Let’s say you’re to officiate the FIFA World Cup final between (you guessed it) the finalists. As a FIFA class one referee, you get to toss a coin just to decide which team kicks off. So is it heads or tails? How fair is even a coin toss if FIFA is all about “My Game Is Fair Play!”
Related media: How Random Is A Coin Toss? – Numberphile
Let’s Toss A Coin: Heads Or Tails?
According to a 2004 mathematical analysis by Persi Diaconis from the Department of Statistics at Stanford University, a penny is more likely going to land tails 80 percent of the time. We even bet that this probability is a 50-50 guess — its either heads or tails, isn’t it? Well… the technicalities seems to be against your thinking odds.
This is because a penny is slightly heavier on it’s head side than it’s tail, thus skewing the center of it’s mass and making the it uneven and more likely to land heads. However, the nickel is with underrated edges, and also more likely to be slightly biased when tossing.
(Fun fact: Magicians often shave the tails of their stunt coins, making it even more likely to land tails).
Whence Cometh Biases?
Tossing a coin doesn’t seem fair as you hope it does. If you toss a coin in air and let it freely land on the ground, it tends to spin for a while before settling down — that’s technically known as precession; and aforementioned, that spinning coin is ever more likely to land on… well, the uncertainty looms. Take note: the older the penny, the more likely that land bias looms, and a new penny… doesn’t change the odds, either. It seems all that dirt and junk on coins over time could set off it’s center of mass. Hmmm!
So is there any fair means of tossing a coin? Or you’re just being unfair? Maybe! Let’s ask: what if you catch it or let it drop? That’s silly! But not according to Diaconis. He claims it fairer to catch a coin in mid air than to let it bounce off the ground, spin unevenly, lose it’s balance until it falls flat. Here’s the deal: your hand isn’t that firm as that of the ground, so it’ll land whatever you stick your hand as it touches your palm. Spoiler: that’s not truly random.
What Are The Odds
But as it turns out, Diaconis still holds the belief that tossing a coin will more likely land on the head — 51 – 49 against the odds. It seems we didn’t answer our first question. Sorry about that. But once upon a time in 1986, mathematician Joseph Keller claimed to have proven that. He said the only fair means to toss a coin is to flip it in such a way that it spins perfectly around a horizontal axis through it’s center. But this would require someone with SuperMan abilities, so its a none starter. Next time you toss coins with a friend, opt for whatever side — the odds are against you both.
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Written by: Nana Kwadwo, Thu, Sep 12, 2019.