are exactly the same (and I do mean exactly) for a series of coin tosses, one would fully expect the results to be exactly the same each time (all heads or all tails) even for 1,000 tosses. While I am not arguing that anyone can achieve that exactness, I am arguing that there is no such thing as random. Just because we don’t know (or aren’t trying to control) what the result will be when we toss the coin doesn’t mean that the toss is random. At best, all we can claim is that we are trying to get a result that we are not trying to control or influence.

## Re: Re:

Problem is in knowing *all* the conditions *exactly* – see Chaos Theory.

Also, for the “no such thing as random”, the decay of individual radioactive atoms currently does appear to be random (although I know there are arguments that it is merely chaotic, and I guess that there could be further developments that can aid predictions of decay? IANAP …)

## Reliable

I’ve been able to flip a coin in a controlled manner since I was a kid. It always lands opposite side up from how I flip it. So catch and it’s opposite, catch and slap to the back of the other hand and it lands same side up. Never let a coin flip decide something with me. I always win.

I don’t know why I can so consistently flip a coin, I’ve just always been able to do it.

## True randomness is hard to find

Rather than rely on a coin toss (which has always been easy to manipulate), it is better to use a random number generator.

However, recently I discovered that the random numbers generated by computers and smart phone applications aren’t as random as you would want. They use mathematical formulas which are generated in a predictable way.

However, Random.org is a great resource as they generate random numbers, flip virtual coins, roll virtual die, and shuffle virtual cards using atmospheric noise. They believe this is a better way to create random events.

## Defining Randomness

The problem with the coin toss is its actually not random at all, if you understand what randomness is really all about. Flipping a coin, by nature, is a completely non random event – all possible outcomes are strictly set, the odds of which are perfectly known. Randomness is unexpected and unpredictable with unknown outcomes – a coin toss could be random, if somehow the coin lands on its side or gets destroyed somehow I would call that outcome random.

I suggest reading “The Black Swan” by Nassim Nicholas Taleb, or his previous book “Fooled by Randomness” probably the only guy who can explain this idea correctly. In it you’ll discover that even gambling in a casino is completely non-random, it’s fixed, we all know that. The randomness that effects casino’s are truly random events such as entertainers getting mauled by tigers. (The biggest losses in casino history have been true random events, such as being robbed, or the classic Sigfried and Roy tiger mauling at the Mirage, which resulted in huge losses)

So remember – randomness is unpredictable, with an unknown set of possible outcomes. Flipping a coin is almost the opposite of randomness, its the kind of predetermined experiment that you’ll rarely find in nature.

## Re: Defining Randomness

It depends on how one defines randomness. Two generally accepted characteristics of randomness are

A: Past outcomes do nothing to help predict future outcomes.

B: Non compressibility. That is, a file full of random bytes should not compress very much when a compression algorithm is applied to it.

These are also characteristics that people try to make encrypted files exhibit so that they appear random.

## Re: Re: Defining Randomness

also, for A the reverse is true as well, future outcomes should do nothing to help determine what past outcomes were.

## Re: Re: Defining Randomness

So like you said, for random things, A: Past outcomes do nothing to help predict future outcomes.

This principle is nowhere to be found in the coin toss scenario. This may not sound intuitive, but I can predict with nearly 100% certainty based on past coin flipping data that the coin will land on either heads or tails. (the randomness only comes in, as I explained before, if something else happens, like the coin lands on its side or is hit by a stray bullet and destroyed). A coin toss is almost perfectly predictable.

Something is not random if you can known all the possible outcomes and their chances of occurring. Randomness involves unknown outcomes (or at least unknown probabilities for known outcomes)

The problem is dependent on defining randomness, and sadly the conventional definition of randomness is very based on statistically non-random events such as casino gambling and coin tosses, and not on the kind of randomness thats found in the chaos of nature.

## Re: Re: Defining Randomness

So like you said, for random things, A: Past outcomes do nothing to help predict future outcomes.

This principle is nowhere to be found in the coin toss scenario. This may not sound intuitive, but I can predict with nearly 100% certainty based on past coin flipping data that the coin will land on either heads or tails. (the randomness only comes in, as I explained before, if something else happens, like the coin lands on its side or is hit by a stray bullet and destroyed). A coin toss is almost perfectly predictable.

