Probability, geometry, and dynamics in the toss of a thick coin
Ee Hou Yong, L. Mahadevan · American Journal of Physics · 2011
When a thick cylindrical coin is tossed in the air and lands without bouncing on an inelastic substrate, it ends up on its face or its side. We account for the rigid body dynamics of spin and precession and calculate the probability distribution of heads, tails, and sides for a thick coin as a function of its dimensions and the distribution of its initial conditions. Our theory yields a simple expression for the aspect ratio of homogeneous coins with a prescribed frequency of heads or tails compared to sides, which we validate using data from the results of tossing coins of different aspect ratios.