Heads or tails? Choose wisely — the chances aren’t as equal as you think they are.
Scientists have discovered that there’s a natural bias that occurs when flipping a coin, according to a pre-print study published on arXiv.
Researchers at the University of Amsterdam were hoping to get an answer to the question: “If you flip a fair coin and catch it in hand, what’s the probability it lands on the same side it started?”
A team of experts flipped coins 350,757 times and discovered that the side that was originally facing up came back to the same position 50.8% of the time.
While just over 50% seems insignificant, the researchers said their findings are “overwhelming evidence for a same-side bias.”
So, if the coin starts heads up, it’s more likely it will land heads up, and vice versa.
Frantisek Bartos, lead author of the study and a psychological methods Ph.D. candidate at the University of Amsterdam, said that while it might not seem like a significant advantage to many, it’s more evident in the gambling world.
“If you bet a dollar on the outcome of a coin toss 1000 times, knowing the starting position of the coin toss would earn you $19 on average,” Bartos wrote on X, formerly Twitter. “This is more than the casino advantage for 6deck blackjack against an optimal player ($5) but less than that for single-zero roulette ($27).”
The study’s findings showed “compelling statistical support” for the bias originally predicted by Stanford mathematician Persi Diaconis and colleagues in 2007.
Diaconis originally predicted that the bias was 51%.
“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,” the study reads. “Our data lend strong support to this precise prediction: the coins landed on the same side more often than not.”
Diaconis realized that the chances of a coin flip weren’t even when he and his team rigged a coin-flipping machine, getting the coin to land on tails every time.
“Naturally tossed coins obey the laws of mechanics and their flight is determined by their initial conditions,” the 2007 paper said.
Bartos agreed, writing in his study, “Same-side bias originates from off-axis rotations (i.e., precession or wobbliness), which can reasonably be assumed to vary between people.”
“Future work may attempt to verify whether ‘wobbly tossers’ show a more pronounced same-side bias than “stable tossers,'” Bartos shared.