Is a coin toss a 50/50 call?
Contrary to popular belief, some say it’s no even money shot
It’s amazing what you can find on the internet.
Things which you thought were etched in stone. What you and I would call a “fact”. These are often dispelled, debunked, or at the very least discredited.
So here’s one for you…
Like me, you’ll be familiar with the statistics related to the tossing a coin.
The fact that when you toss it, it’s 50/50 that it’ll be heads or tails, no matter what has happened before.
If the last 10 times its landed on heads (or tails)… it doesn’t make it any more or less likely that the next time you flip the coin it’ll come down as tails (or heads).
(This is something touched upon in a previous post about “recency bias”)
Each time you toss the coin, it is an individual episode. One that contains no element of pre-determinism. It is, in effect, in a vacuum.
In short, whatever has occurred previously will have no bearing on what is to follow.
One coin. Two sides. Heads. Tails. Even money the pair.
Well, here we get lost down one of the many rabbit holes that the internet provides, in this case found on the website that you might have come across – Ripley’s Believe It Or Not!
The article reads as follows…
Is a coin toss fair?
Persi Diaconis did not begin his life as a mathematician.
In fact, as a teenager, he was doing his best to expose scammers at a Caribbean casino who were using shaved dice to better their chances against their customers.
He would go on to tackle other numbers games, like how shuffling decks of cards didn’t really mix up the deck.
By that time he’d dropped out of high school and was traveling the country with a magician, perfecting his sleight of hand. He did that for 10 years, and by age 24, he was taking classes at City College of New York, paying his way by doing magic tricks during the day. After getting two of his mathematical card tricks published in Scientific American, he used his editor’s recommendation to get him into Harvard as a statistics student. Three years later, he’d earned his doctorate and joined the Stanford faculty.
Diaconis then began to study other instances of change, questioning whether the things we think we know are, in fact, true.
Like the coin toss, for example. Most people assume the toss of a coin is always a 50/50 probability, with a 50 percent chance it lands on heads, and a 50 percent chance it lands on tails.
Not so, says Diaconis. And, like a good mathematician, he’s proven it.
“I have spent years analyzing the basic images of randomness” he said in an episode of the Annenberg Learner Against All Odds series.
“First of all, it’s possible to make things random. If you flip a coin quite vigorously, it’s as close to being a fair event – 50/50 – as I know, if you flip it and catch it on your hand…”
“However, we usually don’t do them vigorously… If you think about it the least little bit, you’ll realize it’s not random at all. In fact, there are people around carnivals, and I, on occasion, have been able to flip a coin and keep control over it.”
Probability versus physics
The coin toss is not about probability at all, he says. It is about physics, the coin, and how the “tosser” is actually throwing it. The majority of times, if a coin is heads-up when it is flipped, it will remain heads-up when it lands. Diaconis has even trained himself to flip a coin and make it come up heads 10 out of 10 times.
A similar effect is seen if the coin is spun.
Because of the way most coins are made, the “heads” side can weigh more, which means it will fall on that side, leaving the other side up more often. Further, some magicians will have coins that are shaved, giving more weight to one side. The point? It’s not 50/50 at all.
“Most people think, this guy’s nuts” Diaconis said in an interview with the Numberphile website.
“But if pressed, people, when pushed, seem to think that a coin dropping on the floor is fairer… when a coin hits the ground, before it dies, often it spins around on its edge. And some of that edge bias comes in.”
“Coin tossing is pretty close to fair.”
But it’s not 50/50.
So there you have it.
Tossing a coin isn’t what we thought it was all along.
And, by the application of physics (or gravity, you might say), as well as some clever slight of hand, you can influence the outcome to suit your own purposes.
Well, I guess it makes for an interesting read.
But if the two sides of the coin are of equal weight – the image of the head and tail being the same – then that would take out part of the argument made by Diaconis.
Likewise if we toss the coin “vigorously” we take out the ability of the tosser to use some degree of skill or manual dexterity to affect the way the coin lands.
So doesn’t that dispel what the author is trying to argue?
OPINION: Whilst it makes a good headline, and provides a bit of “click bait” for the website in question, the evidence used to prove this argument actually goes a long way to proving the exact opposite of what Diaconis is trying to say. Namely that an equally weighted coin, thrown at random, will have a 50/50 probability of landing heads or tails. It’s only when you influence the experiment by external forces that you can affect the way the coin lands and slew the odds one way or another. That said, I’ll probably call heads over tails next time I’m asked!!