“Fair Coins Tend to Land on the Same Side They Started: Evidence from 350,757 Flips”, František Bartoš, Alexandra Sarafoglou, Henrik R. Godmann, Amir Sahrani, David Klein Leunk, Pierre Y. Gui, David Voss, Kaleem Ullah, Malte J. Zoubek, Franziska Nippold, Frederik Aust, Felipe F. Vieira, Chris-Gabriel Islam, Anton J. Zoubek, Sara Shabani, Jonas Petter, Ingeborg B. Roos, Adam Finnemann, Aaron B. Lob, Madlen F. Hoffstadt, Jason Nak, Jill de Ron, Koen Derks, Karoline Huth, Sjoerd Terpstra, Thomas Bastelica5, Magda Matetovici, Vincent L. Ott, Andreea S. Zetea, Katharina Karnbach, Michelle C. Donzallaz, Arne John, Roy M. Moore, Franziska Assion, Riet van Bork, Theresa E. Leidinger, Xiaochang Zhao, Adrian Karami Motaghi, Ting Pang, Hannah Armstrong, Tianqi Peng, Mara Bialas, Joyce Y. -C. Pang, Bohan Fu, Shujun Yang, Xiaoyi Lin, Dana Sleiffer, Miklos Bognar, Balazs Aczel, Eric-Jan Wagenmakers2023-10-06 (science, probability theory)⁠:

Many people have flipped coins but few have stopped to ponder the statistical and physical intricacies of the process. In a preregistered study we collected 350,757 coin flips to test the counterintuitive prediction from a physics model of human coin tossing developed by Persi Diaconis. The model asserts that when people flip an ordinary coin, it tends to land on the same side it started—Diaconis estimated the probability of a same-side outcome to be about 51%.

Our data lend strong support to this precise prediction: the coins landed on the same side more often than not, Pr(same side) = 0.508, 95% credible interval (CI) [0.506, 0.509], BF_{same-side bias} = 2,364. Furthermore, the data revealed considerable between-people variation in the degree of this same-side bias.

Our data also confirmed the generic prediction that when people flip an ordinary coin—with the initial side-up randomly determined—it is equally likely to land heads or tails: Pr(heads) = 0.500, 95% CI [0.498, 0.502], BF_{heads-tails bias} = 0.183. Furthermore, this lack of heads-tails bias does not appear to vary across coins.

Our data therefore provide strong evidence that when some (but not all) people flip a fair coin, it tends to land on the same side it started. Our data provide compelling statistical support for Diaconis’ physics model of coin tossing.