Fair Coins Tend to Land on the Same Side They Started: Evidence from 350,757 Flips

Abstract

Many people have flipped coins but few have stopped to ponder the statistical and physical intricacies of the process. We collected 350,757 coin flips to test the counterintuitive prediction from a physics model of human coin tossing developed by Diaconis, Holmes, and Montgomery (DHM; 2007). The model asserts that when people flip an ordinary coin, it tends to land on the same side it started. Our data support this 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], BFsame-side bias=2359. 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], BFheads-tails bias=0.182. Additional analyses revealed that the within-people same-side bias decreased as more coins were flipped, an effect that is consistent with the possibility that practice makes people flip coins in a less wobbly fashion. 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. Supplementary materials for this article are available online, including a standardized description of the materials available for reproducing the work.