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Mathematics > History and Overview

arXiv:2310.04153 (math)
[Submitted on 6 Oct 2023]

Title:Fair coins tend to land on the same side they started: Evidence
from 350,757 Flips

Authors:Frantisek Bartos, 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 Wagenmakers
Download a PDF of the paper titled Fair coins tend to land on the
same side they started: Evidence from 350,757 Flips, by Franti\v{s}ek
Barto\v{s} and 49 other authors
Download PDF

    Abstract: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, $\text{Pr}(\text{same side}) = 0.508$, 95%
    credible interval (CI) [$0.506$, $0.509$], $\text{BF}_{\text
    {same-side bias}} = 2364$. 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: $\text{Pr}(\text{heads}) = 0.500$, 95% CI [$0.498$,
    $0.502$], $\text{BF}_{\text{heads-tails bias}} = 0.183$.
    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.

          History and Overview (math.HO); Data Analysis, Statistics
Subjects: and Probability (physics.data-an); Other Statistics
          (stat.OT)
Cite as:  arXiv:2310.04153 [math.HO]
          (or arXiv:2310.04153v1 [math.HO] for this version)
          https://doi.org/10.48550/arXiv.2310.04153
          Focus to learn more
          arXiv-issued DOI via DataCite

Submission history

From: Frantisek Bartos [view email]
[v1] Fri, 6 Oct 2023 11:00:15 UTC (138 KB)
Full-text links:

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    Download a PDF of the paper titled Fair coins tend to land on the
    same side they started: Evidence from 350,757 Flips, by Franti\v
    {s}ek Barto\v{s} and 49 other authors
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