# The Story of Heads and Tails

We are all very used to saying “heads and tails” when describing opposite sides of a coin, but have you ever stopped to wonder why they are called such? On many coins, the “head” element is clear – the head of a king, queen, emperor, president, or other notable person appears on one side.

But it is rare to find an actual tail on the opposite side. In fact, the two sides are more correctly called the obverse side and the reverse side, with heads being obverse and tails being reverse.

In ancient China, the two sides were known as “ship” and “head”, as one side of a coin often showed a ship, and the other side showed a head.

The most likely theory as to why we choose to say heads and tails is that they are considered to be body-opposite parts. Imagine a cat or a dog – there’s a head at one end, and a tail at the other.

Coins were first developed around 700 years BC – that’s almost 3000 years ago. There have not always been heads marked on a coin, but all coins usually had a way of telling one side from another, even if it were as simple as having a cross on one side and leaving the other side blank.

As manufacturing techniques developed over time, intricate patterns and pictures were added to coins, including mythological creatures and animals. As the creatures were often on the opposite side to the picture of a head, this may be another reason that the reverse side of a coin is named tails.

The patterns and marks were originally put on to coins individually, but it didn’t take long for stamps to be developed. These are engraved with the pattern that will end up on the face of the coin, only in reverse – the image is mirrored, and any raised areas are made lower on the stamp. While the coin is being made it is heated to allow it to be formed into a shape. As it cools, striking it with the stamp will create an impression on the coin, giving the desired pattern.

Alternate methods for creating coins include using a mold with the pattern built into it which in earlier times allowed for a more accurate centering of the image. These days, industrial machines take care of the process.

Modern coins are made in such a way that if they are rotated on a vertical axis, the front and back images both appear upright. Mis-struck coins, or those where the front and back do not line up, can become worth far more than their face value due to their rarity.

## Heads and Tails and Edges?

When considering choices, a element of chance is often required. Rolling dice won’t help if you need a simple yes or no result unless you choose a set of number to represent each option, and so flipping a coin is the preferred and easier method for many. When used in this way, a coin could be considered a 2-sided die.

However, a third option remains. What if the coin were to land on its edge? While it sounds like a ridiculous notion, it is not at all impossible. In fact, the odds of an American nickel landing on its edge is something like 6000 to 1.

Many physical factors work to prevent this happening regularly, such as the rotational force with which a coin is flipped. But if the coin were to land against another object, for example a stone or a wall, the chances of it remaining on its edge increase as it will be propped up on at least one side.

Coins are not always round. Some have flat edges and have five or more angles to these edges. This makes it even more likely that the coin will come to rest on its edge under the right conditions.

## Do different shaped coins flip differently?

Round coins and other coins will have the same chance of landing on heads or tails when flipped, as there is nothing intrinsically different about them. Of course, manufacturing defects or excessive decoration on one side of a coin may make it more likely to land in a particular way, but this is not a product of the silhouette of the coin.

Coins with angles rather than a smooth circular edge may encounter more wind resistance than their round counterparts, which may reduce the number of times it is able to spin through the air.

This will not affect the chance of heads or tails coming up but may make it easier to “force” a result – if you know that the coin will only have a limited number of rotations, it may become obvious how it will land from noting which side was up when it was initially flipped.

A good strong spin on the coin should reduce the chance of this happening, and in any case the result will only go one way or the other.

## Will it be head or tails?

#### Coin throwing has always been something that you have been looking at when it comes to deciding something for a fight.

Whether it has been sport-related events or political choices, the coin flip method has always been popular. You have always chosen this method as it ensures that the outcome will always be random and that there are no people who are being disadvantaged. In other words, the chance of winning or the risk of losing has always been 50/50.

## But is it always a 50%50 chance?

In fact, there are more researchers who have queued for some doubt about this historical method of determining outcome of controversy. Nothing less than 3 American researchers have reported as advocates that this method is actually not as 50/50 based as one has just believed and believed.

Throughout their 30-page long report, they have explained that a coin box actually has a tendency to show one side to another. Through continuous tests and performances, these researchers have come to the conclusion that the side of the coin facing is the side that has the greatest chance of showing when it falls. Of course, there have also been a lot of mathematics and physics with over to create a precedent for their postulates.

The skepticism among the general people and, in fact, a large part of the research circle is great. Could it really take care that some of the most fundamental in our logical understanding, in fact, is not entirely true? Man has almost per definition understood that the outcome of a coin throw is 50/50, but now someone comes and claims opposite. The actual coin throwing the idea and the theory is fundamental in the world of mathematics and physics. This theory has often formed precedence for the general probability calculation.

There are some Danish researchers who have been asked to take a closer look at it to see if there should be anything to come.

## Dynamical bias in the coin toss?

If we start to focus on what it actually was that the report “Dynamic bias in the coin toss” said about the phenomenon of coin throw. The report was published in the highly reputed magazine, SIAM Review, back in 2007.

As said, the conclusion was that we could no longer rely on one of the very basic elements in probability and statistics, namely that the outcome of a coin throw is completely random – that is, the so-called fifty fifty. In their scientific report, it appears that it actually means that a player can gain a statistical advantage if the player has the opportunity to see which side is facing the coin. The actual probability of the outcome would be 51/49 as it is more likely to land on the side that had turned up when it was thrown. So if we say you’re ready for a flat or crown, and for example you can win by guessing correctly, you would get an advantage if you knew which page is coming up. If the coin is so that it faces the side of the page, then choose this as you are more likely to win. That is what the American researchers have achieved through their report.

