Flashback 2023 – The toss is not completely random

Coin tosses are a typical example when it comes to probability theory. This is pretty crazy, because such a throw could be described using classical mechanics. In principle, the outcome of the toss is completely predictable if you know the coin’s initial position, angle and speed. Twenty years ago, American mathematician Percy Diaconis had designed a setup to illustrate this: If you put a coin face down into the machine, it flips it up and you always get heads as a result.

Without this device, predicting the outcome of a coin toss would not be so easy, because the coin would have to spin to make the outcome as random as possible. Since people catch the coin in the air, you must also take into account the variable height at which they do so.

In 2007, Diaconis, in collaboration with Susan Holmes and Richard Montgomery, found that a fair coin launched with heads up has a slightly higher chance of landing that way: not a 50% chance, but a 51% chance. Are their theoretical predictions also true in practice? In October 2023, sports psychologist Erik Jan Wagen Makers from the University of Amsterdam published the answer as follows:

He received assistance from nearly forty co-authors: together they recorded 350,757 runs. For example, they found that coins have a 50.895% chance of landing on the same side they were launched. The good fit with the 51% prediction is even more surprising when you know that there is strong variation between individual results. I expect an IgNobel nomination.