Coin Flip

What a fair coin actually does

The range a genuinely fair coin lands in 95% of the time, computed from the exact binomial distribution when this page was built. This is the same calculation behind the fairness line in the tool.

• 10 flips 2 to 8 heads (20.0% – 80.0%) A run outside that range happens to a perfectly fair coin about one time in twenty. Longest streak you would typically see: 3 in a row.
• 20 flips 6 to 14 heads (30.0% – 70.0%) A run outside that range happens to a perfectly fair coin about one time in twenty. Longest streak you would typically see: 4 in a row.
• 50 flips 18 to 32 heads (36.0% – 64.0%) A run outside that range happens to a perfectly fair coin about one time in twenty. Longest streak you would typically see: 6 in a row.
• 100 flips 40 to 60 heads (40.0% – 60.0%) A run outside that range happens to a perfectly fair coin about one time in twenty. Longest streak you would typically see: 7 in a row.
• 500 flips 228 to 272 heads (45.6% – 54.4%) A run outside that range happens to a perfectly fair coin about one time in twenty. Longest streak you would typically see: 9 in a row.
• 1,000 flips 469 to 531 heads (46.9% – 53.1%) A run outside that range happens to a perfectly fair coin about one time in twenty. Longest streak you would typically see: 10 in a row.
• 10,000 flips 4902 to 5098 heads (49.0% – 51.0%) A run outside that range happens to a perfectly fair coin about one time in twenty. Longest streak you would typically see: 13 in a row.

Is a coin flip really 50/50?

A digital one is. A physical one is close, and interestingly not exact.

A coin flipped into the air does not spin neatly about a single axis. It wobbles, and that wobble means it spends slightly more of its flight showing the face it started on. Persi Diaconis and colleagues predicted this from the mechanics, and in 2023 a large team tested it properly by flipping coins 350,757 times across dozens of currencies. They found the coin landed on the same side it started about 50.8% of the time — a real effect, consistent across coins, and far too small to notice in ordinary use.

Spinning a coin on a table is a different matter and can be badly unfair. The rim of a coin is rarely symmetric, and a spinning coin falls toward the heavier side. Some coins spin heads-up closer to 80% of the time. If someone offers to spin rather than flip, that is the one to refuse.

A digital flip has no physics to be biased by. What it can have is a badly built random number generator, which is worth a paragraph of its own.

What makes this one unbiased

Two things, and the second is the one most tools get wrong.

First, the randomness comes from your browser’s cryptographic generator rather than the ordinary one. The ordinary generator is fine for shuffling a playlist and is not designed to be unpredictable.

Second, the conversion from a random number to a side is done carefully. The obvious approach is to take a large random number and use its remainder after division — and unless the range divides evenly, that quietly favours some outcomes over others. For a two-sided coin the effect is negligible, but the same code path drives our dice and wheel where it is not, so we do it properly everywhere: values that would cause the skew are discarded and a fresh one is drawn.

There is also something this tool deliberately does not do. Some flip tools quietly break up long runs to make the output look more random. That makes it less random. Real randomness produces streaks, and a sequence with no streaks in it is the suspicious one.

Why streaks feel wrong

The most common reason people go looking for a coin flip tool is that a real one just gave them five tails in a row and they want to know whether that is normal. It is.

The longest run in a sequence of fair flips grows roughly with the logarithm of how many flips you make. In 32 flips you would typically see a run of about five. In 100, about seven. In 1,000, about ten. Those are typical values, not extremes — half of all sessions will do better than that.

Put the other way round: if you flip 100 times and the longest run you see is three, that is far more surprising than seeing a run of seven. Human beings asked to write down a "random" sequence almost always produce one with too few streaks, which is how researchers spot fabricated data.

The tool shows your longest run alongside what is typical for the number of flips you have done, so you can check your intuition against the arithmetic instead of your gut.

The gambler's fallacy, and the true thing it gets confused with

After five tails, heads is not "due". The coin has no memory and the next flip is 50/50. Everyone knows this and almost everyone feels otherwise, which is worth understanding rather than just being told off about.

The confusion comes from a real law that says something adjacent. The law of large numbers says that as you keep flipping, the proportion of heads converges on one half. That is true. What people hear is that the counts even out, and that is false. Consider what actually happens:

• After 10 flips you might be 7–3. That is 70%, and a gap of 4.
• After 1,000 flips you might be 530–470. That is 53%, and a gap of 60.
• After 100,000 flips you might be 50,200–49,800. That is 50.2%, and a gap of 400.

The percentage marches steadily toward half. The raw gap typically gets bigger. The early imbalance is never corrected; it is diluted. Nothing reaches back to fix a run of tails, and that is exactly why the fairness line in this tool is stated as a range of counts that widens with the number of flips rather than as a fixed target.

How to actually use a coin flip to decide something

There is a well-known trick and it is better than it sounds. Flip the coin, and before you look, notice what you are hoping for. If you catch yourself wanting tails, you have your answer and the coin has done its job without needing to be obeyed.

This works because most decisions that feel balanced are not. They feel balanced because one option is easier to justify and the other is what you want, and being forced into a moment of anticipation separates the two. A coin flip is a preference detector at least as often as it is a randomiser.

