Main content
How fair is a fair coin flip?
Date created: | Last Updated:
: DOI | ARK
Creating DOI. Please wait...
Category: Project
Description: Coin flipping has been used as a classic example of a random process in introductory statistics classes for centuries. A good old-fashioned coin flip is still used as a way of determining the starting party in games such as soccer, football, or volleyball, which can lead to a slight advantage. Is it, however, possible to justify decisions based on a coin flip to be random, even though the standard physics model can describe the outcome of a coin flip as a function of the initial velocity and spin? Keller (1986) showed that, under a sufficient initial speed and spin, even a minor difference in the initial conditions renders the outcome essentially random. Our inability to produce the exact initial conditions then confirms our day-to-day experience of the randomness of a coin-flipping process. Nonetheless, Diaconis and colleagues (2007) expanded the coin-flipping model by accounting for "precession" (a change in the rotational axis of the coin throughout the flip trajectory) and theorized that coins flipped with sufficient initial speed and spin would more often land on the same side as they were flipped from. Diaconis and colleagues estimated that the degree of the same-side bias is small (~1%), which could still result in observations mostly consistent with our limited coin-flipping experience. This project aims to compare Diaconis's and the fair coin flip hypothesis experimentally. Diaconis, P., Holmes, S., & Montgomery, R. (2007). Dynamical bias in the coin toss. SIAM Review, 49(2), 211-235. Keller, J. B. (1986). The probability of heads. The American Mathematical Monthly, 93(3), 191-197.