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

arxiv.org · 22,679 words · saved by 1 readers

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 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—DHM 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 = 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 ⁢

Fair Coins Tend to Land on the Same Side They Started: Evidence from 350 , 757 350 757 350{,}757 350 , 757 Flips František Bartoš 1∗ , Alexandra Sarafoglou 1 , Henrik R. Godmann 1 , Amir Sahrani 1 , David Klein Leunk 2 , Pierre Y. Gui 2 , David Voss 2 , Kaleem Ullah 2 , Malte J. Zoubek 3 , Franziska Nippold, Frederik Aust 1 , Felipe F. Vieira 4 , Chris-Gabriel Islam 5,6 , Anton J. Zoubek 7 , Sara Shabani 8 , Jonas Petter 1 , Ingeborg B. Roos 9 , Adam Finnemann 1,10 , Aaron B. Lob 2,11 , Madlen F. Hoffstadt 1 , Jason Nak 2 , Jill de Ron 2 , Koen Derks 12 , Karoline Huth 2,13 , Sjoerd Terpstra 1

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