Coin Tosses Not Totally Random

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):

  1. 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).
  2. 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).
  3. If the coin is tossed and allowed to clatter to the floor, this probably adds randomness.
  4. 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.
  5. A coin will land on its edge around 1 in 6000 throws, creating a flipistic singularity.
  6. 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.
  7. 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.