The interesting thing about a coin is not the 50/50
Everybody knows a coin is half and half. Nobody knows what a hundred flips of one actually looks like, and the gap between those two facts causes real trouble.
Ask somebody to write down a hundred imaginary coin flips. They will produce something with a longest streak of about four, because by the fifth head in a row it starts to feel wrong to keep writing them.
A real hundred flips contains a run of five or more 97% of the time. Six or more, 81%. Seven or more, 54%.
Which means the invented sequence is instantly identifiable, and it gives itself away by looking too random. Too even. Too well behaved. That is the opposite of what most people would guess.
The percentages here are exact
They are not estimates from repeated sampling. A small dynamic program carries the current run length through every flip and works out precisely how often a streak of any given length appears.
It is checked against a brute-force count of every possible sequence up to eight flips, so the figures are verified rather than believed. That matters, because the whole point of the page is telling you whether what you just saw was normal, and a number you cannot trust cannot do that.
Why this costs people money
The belief that a streak makes the opposite result "due" is the gambler's fallacy, and it is the engine under every roulette system ever sold.
After six heads the chance of another head is still exactly a half. The coin does not know. It has no way to know. And yet the feeling that the balance must be restored is close to universal, because we expect randomness to look tidier than it is.
Flipping ten thousand here and watching a run of thirteen turn up is the cheapest available correction for that instinct.
Two things get further apart as you flip more
Flip a million and two things happen at once, and they seem to contradict each other.
The split gets tighter. At a million flips it will sit within a fraction of a percent of half, every time.
The longest run gets longer. At a million flips expect a streak of around twenty identical faces in a row.
Both are consequences of the same fairness. The average tightens because the errors cancel; the streaks lengthen because more attempts means more chances for an unlikely thing to appear somewhere. "That cannot be random" gets said far more often about large samples than small ones, for exactly this reason.
Why it should not be exactly half
On ten thousand flips you would expect to end up about one percentage point off the middle just from chance.
Landing on precisely five thousand each would be the surprising outcome, not the reassuring one. This page tells you how far off is normal for the number you actually flipped, so a small gap reads as ordinary rather than as evidence of something.
The seed, and its honest limit
Every flip is seeded and the seed is shown, so a single result can be reproduced and shown to somebody who was not there.
It is a pseudorandom generator, which is exactly right for settling who buys the tea and exactly wrong for anything where somebody has money on predicting the next one. This does not pretend otherwise.
Common questions
I got seven heads in a row. Is it broken?
Almost certainly not, and this is the thing the tool is really for. In a hundred flips, a run of five or more happens 97% of the time, six or more 81% of the time, and seven or more 54% of the time. A long streak is not a fault, it is the expected outcome. What would be strange is a hundred flips with no run past three.
How do you spot a faked list of coin flips?
By the runs. Ask somebody to invent a hundred flips and they will almost never write a streak past four, because five in a row feels wrong to write down. Real flips streak far more than people expect. The forgery is spotted because it looks too random, too evenly alternating, not because it looks too lumpy.
Are the streak percentages exact?
Yes. They come from a small dynamic program that carries the current run length through every flip, which gives the exact probability rather than an estimate from repeated sampling. It is checked in the tests against a brute-force count of every possible sequence up to eight flips, so the maths is verified rather than assumed.
After six heads, is tails more likely?
No. The coin has no memory and the next flip is still a half. That feeling is the gambler's fallacy and it is one of the most expensive intuitions people have, because it is what roulette systems are built on. Flipping ten thousand here and watching the streaks happen anyway is the cheapest possible cure.
Why is it not exactly 50/50 on ten thousand flips?
Because it should not be. On ten thousand flips you would expect to land about one percentage point off the middle purely by chance, and landing on exactly half would be the odd result rather than the reassuring one. The tool tells you how far off is normal for the number you flipped.
Can I flip a million?
Yes, in about a second. Above five hundred it stops keeping the individual flips, because nobody reads half a million coins, but the counts and the streak analysis still work. That is where the split gets genuinely tight and the longest run gets genuinely long, which is the pair of facts most people find surprising together.
Is it really random?
It is a seeded pseudorandom generator, and the seed is shown so a single flip can be reproduced and shown to somebody. That is the right trade for settling an argument. It is not the right tool where somebody has a serious incentive to predict the next flip, and it does not claim to be.