Fair coins tend to land on the same side they started: Evidence from 350,757 flips
arxiv.org
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, $\text{Pr}(\text{same side}) = 0.508$, 95% credible interval (CI) [$0.506$, $0.509$], $\text{BF}_{\text{same-side bias}} = 2359$. 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: $\text{Pr}(\text{heads}) = 0.500$, 95% CI [$0.498$, $0.502$], $\text{BF}_{\text{heads-tails bias}} = 0.182$. Furthermore, this lack of heads-tails bias does not appear to vary across coins. Additional exploratory 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. Our data provide compelling statistical support for the DHM physics model of coin tossing.

The paper shows some significant evidence that human coin flips are not as fair as I would have expected (plus probably a bunch of people would agree with me). There’s always some probability that this happened by chance, but this is pretty low.

Of course, we should be able to build a really accurate coin flipping machine, but I never would have expected such a bias for human flippers.

This is why science is awesome and challenging your ideas is important.

Edit: hopefully this is not too wrong a place, but Lemmy is small, and I didn’t know where else I could share such an exciting finding.

  • wmassingham@lemmy.worldEnglish
    0·
    9 months ago

    tl;dr:

    The standard model of coin flipping was extended by Persi Diaconis [12] who proposed that when people flip a ordinary coin, they introduce a small degree of ‘precession’ or wobble—a change in the direction of the axis of rotation throughout the coin’s trajectory. According to the Diaconis model, precession causes the coin to spend more time in the air with the initial side facing up. Consequently, the coin has a higher chance of landing on the same side as it started (i.e., ‘same-side bias’).

    “Higher chance” being 50.77% to land on the same side it started from. But this varies by person; apparently some people introduce more precession than others. But even if you could figure out how to do it reliably, I wouldn’t bet the farm on it.