When the decision genuinely is balanced, the flip settles it and saves everyone the discussion. That is the other legitimate use: not to find the right answer, but to stop spending time on a question where both answers are fine.

When a coin flip is a bad idea

It is the wrong tool when the options are not equally good, when you would ignore the result, or when the cost of being wrong is high. Randomising a decision you would agonise over is not decisiveness; it is a way of avoiding the thinking. And if you would re-flip on a result you did not like, you were not really asking the coin.

Yes or no, and your own options

Heads and tails are conventions, not constraints. The sides selector switches to plain yes/no for questions that want a direct answer, or to two labels of your own for anything else — two restaurants, two names, who goes first.

Your labels appear on the coin itself and in the tally underneath. Changing what the sides mean resets the running count, because a tally that mixed "heads" with "pizza" would not mean anything.

For more than two options a coin is the wrong shape. Flipping twice to pick between four things works and is easy to get wrong; the Name Wheel handles any number of options directly and shows each one its real share. For picking a number, the Dice Roller covers everything from d4 to d100.

Flipping many at once

The count control goes up to 100 coins in a single flip, which is the fastest way to watch the statistics behave. Flip 100 at a time a few times over and two things become obvious: the percentage creeps toward 50 and stays near it, while the raw difference between the two sides wanders further from zero than you would expect.

It is also just practical. Simulating a hundred trials of something with a 50% chance takes one click instead of a spreadsheet.

Reading the fairness line

Once you have flipped at least twenty times, the tool compares your result against the range a fair coin produces 95% of the time and says whether you are inside it.

That range is computed exactly, from the binomial distribution, rather than from the usual normal approximation. The approximation is genuinely poor at the counts people actually flip — at twenty or thirty flips it is off by enough to change the verdict — and the exact calculation is not much harder.

Two cautions on interpreting it. Falling outside the range is not proof of bias: by construction it happens to a perfectly fair coin about one session in twenty, and if you keep starting fresh sessions you will hit one eventually. And falling inside is not proof of fairness either; with fifty flips, a coin would have to be very heavily weighted before you could tell. Detecting a small bias takes thousands of flips, which is precisely why the 2023 study needed 350,757 of them.

Related tools

The Dice Roller handles anything with more than two outcomes and shows the exact probability curve for whatever you roll. The Name Wheel picks one entry from a list, with weighting and automatic removal. The Team Splitter divides a group into balanced teams, and the Secret Santa tool draws names so that nobody gets themselves.

Common questions

Is this coin flip actually 50/50?

Yes, and more reliably than a real one. Each flip comes from your browser’s cryptographic random number generator, and the raw value is rejection-sampled so neither side is even fractionally favoured. There is no tracking of what you flipped before, no weighting, and no attempt to make the results "look random" by breaking up streaks — which would make them less random, not more.

Is a real coin flip 50/50?

Very nearly, but not exactly. A coin caught in the hand lands slightly more often on the face it started on, because a flipped coin precesses rather than rotating cleanly about one axis. This was predicted by Persi Diaconis and colleagues and then tested in 2023 by a team who flipped coins 350,757 times: they found the same-side result came up about 50.8% of the time. Spinning a coin on a table is much worse, because the rim is usually not symmetric, and can be badly biased on some coins.

The effect is far too small to exploit casually, but it does mean a digital flip is the fairer of the two.

I got six heads in a row. Is something broken?

Almost certainly not. Runs are much more common than intuition suggests. In 100 flips the longest run is typically six or seven, and a run of six somewhere in a session of that length is the ordinary case rather than the exception. The tool shows your longest run next to what is typical for the number of flips you have done, so you can see whether it is actually unusual.

A run alone is never evidence of bias. What would be evidence is the overall split drifting outside the range shown in the fairness line, and staying there as you keep flipping.

After five tails, is heads now more likely?

No. The coin has no memory, so the next flip is 50/50 regardless of what came before. This is the gambler’s fallacy and it is remarkably persistent, partly because of a real effect that gets misremembered: the law of large numbers says the proportion converges on half as you keep flipping, but it does so by swamping early results with later ones, not by correcting them. The gap in raw counts typically grows; it is the percentage that settles down.

What does the fairness line mean?

It compares your results against the range a genuinely fair coin produces 95% of the time. In 100 flips a fair coin lands between 40 and 60 heads with about that probability, so anything in that window is unremarkable. Falling outside is not proof of anything either — by definition it happens to a fair coin roughly one session in twenty.

Can I use my own two options instead of heads and tails?

Yes. Switch the sides selector to "my own two options" and type whatever you are deciding between. The labels appear on the coin itself and in the running tally. There is also a yes/no mode for questions that need a straight answer.

Can I flip more than one coin?

Up to 100 at once. The coin shows the first result and the rest are listed beside it, with everything folded into the running tally. Flipping in batches is the quickest way to watch the percentage settle toward half while the raw gap between the two sides keeps wandering.

Is anything I flip sent anywhere?

No. Every flip happens in your browser. Nothing is transmitted, nothing is stored on a server, and your tally disappears when you close the tab.