# Coin Flips Aren’t Fair

April 19, 2009 Leave a comment

Categorize this under: I always thought that was true but never really *cared*. As it turns out, flipping a coin has a very slight bias towards the position it was flipped from. This tiny 51-49 ratio has to do with the aggregate amount of time flipping through the air. This link explains it pretty well:

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 17No 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 numbersWhat 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 HAt 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.

Another important point brought up is that spinning a coin has a relatively huge bias towards land tails up (20-80), so in those cases bet on tails. Another pro-tip: try to be the flipper so you know the side the coin starts in and thus can flip it into your other hand after catching it.