Coin Flip
Genuinely fair, which is more than a real coin manages.
Flip a coin online, one or a thousand at a time. Genuinely fifty-fifty, which a real coin is not: a hand-flipped coin favours its starting face.
Is this actually fair?
Each flip is drawn from your browser’s cryptographic random source, the same one used to generate encryption keys, rather than from Math.random, whose sequence can be reconstructed from a handful of its own outputs. Both outcomes are exactly equally likely.
Which is more than can be said for a real coin. A physical coin flipped by hand lands on the face it started on about 50.8 percent of the time. Diaconis, Holmes and Montgomery predicted it in 2007, from the slight wobble a thumb imparts, and Bartoš and colleagues confirmed it in 2023 by flipping 350,757 coins across 46 currencies.
The nuance matters, though, and most write-ups drop it. The bias is toward the starting face, not toward heads. If you call heads or tails before the toss without seeing which way up the coin began, the same study found no advantage either way. A real coin is only exploitable if you can see how it starts.
Why the streaks look wrong
A run of six heads in a hundred flips feels like something has broken. It has not: the chance of seeing a run of six or more somewhere in a hundred flips is a little over even money. People asked to write down a fake sequence of flips almost always switch too often, which is how fabricated data gets caught.
How the Coin Flip works
Flip one coin or a thousand, drawn from your browser's cryptographic random source so both outcomes are exactly equally likely. The running tally shows the thing that makes repeated flips interesting: the percentage creeps toward fifty while the raw gap between heads and tails usually grows, which is the law of large numbers doing exactly what it promises and not what most people expect.
Also known as: flip a coin · heads or tails · coin toss online · coin flip simulator · random coin toss
A real coin is not fifty-fifty
In 2007 Persi Diaconis, Susan Holmes and Richard Montgomery published a physical model of a hand-flipped coin and predicted something odd: a coin is slightly more likely to land on whichever face it started on. The reason is precession. A thumb never imparts perfectly clean rotation, so the coin wobbles about an axis that is tilted a little off the flip axis, and that wobble means it spends marginally more of its flight with the starting face upward.
The prediction sat untested for sixteen years, because testing it properly meant flipping coins tens of thousands of times and recording which way each one started. In 2023 František Bartoš assembled a team of 48 people who flipped 350,757 coins across 46 currencies and measured 50.8 percent same-side landings, which is squarely in line with the model.
The nuance that most write-ups drop is the one that decides whether any of this is useful. The bias runs toward the starting face, not toward heads. Call heads or tails before the toss without seeing which way up the coin began, and the same data shows no advantage either way. A physical coin is exploitable only by someone watching how it starts, which is a good reason to have the caller decide before the flipper picks the coin up.
Why the streaks look wrong
Flip a hundred times and you will almost certainly see a run of six or more of the same face. The chance is a little better than even money. Most people find that surprising, and the surprise is robust enough to be useful: when researchers ask people to write down an invented sequence of coin flips, the fakes are identifiable because they switch too often. Real randomness clumps, and human intuition smooths.
It is the same instinct behind the gambler's fallacy, the belief that a run of heads makes tails due. The coin has no memory. After six heads the chance of a seventh is still exactly one half, and any tool that tries to correct for a run to make the results look more balanced is not a random generator at all.
The running tally here shows the longest run for exactly this reason. Watching a run of seven appear in a few hundred flips, and knowing the coin is provably fair, is a faster education in randomness than any amount of being told.
The proportion converges, the difference does not
The law of large numbers is one of the most widely half-remembered results in mathematics. It says that as the number of flips grows, the proportion of heads approaches one half. It does not say the number of heads approaches the number of tails, and those are very different promises.
In ten thousand fair flips you should expect to be around fifty flips apart in absolute terms, and simultaneously within about half a percent of even in proportional terms. Both are correct at once, because the absolute gap grows roughly with the square root of the number of flips while the total grows with the number of flips, so the ratio shrinks even as the gap widens.
This page shows the percentage and the raw difference side by side, and keeping an eye on both while flipping a thousand at a time makes the point better than the explanation does. It also quietly explains why a losing streak in a fair game does not have to correct itself: nothing pulls the counts back level, only the arithmetic of division makes the imbalance matter less.
Frequently asked questions
Is this actually random?
Yes, and more so than a physical coin. It draws from the same source a browser uses to generate encryption keys, seeded from the operating system's entropy pool, rather than from Math.random, whose sequence can be reconstructed from a handful of its own outputs.
Is a real coin toss fifty-fifty?
Not quite. A coin flipped by hand lands on the face it started on about 50.8 percent of the time. Diaconis, Holmes and Montgomery predicted it in 2007 from the wobble a thumb imparts, and Bartoš and colleagues confirmed it in 2023 by flipping 350,757 coins across 46 currencies.
So can I win by always calling heads?
No, and this is the part most write-ups drop. The bias is toward the starting face, not toward heads. If you call before the toss without seeing which way up the coin began, the same study found no advantage either way. A real coin is only exploitable if you can see how it starts.
Why did I get six heads in a row?
Because that is normal. The chance of a run of six or more appearing somewhere in a hundred flips is a little better than even money. People asked to invent a fake sequence almost always switch too often, which is one way fabricated data gets caught.
Why does the difference between heads and tails keep growing?
Because the law of large numbers promises the proportion converges, not that the counts stay level. In ten thousand flips you would expect to be around fifty apart in absolute terms while sitting within half a percent of even. Both figures are shown for exactly that reason.
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