You Can Load a Die, but You Can’t Bias a Coin (2002) [pdf]
stat.columbia.edu
stat.columbia.edu
The article makes assumes that conservation of momentum guaranteeing a constant rotation rate guarantees fairness. But this relies on the assumption that biasing the coin cannot affect the timing of when it lands.
Of course, this doesn't bias the coin in either direction, it just lets the flipper choose which way to bias a particular flip.
If I toss a fair die and catch it in mid air with a robotic arm and high-speed camera so that I always catch it with the two face on top, it's still an unbiased die.
There's a big difference between "you can't bias a coin using weight" and "you can't bias a coin."
https://izbicki.me/blog/how-to-create-an-unfair-coin-and-pro...
It still seems to me possible to bias it with weight, based on angular momentum. I think a cavity internally that went from the center of the coin towards one side, with a small weight that moved up and down freely would cause one part of the spin to go faster (when the weight was in the center) than the other part, and would cause a bias if the spin were slow enough not to keep the weight locked at the outside (maybe a spring would be needed? Turns out I don't have a good intuition for what happens when you mix gravity with fast rotation)
Interesting that it seems to contradict the article linked here.
> In Section Three we prove that the angle ψ between M and the normal to the coin stays constant. If this angle is less than 45 ◦ , the coin never turns over. It wobbles around and always comes up the way it started. Magicians and gamblers can carry out such controlled flips which appear visually indistinguishable from normal flips.