Have you ever flipped a coin as a way of deciding something with another person? The answer is probably yes. And you probably did so assuming you were getting a fair deal, because, as everybody knows, a coin is equally likely to show heads or tails after a single flip—unless it’s been shaved or weighted or has a week-old smear of coffee on its underbelly.
Let’s assume the coin is fabricated perfectly, down to the last vigintillionth of a yoctometer. And, since it’s possible to train one’s thumb to flip a coin such that it comes up heads or tails a huge percentage of the time, let’s assume the person flipping the coin isn’t a magician or a prestidigitator. In other words, let’s assume both a perfect coin and an honest toss, such as the kind you might make with a friend to decide who pays for lunch.
In that case, there’s an absolute right and wrong answer to the age-old question
Heads or tails?
The 50-50 proposition is actually more of a 51-49 proposition, if not worse. The sacred coin flip exhibits (at minimum) a whopping 1% bias, and possibly much more. 1% may not sound like a lot, but it’s more than the typical casino edge in a game of blackjack or slots. What’s more, you can take advantage of this little-known fact to give yourself an edge in all future coin-flip battles.
A good way of thinking about this is by looking at the ratio of odd numbers to even numbers when you start counting from 1.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
No matter how long you count, you’ll find that at any given point, one of two things will be true:
- You’ve touched more odd numbers than even numbers
- You’ve touched an equal amount of odd numbers and even numbers
What will never happen, is this:
- You’ve touched more even numbers than odd numbers.
Similarly, consider a coin, launched in the “heads” position, flipping heads over tails through the ether:
H T H T H T H T H T H T H T H T H T H T H T H T H
At any given point in time, either the coin will have spent equal time in the Heads and Tails states, or it will have spent more time in the Heads state. In the aggregate, it’s slightly more likely that the coin shows Heads at a given point in time—including whatever time the coin is caught. And vice-versa if you start the coin-flip from the Tails position.
