We have always been told that the coin toss is a perfectly random event with a 50% probability of heads vs tails. Turns out that is not exactly true… Researchers at the University of Amsterdam did a study where they tossed coins over 350,000 times to see which side they land on and found that instead of being 50-50 probability there is a 51% chance that the coin would land on the same side they started on. This study has been published in the
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], BFsame-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: Pr(heads)=0.500, 95% CI [0.498, 0.502], BFheads-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.
This means that we need to change the behavior of systems that depend on the coin toss to account for this slight bias. To give more context and the magnitude of the impact of this bias if it is not addressed the paper calculated the following:
Could future coin tossers use the same-side bias to their advantage? The magnitude of the observed bias can be illustrated using a betting scenario. If you bet a dollar on the outcome of a coin toss (i.e., paying 1 dollar to enter, and winning either 0 or 2 dollars depending on the outcome) and repeat the bet 1,000 times, knowing the starting position of the coin toss would earn you 19 dollars on average. This is more than the casino advantage for 6 deck blackjack against an optimal-strategy player, where the casino would make 5 dollars on a comparable bet, but less than the casino advantage for single-zero roulette, where the casino would make 27 dollars on average. These considerations lead us to suggest that when coin flips are used for high-stakes decision-making, the starting position of the coin is best concealed.
This is a fascinating study that kind of shows that nothing is ever random and that there is some implicit/explicit bias towards a particular outcome. Be it a coin toss or something else. Some people will take this example as more evidence that the universe we are in is actually a simulation, but I don’t agree with that. This is more of at a granular enough level nothing is chaotic/random.
Source: Boingboing: Coin toss not so random after all, says groundbreaking study
– Suramya