In the Physics of a Coin Toss, It Turns Out, There’s No Such Thing as 50-50 Odds
Three academics — Persi Diaconis, Susan Holmes and Richard Montgomery — made an interesting discovery through vigorous analysis at Stanford. As they note in their published results, “Dynamical Bias in the Coin Toss,” the laws of mechanics govern coin flips, meaning that “their flight is determined by their initial conditions.”
The physics and math behind this discovery are complex. To understand more about flips, the academics built a coin-tossing machine and filmed it using a slow-motion camera. This confirmed that the outcome of flips is not random. The machine could produce heads every time.
When people flipped the coin, results were less predictable, but there was still a slight physical bias favoring the coin’s initial position 51 percent of the time. The reason real flips are less certain isn’t just that the force can vary, it’s that coins flipped manually tend to rotate around several axes at once. They tumble over and over, but they also spin around and around, like pizza dough being twir