Coin Flip
Flip once, or ten thousand times
One flip shows a coin with the result. Set a higher count and the tool shows the whole sequence instead, plus how many landed each way and how long the longest run of the same side was.
Every flip comes from crypto.getRandomValues(). Nothing is sent anywhere.
A browser flip is fairer than a real coin
A tossed coin is not quite 50/50. Persi Diaconis and colleagues showed that a coin caught in the hand lands the same way up as it started about 51% of the time, because a spinning coin precesses — it spends slightly more of its flight with the starting face upward.
A 2023 study of 350,757 real flips confirmed it: 50.8% same-side. Small, but real, and it is a bias no amount of “flip it higher” fixes.
Spinning a coin on a table is worse. The rim of most coins is very slightly tapered, so a spun coin falls toward the heavier side far more often than half the time — for some coins as lopsided as 80/20.
This tool has no physical coin, no rim and no starting face. Both outcomes have exactly the same probability.
Streaks are longer than people expect
Ask someone to fake a hundred coin flips and they will almost never write a run of seven heads. In real flips, a run of seven or more shows up in about half of all hundred-flip sequences.
That gap is why the longest streak is shown. People reading a genuine random sequence often conclude it is broken, when a long run is exactly what randomness looks like. Statisticians use this — unusually short streaks are a good sign that data was made up.
The gambler’s fallacy grows from the same misreading: after six heads, the seventh flip is still 50/50. The coin has no memory of the previous six.
The flip you ignore tells you the answer
There is an old piece of advice: when you cannot decide, flip a coin — not to obey it, but to notice how you feel while it is in the air. Relief or disappointment at the result is information you already had and were not admitting.
It is more than folklore. Economist Steven Levitt ran a study where volunteers facing a genuine dilemma — quit the job, end the relationship — let a coin decide. Six months later, the people whose coin told them to make the change reported being measurably happier than those told to stay. The coin was not wise; it just broke a deadlock that inertia was winning.
So a flip is useful in two opposite ways: as a decision when the options really are equal, and as a diagnostic when they are not.
Coin flips as a privacy tool
Randomised response is a survey technique built on coin flips. Before answering a sensitive yes/no question, the respondent flips a coin in private. Heads, they answer honestly. Tails, they flip again and answer “yes” for heads, “no” for tails.
No individual answer can be held against anyone — any “yes” might have come from the coin. But because the researcher knows exactly how much noise the coin added, the population rate can be recovered by subtracting it. Truthful data, no identifiable admissions.
The same idea underpins modern differential privacy: add noise with a known distribution, and aggregate truth survives while individual truth does not.
Where coin flips get used
- Deciding — two options, no strong preference, no time to argue
- Who goes first — games, presentations, kickoff
- Teaching probability — flip 1,000 times and watch the ratio settle near 50%
- Breaking ties — used in real elections in several countries when a vote is exactly level