Coin Flip
Flip a virtual coin with cryptographic randomness, single or in bulk — plus the research showing real coins are not quite fair.
You could not detect a 51% coin if you tried
Real coins are very slightly unfair: a large 2023 study found that a flipped coin lands on the side that started facing up about 51% of the time, caused by a wobble in the spin rather than by the coin being lopsided. 51% sounds like something you would notice. Here is how many flips it takes to be 80% likely to catch a bias of each size, at the usual 5% significance:
| A coin favouring one side | Flips needed | At three seconds a flip |
|---|---|---|
| 51.0% | 19,615 | 16.3 hours |
| 52.0% | 4,898 | 4.1 hours |
| 55.0% | 778 | 39 minutes |
| 60.0% | 189 | 9 minutes |
| 70.0% | 42 | 2 minutes |
The counts collapse as the bias grows, because the sample you need scales with the inverse square of the deviation — halve the bias and you quadruple the flips. A coin running 60/40 is caught in an afternoon. A coin running 51/49 needs about 19,615 flips, which is over sixteen hours of continuous flipping with no breaks and no miscounts.
Which is exactly why the study that found the effect collected 350,757 flips, and why nobody had pinned it down before. It is not that the bias is hard to believe — it is that it is expensive to see.
And a long streak is not evidence of anything
The same arithmetic, run backwards. In 200 flips of a perfectly fair coin, the chance of getting seven or more in a row at some point is 80% — more likely than not. Streaks are what randomness actually looks like; a sequence that alternated politely would be the suspicious one. If a run of heads makes a coin feel loaded, that is a fact about how people read sequences rather than a fact about the coin.
How to use
- Flip once, or run a batch to see the distribution.
- Read the running tally of heads and tails.
- Use it to settle something genuinely arbitrary.
- Do not expect an even split in a small number of flips.
Frequently asked questions
Is a real coin flip fair?
Very nearly, and not exactly. A large 2023 study of hundreds of thousands of real flips found a small but consistent bias toward the side that started facing up — around 51 per cent — caused by a slight wobble in the coin's spin. It is not the side that is favoured, but the starting orientation.
Is this flip fair?
Yes, to the extent that the browser's cryptographic random source is uniform, which it is designed to be. Unlike a physical coin there is no spin, no starting face and no aerodynamics, so the outcome is a clean fifty-fifty.
Why did I get seven heads in a row?
Because that is what randomness looks like. A run of seven has a probability of about one in 128, which means it happens regularly across many flips. Genuinely random sequences contain more streaks than people expect, and sequences without streaks look suspicious to statisticians.
Does a run of heads make tails more likely next?
No — this is the gambler's fallacy, and it is remarkably persistent. Each flip is independent, so the probability stays at one half regardless of history. The coin has no memory, and no amount of previous heads makes tails due.
Why do results not even out in a short run?
Because the law of large numbers governs proportions over many trials, not absolute counts, and it never promises a correction. The proportion approaches one half as flips accumulate, while the absolute difference between heads and tails typically grows rather than shrinks.
What is it useful for?
Settling something genuinely arbitrary, breaking a deadlock, or making a decision you have already spent too long on. There is a reasonable argument that noticing which result you hoped for is more informative than the flip itself.
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