It’s generally assumed that a coin toss is “fair” because it’s considered “random” as long as you don’t use a double headed coin. In fact professional sports like football use it. While previously known or at least suspected, it’s not so random. Research shows it has a 1% bias. Making the odds 51-49, hopefully in my favor. They were even able to build a machine to predictably flip a coin.
James Devlin at Coding The Wheel has a great writeup simplified for those who don’t have a head for all the math (pun intended):
- If the coin is tossed and caught, it has about a 51% chance of landing on the same face it was launched. (If it starts out as heads, there’s a 51% chance it will end as heads).
- If the coin is spun, rather than tossed, it can have a much-larger-than-50% chance of ending with the heavier side down. Spun coins can exhibit “huge bias” (some spun coins will fall tails-up 80% of the time).
- If the coin is tossed and allowed to clatter to the floor, this probably adds randomness.
- If the coin is tossed and allowed to clatter to the floor where it spins, as will sometimes happen, the above spinning bias probably comes into play.
- A coin will land on its edge around 1 in 6000 throws, creating a flipistic singularity.
- The same initial coin-flipping conditions produce the same coin flip result. That is, there’s a certain amount of determinism to the coin flip.
- A more robust coin toss (more revolutions) decreases the bias.
There’s also some potential strategy, a worthwhile read.
There paper is also available as as well if your so inclined, though you’d need to be a real math/stats nerd to want to read that.