Something is not random if you can known all the possible outcomes and their chances of occurring. Randomness involves unknown outcomes (or at least unknown probabilities for known outcomes)

The problem is dependent on defining randomness, and sadly the conventional definition of randomness is very based on statistically non-random events such as casino gambling and coin tosses, and not on the kind of randomness thats found in the chaos of nature.

## Of course!

Scientists are just now figuring out that one can flip a coin to make it land on heads or tails? Try this, grab a coin, place it on your indexfinger resting on the fingernail of your thumb, pay attention to which side is up, flip the coin and catch it flipping it to the oppisite wrist. What is it? Repete steps above a few times. Now place the coin with the heads side always up, and flip the coin. Your probably going to get the same % of results as the study in the story. What would be a real interesting story would be the nano second timing the human brain has to be able to catch the coin at nearly the the exact time every time.

## Measuring constants to determine probability still moves the goal post only 1 to 2%

Section 19.2 describes how to cheat at a coin-toss:

http://bayes.wustl.edu/etj/science.and.engineering/lect.19.pdf

There exist coin-toss programs that remains slightly more reliable because they are based on Numismatics which take into consideration variability of a coin’s size, distribution of weight, all are factors which can affect the outcome, and are incorporated into the algorithm.

You could get real crazy and incorporate environmental factors such as atmospheric pressure, wind speed and turbulence to further complicate your statistical prediction model, but at this point, you’re measuring environmental constants which affect a 1 to 2% variability from say, a 49-51 split. Visual representations of these complex equations can be quite beautiful. Consider the Mandelbrot set.

But why go to all this effort? Besides, you’re measuring the probability, it is just that- probability, and not the event’s outcome. The full accurateness of such a complex probability equation is truly non-computable until the actual event occurs. But attempting to go to such lengths to measure probability could at one point or another may influence the outcome, and that just ruins the fun.

well, that settles it, only a 20 sided dice roll is random enough for any kind of life and death (or stupid and dumb) decisions anyone might have.

## coin flipping

i know someone who can make you a double-headed £2 coin.

costs you £4 and you can never spend it, but it will make it’s value back quickly…

Flipping a coin is NOT random if you pay attention to all of the variables at work. The position the coin is in before it is flipped, the number of “flips” the coin does in the air, the result of the coin after that number of flips.

In fact, if you were to know those variables, you could predict the outcome 100% of the time.

1. Coin is on heads

2. Coin flips 4 times in the air.

3. Catch the coin and do the smacking on the back of your hand

4. Result will be tails. Every time.

If the coin only only made 3 flips, it will be heads. If the coin made 5 flips, it will be tails.

To full keep things random, the person flipping the coin must NOT be aware of what position the coin is before flipping, and they must NOT be able to manipulate or predict the number of flips it would make in the air.

A “coin toss” program in a computer will always be fully random because it does not take these variables into account. Since humans can, of course it’s not fool proof.

Calling 68% extremely predictable though…….. I don’t know if I agree with that in any case. Keep in mind that as unlikely as it is that all outcomes will be heads, it’s still theoretically possible for it to happen. It may have been just as likely to be 68% tails. Come back to me when it’s 90%.

## Re: Re:

True, but radioactive decay does seem to exhibit some randomness. You can make statistical analysis but you can’t know exactly when something will decay or not. Some other physical properties seem to exhibit some degree of randomness (even ones known to do so as far back as Newton).

Then again, from a theological perspective true randomness doesn’t really exist. Everything is ultimately the product of divine providence.

## random

http://dilbert.com/dyn/str_strip/000000000/00000000/0000000/000000/00000/2000/300/2318/2318.strip.gif

## Did they try it the other way around?

instead of trying to get more heads than tails, trying to get more tails than heads…

## Random vs uncertain

By “random”, we mean an event where all possible outcomes can be enumerated and we can attach probabilities to those outcomes.

If the outcomes and/or the probabilities cannot be enumerated, the situation involves “uncertainty” rather than randomness: That is, we do not know what we do not know.

The distinction is important.

The distinction is important.

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## Amazing

Amazing informtaion really interesting results

## 3D games

This is not a shuttlecock with a feathered tail and one end highly weighted far away from the tail. The embossed characters on either side are opposed only on the shortest axis if a basically flat object. The torque a heavier side would exert on the flipping coin is trivial.

## Surprising but true

Heads or tails makes common sense so wrong, but this experiment is truly surprising. Heads weight though, as pointed in the comments already.