Long the premise of every lesson on probability, coin tosses are taking a beating (thanks Boing! Boing! for the share). Some interesting research (Diaconis, Holmes, and Montgomery) uncovered these biases:
- 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.
Always the hacker, I suggest following the link for strategies to winning a coin toss.
Is there a place for this research in my math classes?
Filed under: spherical cows-and-Other-Oversimplifications.