The oldest decision-maker there is
Romans played navia aut caput, ship or head, calling the side of a bronze coin before it landed. The appeal has not changed in two millennia: a coin is the fastest fair arbiter humans ever invented. It cannot be argued with, it holds no grudge, and it splits any two-way decision down the exact middle.
Except, it turns out, not quite. In 2007 the statistician Persi Diaconis showed that a caught coin precesses as it spins and spends slightly longer with its starting side up. A team in Amsterdam then put students through 350,757 recorded flips and measured the bias: about 50.8% for the side that started up. Small, but real, and enough to matter over many flips. The coin on this page has no starting side, so the fifty-fifty here is exact by construction.
- Exactly 50% heads, 50% tails, cryptographic source
- About 50.8% for the side that started face-up
- 1 in 4
- 1 in 32
- 1 in 1,024
- None; every flip starts from scratch
Coin flipping — frequently asked
This one is; a physical one isn't quite. A 2023 study that recorded 350,757 real coin flips found coins land on the same side they started on about 50.8% of the time, confirming a bias physicists had predicted from the wobble of a spinning coin. A digital flip has no starting side and no wobble: both outcomes are exactly 50%.
Assign the options before you flip, not after, and commit to the result. One flip settles a two-way choice; for three options, flip twice (heads-heads, heads-tails, tails-heads) and re-flip on tails-tails. There is also a classic shortcut: if you notice you're hoping for one side while the coin is in the air, you already have your answer.
Rome. The game was navia aut caput, "ship or head", after coins stamped with a ship on one side and the emperor's head on the other. The English kept the head and replaced the ship with whatever occupied the reverse, which is how the back of a coin became tails, the opposite end of the head.
Halve, and halve again: two heads in a row is 1 in 4, five in a row is 1 in 32, ten in a row is 1 in 1,024. Streaks look meaningful and aren't; each flip is independent and the coin keeps no memory. The tally above the coin tracks your session, and over enough flips it drifts toward even without ever owing you a correction.
Plenty. Portland, Oregon got its name on a best-of-three in 1845 (the loser would have called it Boston). The Wright brothers flipped for the first powered flight in 1903; Wilbur won the toss, stalled the plane, and the honor passed to Orville three days later. Every NFL game still opens with one, under rules that specify the coin toss in surprising detail.