It also means that you may end up putting yourself in a potentially worse situation if you know the position of the coin from the start. So if it’s about losing, then you’ll be able to guess by the side down, with 49% probability guessing the correct outcome, which of course is worse odds than the other side.

It’s not a cheating coin, it’s a cove for a flat or crown

For many people, this whole experiment seems quite stupid, as it does not make sense for one side of the coin to be better than the other when it is going to hit a flat or crown. It depends only on how fast it is thrown around, how long it is up and such things.

However, American scientists have tried to make this experiment as perfect as possible. This means that they did not use humans as this could contaminate the whole experiment. Instead, they built a machine that made sure to throw the coin up. This machine was filmed, so you could reproduce each single image in slow motion so that you could study and analyze more easily. To get to the results a lot of different math and physics have been used.

## Why have one ever questioned the essence of a coin throw?

To many, there would hardly be anything imaginative enough to question. Would you ever doubt whether 2 and 2 are 4? Similarly, this seems unlikely, of course, why you also ask yourself – how did American scientists come up with this idea?

The inspiration should come from one of the three researchers themselves – more specifically Persi Diacons. The idea originated early in his career, where his profession was a little different than his professor’s profession in mathematics at Stanford University. He was nothing less than a magician, and had learned how he could determine the outcome of the coin when he hit the pitch or crown.

As a magician you can see why this property could be quite ideal, so the idea may not seem so crazy.

However, it should be pointed out, for the good reason, that Diacon does not use any cheating coins. It is not heavier on one side or another that could mingle the outcome to his advantage. It’s a whole real coin he’s using.

## Does it make any sense that heads or tails are different?

There are probably some who are sitting and thinking now why why is there any difference in the side when it does not matter anyway. It’s an unfair game, so if you know the side facing up, you’ll always be more likely to guess that’s the side that’s going to turn around by a coin toss.

But why is it actually more likely that the coin lands with the same side as it originally had?

f we try to simplify the process a little, then we can try to get an example, so that could explain it.

We start looking at a coin, which right now has the flat side facing up. You put it on your finger so you’re ready to shoot it up in the air.

Now you shoot it off – the coin has started turning around, just as it should be. One of the following statements will apply in this process. Either, the flat page will turn up several times or they will turn up as many times as well.

It also means that when you look at the crown page, it will never turn up several times than the flat page. It will therefore be possible to turn up the same number of times as the tails.

*Susanne Ditlevsen, is a professor at the University of Copenhagen explaining the following:*

»In some cases, the coin may not rotate around when you throw it into the air. For example, the heads side might continue to turn upward while the coin is up in the air. Overall, it helps to give this oversight a coin landing with the same side upwards as when it started.«

## Man wants to control everything – but it is not always possible!

It is possible to get a coin to land in exactly the same way if you can set up the perfect conditions, says Susanne Ditlevsen. If you take the exact same starting point for the coin every time, while throwing it up at exactly the same speed, you will be able to control the outcome of how the coin will land – for it will land the same way each time.

“It also shows the Americans in their trials where they build a machine that causes the coin to land one’s positions in 100 percent of the cases. Of course, in such scenarios there is of course no coincidence. Everything is controlled and ruled around this coin box “, says Susanne Ditlevsen, adding further:

»The reason we humans can not recreate this scenario – the opposite coin-throwing machine – is that we can not control the same parameters as a machine can. It has been done mathematics. For good reasons, we can not always ensure that the coin is perfectly placed on the finger nor guarantee that we will throw the coin with the same cancer. Therefore, American researchers calculate the many possible starting positions a coin may have. Based on these calculations, they can predict that there will still be an overweight of distributions where the coin lands with the same side upwards.«

## The same is true of something like dice toss, too

The report taken by the team of American scientists is not completely stupid, it is actually that, in fact, is something that applies to several of these common probabilities as we know today. Another model is the dice box, which does not quite have the same two possible outcomes, but in principle it has the same tendencies in its form and performance.

However, it is important to note that when looking at the Americans’ report about coin throws, it seems that this only works when the coin is caught in the air. As soon as the coin falls on a surface, there will be external variables that are not controllable – at least not in this experiment. It may easily be possible to find mathematical formulas that could apply to this scenario, but that was not what they wanted to demonstrate with this experiment.

However, such models were used by Carsten Knudsen when he started his own research on dice cast in the late 80’s.

## Should we then withdraw everything from the theory of probability?

Now you are sitting safely and have yelled at the gun. In no way can we continue to teach that the probability is 50/50 by coin, nor can we use this as a priority when it comes to explaining about it. We have just concluded that this is no longer the case, we should not all know that? Good points – but it’s not so bad that we have to change the teaching.

“Pure statistics we operate with such small differences that you would never actually be able to take advantage of this if you just throw the coin up as a regular user. That does not mean that you theoretically could not get a crown 20 times in a row, if the flat side turns up when the coin is thrown. ”

“You usually do not sit and think about which side is on top of the coin when, for example, you have to draw lots of football. You only get something. It’s not like watching football players go to the referee to look at the side facing up. In the majority of cases, the coin is also just raised by the pocket and thrown into the air, after which you have to call the page you want. There is nevertheless no way to see if it was the one side or the other side that turned up. “Carsten Knudsen explains.

Susanne Ditlevsen totally agrees, and she certainly does not see any problems because we say in Denmark that the coin throw gives a 50/50 chance.

»After I have read this survey, I can not say that I will try to keep an eye on the page facing up, and then take that page. It’s not because it certainly would give me justice, there’s almost no difference in probability, but that would nevertheless give me a little advantage.« the professor Susanne Ditlevsen says.