Researchers at the University of Amsterdam recently made a surprising discovery that challenges long-held assumptions about the randomness of coin tossing. After flipping coins over 350,000 times, the largest study of its kind, they found that coins have a slight tendency to land on the same side they started on.
The data showed a small but statistically significant same-side bias of 51%, just slightly higher than the 50% predicted by chance. This subtle yet remarkable finding defies the conventional wisdom that coin flips represent a random and unpredictable 50/50 outcome.
Coins of 46 different currencies were flipped by hand and caught in the palms of 48 student participants to record the landing side. The data collection process required meticulous recording over many months, with flipping sessions videotaped to validate the results.
This same-side bias was first predicted in a physics model by scientist Persi Diaconis. His theory suggested that the physics of coin flipping, with the wobbling motion of the coin, makes it slightly more likely to land on the same starting side. The Amsterdam team’s real-world data provides strong evidence confirming this counterintuitive idea.
The implications of the findings suggest the possibility that activities relying on coin flips — like gambling and certain random number generation processes — may need to adjust to account for this newly discovered bias.
From the paper:
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.