Flip a Coin

A fairer coin than the one in your pocket

A real coin toss is less random than it looks. In 2007 the mathematicians Persi Diaconis, Susan Holmes and Richard Montgomery analysed the physics of a flipped coin and concluded that it lands on the side it started on about 51% of the time, because a tossed coin wobbles as it spins. In 2023 a team led by František Bartoš tested that with 350,757 real flips by 48 people and measured the same-side tendency at roughly 50.8%. Small, but real — and a coin slapped onto the back of a hand, or one that bounces on a table, adds physics of its own.

This coin has no starting side and no physics. Each flip is one unbiased draw between two outcomes from crypto.getRandomValues, the generator browsers provide for cryptography: heads and tails are exactly 50% each, every flip is independent of every other, and nobody — this site included — can predict or steer the next one. The spinning animation is drawn after the result has been decided.

Streaks are normal

People expect a fair coin to alternate more than it does. In 100 fair flips, a run of at least six identical results — six heads or six tails in a row — happens about 81% of the time, and a run of seven or more about 54% of the time. In just 20 flips, a run of five or more turns up in roughly 46% of sequences. So when the tally shows a long streak, the line beneath it works out how likely a streak that long was for the number of flips so far. Usually the answer is: very.

The opposite mistake is the gambler's fallacy — the belief that after five heads, tails is 'due'. It is not. A coin has no memory, and the next flip is 50/50 whatever came before. Long-run percentages drift towards half because the number of flips grows, not because the coin corrects itself.

What the percentages will look like

Flip one coin ten times and seven heads is unremarkable. Flip a thousand and the share of heads will almost always be within a few points of 50%. With 100 flips, landing between 40 and 60 heads happens about 96.5% of the time — yet exactly 50 heads, the 'expected' result, happens only about 8% of the time. Flipping 100 or 1,000 coins at once shows both effects quickly: the percentage closes in on half while the exact count keeps wandering.

Using a coin flip to decide

A flip is the fairest way to settle a choice between two equal options — who goes first, which of two restaurants, who takes the first shift — because neither side can influence it. Agree which side is whose before flipping, and agree that one flip decides. 'Best of three' takes longer but still gives each side exactly 50%, so it changes nothing about fairness.

An old trick helps with decisions you care about: flip, and notice your reaction to the result. Relief means that was your answer; disappointment means you wanted the other option. The coin did not decide — it showed you what you had already decided.

In sport the toss chooses ends or kick-off in football and who bats first in cricket. For a casual game, a flip on a phone that both captains can see works just as well.

How multi-coin flips and the tally work

Choosing more coins flips them all at once. The first is shown on the big coin, and every coin appears in a row of small coins (the first 100 for very large flips). The tally counts every coin in order, so streaks carry across flips: tails at the end of one flip and tails at the start of the next continue the same streak. Everything stays in this tab — nothing is uploaded or stored — and Reset tally starts again from zero. If your device asks for reduced motion, the coin shows its result without spinning.