Coin Toss Modeling

TL;DR

This paper models the physics of a coin toss, analyzing the rigid body dynamics to determine unbiased probabilities of landing heads or tails under typical conditions.

Contribution

It introduces a physics-based model of coin tossing that accounts for rigid body motion and initial conditions to predict unbiased outcomes.

Findings

Unbiased probabilities of heads and tails are derived for typical initial conditions.

The model assumes no bouncing and no air resistance, simplifying real-world dynamics.

Probabilities depend on initial angular momentum and orientation.

Abstract

The torque-free motion of rigid body in gravitational field is analyzed. The coin lands on a soft surface (such as the palm of the hand) that allows no bouncing. The model assumes the coin as a rigid body with constant angular momentum vector in the body frame, and no air resistance. Unbiased probabilities of heads and tails are obtained for various initial conditions accessible to a usual person.