A coin with rounded edges won't land on its edge 1 out of 6000 tosses. A coin with a flat edge that is thicker than either of its faces (or just thick in general; doesn't have to be thicker than the faces) will land on its edge a great deal more often.
Also, a coin with a heavier "tails" side will more often land on heads in a spin.
I guess I should read the paper. Maybe it clarifies.
The 1/6000 figure comes from a paper "Probability of a tossed coin falling on its edge" from 1993. I looked for it in the hopes it clarified the type of coin used, but the paper, as far as I could find, is behind a paywall.
Nevermind, found a link that talked about the paper. They used a US 5¢ coin, a nickel which has a flat edge and I think the thickest edge out of all (common?) US coins. At least it has the thickest edge to face ratio in terms of width.
A coin with rounded edges won't land on its edge 1 out of 6000 tosses. A coin with a flat edge that is thicker than either of its faces (or just thick in general; doesn't have to be thicker than the faces) will land on its edge a great deal more often.
Also, a coin with a heavier "tails" side will more often land on heads in a spin.
I guess I should read the paper. Maybe it clarifies.