Coin Flipper
Flip one coin or many, and see the running tally.
Fifty-fifty does not mean an even tally
Across 100 flips of a fair coin, landing exactly 50 heads happens only about 8% of the time. Ending up 10 or more away from even — 60 heads, or 40 — happens around 5% of the time and is entirely unremarkable. The proportion converges towards 0.5 as flips accumulate, but the absolute gap between heads and tails typically grows rather than shrinks. Both facts are true simultaneously and the second one surprises almost everyone.
This is the law of large numbers correctly stated: proportions converge, differences do not. A coin that is "behind" on heads has no mechanism to catch up, because each flip is independent.
Real coins are slightly biased
Physical coin flips are not perfectly fair. A large 2023 study of over 350,000 flips found a small but consistent bias towards the side that was facing up when the coin was launched — roughly 51% — caused by precession during flight. Spinning a coin on a table is much worse: the mass distribution around the rim makes some coins land on one side substantially more often. A digital flip drawn from a cryptographic random source has neither problem.
Independence, and why streaks feel wrong
The chance of seven heads in a row is about one in 128 — which means in a session of a few hundred flips you should expect to see it. People asked to write down a "random" sequence of coin flips produce far fewer long runs than a real coin does, which is how fabricated data is often detected. If a run makes you suspicious, that reaction is the well-documented gambler's fallacy rather than evidence of a broken generator.
How to use it
- Choose how many coins to flip at once.
- Flip, and watch the running tally accumulate across sessions.
- Expect the proportion to approach 50% while the raw gap keeps wandering.
- Treat long runs as expected rather than as a malfunction.
Before you draw
Why is the tally not exactly even?
It rarely is. Exactly 50 heads in 100 flips occurs only about 8% of the time. The proportion converges towards half as flips accumulate, but the absolute difference between heads and tails tends to grow.
Are real coin flips fair?
Not quite. A large study found roughly a 51% bias towards the side facing up at launch, caused by precession in flight. Spinning a coin on a table is considerably more biased than flipping it.
I got eight heads in a row — is that suspicious?
No. Eight in a row has roughly a one in 256 chance, so it shows up regularly across a few hundred flips. Genuinely random sequences contain more long runs than people expect.
Is the next flip more likely to be tails after a run of heads?
No. Each flip is independent and the coin has no memory. Expecting a correction is the gambler's fallacy.
Disclaimer: These tools are for games, classrooms, and informal group decisions. They are not audited for regulated lotteries, gambling, or any draw with legal requirements, and should not be used to make financial, medical, legal, or safety decisions.