The more you flip, the closer the split gets to 50/50 — but a run of six heads is perfectly ordinary along the way.
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A fair coin has no memory, and no obligation to even out soon
People expect a fair coin to correct itself: six heads, so tails is due. It is not. Each flip is independent, and what actually happens is subtler — the gap between heads and tails tends to grow, while the ratio drifts towards half.
How it works
- Flips one coin, or a hundred at once, from the browser's cryptographic random source.
- Tracks the running heads-and-tails split and shows it as a bar that converges on 50/50.
- Records the longest run of the same face anywhere in the session.
P(heads) = P(tails) = 0.5 on every flip, regardless of history P(a specific run of k identical faces) = 0.5^k expected longest run in n flips ≈ log2(n)
Worked example
Flipping 100 times, then 1000 times.
- 100 flips: a 55/45 split is entirely ordinary — the ratio is 55%, the gap is 10
- 1000 flips: a typical result might be 517/483 — the ratio is 51.7%, but the gap has grown to 34
- expected longest run in 1000 flips ≈ log2(1000) ≈ 10 identical faces in a row
The percentage moves towards 50 while the raw difference gets bigger. Both are what a fair coin does; only the first is what people expect.
Reading the result
- The gambler's fallacy is the belief that a run of heads makes tails more likely. It does not: the coin has no record of the previous flip. What corrects the ratio is not compensation but dilution — later flips outnumber the early imbalance.
- A run of six identical faces in 100 flips is unremarkable; the expected longest run is around log2(100) ≈ 7.
- A real coin is very slightly biased towards the face that started upwards, because it spins about an axis rather than tumbling perfectly. A drawn bit has no such physics.
Common questions
- I got ten heads in a row. Is that broken?
- Not on its own. Any specific ten-flip sequence has probability 0.5^10 ≈ 1 in 1024, and ten heads is no less likely than any other particular sequence. Flip a few hundred times and long runs stop feeling strange.
- Is a coin flip a fair way to decide something?
- Yes, and it is fair precisely because it is memoryless. Neither side can improve their odds by choosing when to call, which is why it is used for kickoffs and tiebreaks.