## Flipping Out

All bets are off, because it turns out that flipping a coin — which is rather questionably used to tie-break elections across the world — isn't actually a fair fifty-fifty chance.

As part of a new, yet-to-be-peer-reviewed study, a small army of European researchers performed hundreds of thousands of coin flips in what may be the largest effort of its kind — and found "overwhelming evidence" of same-side bias, or that flipped coins are slightly-but-significantly more likely to land on the same side they started on.

"Despite the widespread popularity of coin flipping, few people pause to reflect on the notion that the outcome of a coin flip is anything but random," the researchers wrote in the study.

## Two Faced

This isn't a new conjecture, although it's almost certainly never been so extensively explored before. This latest work builds on the model proposed by Stanford mathematician and professional magician Persi Diaconis, who in 2007 published a paper that suggested coin flips were blemished by same-side bias.

Back then, Diaconis' estimate was that there's a 51 percent chance of a coin landing on the initial side, or just a one percent difference.

He was pretty much on the money. In this latest experiment, the researchers had 48 people — themselves included — endlessly flip coins from various countries, and then record whether they landed on the initial side.

In total, they performed a mind-numbing 350,757 coin flips. But it was worth it: the coins landed on the same side 50.8 percent of the time, they found, varying slightly between each person performing the flip.

## House Odds

If you can't make heads or tails of the finding, here's what happens after a coin leaves your thumb, based on Diaconis' model.

A small degree of precession, or wobble, is introduced into the coin as it tumbles through the air. The wobbling causes the same side to spend more time facing up. And the more time it spends facing up, however small, the more likely it'll be in that position when it lands.

That less than one percent of a difference may not seem like a lot, but František Bartoš, lead author of the study, put it this way: "If you bet a dollar on the outcome of a coin toss 1,000 times, knowing the starting position of the coin toss would earn you \$19 on average," he wrote on X, formerly Twitter.

In sum, that can add up.

"This is more than the casino advantage for [six deck] blackjack against an optimal player (5\$)," he wrote, "but less than that for single-zero roulette (27\$)."

More on mathematics: A Math and Physics Savant Reportedly Figured Out How to Beat Roulette