The art of making an unfair coin fair

Almost every coin has a head and a tail. These are called two states of the coin.

We use these coins in many of our decisions. A boy in love makes his first move towards the woman of his dreams by tossing a coin over & asking for a head (or a tail). The batting order in cricket is decided on the basis of a toss done using a coin. But are these coins a fair means of evaluatng our decisions?

Well I feel, not really.

Take a look at these coins that are/were in circulation in India. On one side, there's a full emblem or map or an animal or any big figure in addition to the year and most of the times, a few more words here and there. This is what we call the head of the coin.

On the other side, we have a number, two small designs, and a word or two. This is called the tail of the coin.

Now let us take a look at these coins that are/were in circulation in Dubai. On one side, there's a big occasion or a map or an animal or any big figure in addition to words written all around the coin. This is what we call the head of the coin.

On the other side, we have a number, a word, and words allound the coin. This is the tail of the coin.

Now this is the Singapore Dollar coin.

A big figure on both sides! However, on close observation, it can be seen that on the tail side of the coin (where $1 is written), the figure captures a wider surface area as compared to that on the head side.

Now, why am I mentioning the structuring of all these coins?

Well, I'm sure you'd have drop an ink pen by mistake at some point of time in your life. What happens? If undistrubed, it always fall nib-headed. Why?
You'd have heard of or seen in movies, people falling freely from big heights e.g. in bungee jumping. They always fall with their head rushing for the ground. Why?
The reason is that these are the heaviest parts in the body of the falling object. Nib is the heaviest part of most fountain pens' body. Head is the heaviest part in human body.

Similarily, the heaviest part of a coin's body should head towards the ground in case of a free fall. The centre of mass of the matter on either side of the coin falls at the centre of the coin. However, its value on both the sides is different. Higher the mass on one side, higher is the probability of getting the other side of the coin as the outcome of the toss. So, coins having a larger picture on the head side, should show you the coin's tail as a more frequent outcome. And the coins having a larger picture on the tail side, should show you the coin's head as a more frequent outcome.

In a nut shell when we toss a coin next time, we should bear in mind that there does not exist an equal probability of getting a head or a tail.

"In statistics, a fair coin is an idealized randomizing device with the two states which are equally likely to occur."
For this purpose, there are three possible solutions that come to my mind:

1. Device a coin with exact proportion of masses on both sides, and take utmost care that it is kept away from the wear and tear
2. Assign probabilities to the two sides of the coin in inverse proportion to their weights, and multiply te outcome of the toss by its respective probability. The final decision in this case would be an aggregate probability of both the outcomes.
3. Toss the coin really hard, so that the centrigugal force does not let the unequal weights on the two sides come into play

The third option is widely used by all of us. However, most of us do not know that this is the art of making an unfair coin fair!!!