Flip a coin with realistic 3D animation & track your statistics
Make quick decisions with our coin flipper featuring realistic 3D CSS animations. Track your flip statistics over multiple flips and use the multi-flip feature for probability experiments. The dice roller supports 1-6 dice with visual dot faces.
| Run | Probability | Odds | Expected once every |
|---|---|---|---|
| 2 in a row | 25 % | 1 in 4 | 4 attempts |
| 3 in a row | 12.5 % | 1 in 8 | 8 attempts |
| 5 in a row | 3.125 % | 1 in 32 | 32 attempts |
| 7 in a row | 0.78 % | 1 in 128 | 128 attempts |
| 10 in a row | 0.098 % | 1 in 1,024 | 1,024 attempts |
| 15 in a row | 0.003 % | 1 in 32,768 | 32,768 attempts |
| 20 in a row | 0.0001 % | 1 in 1,048,576 | about a million attempts |
| Heads | Ways it can happen | Probability |
|---|---|---|
| 0 or 10 | 1 each | 0.098 % each |
| 1 or 9 | 10 each | 0.98 % each |
| 2 or 8 | 45 each | 4.4 % each |
| 3 or 7 | 120 each | 11.7 % each |
| 4 or 6 | 210 each | 20.5 % each |
| 5 | 252 | 24.6 % |
The belief that a run of heads makes tails "due" is called the gambler’s fallacy, and it is the most reliably observed error in probability judgement. Independent events do not correct themselves. The famous illustration is the Monte Carlo Casino on 18 August 1913, when a roulette wheel landed on black 26 times in succession; gamblers lost fortunes betting ever larger sums on red in the belief that it had to come. What the law of large numbers actually says is that the ratio of heads to total flips approaches 0.5 as the number of flips grows — not that the running difference between heads and tails shrinks. That difference typically grows, roughly with the square root of the number of flips.
You flip 8 heads in a row. What is the chance the next two are also heads?
The past flips are irrelevant to future ones.
P(next is heads) = 1/2
P(next two are both heads) = 1/2 × 1/2 = 1/4
25 % — the same answer you would have given before the first eight flips.
A physical coin flip is very slightly biased. A 2023 study led by František Bartoš, using 350,757 recorded flips by 48 people, found coins land on the same face they started on about 50.8 % of the time — consistent with the precession model that Persi Diaconis and colleagues proposed in 2007. The bias is toward the starting side, not toward heads: a coin is not head-heavy, it simply wobbles about an axis and spends marginally more time showing the face it began with. A software coin flip using a properly seeded generator has no such bias, which is why a digital flip is arguably fairer than a real one.
For a fair coin, mathematically yes — each flip is an independent event with probability one half. A real physical flip carries a tiny bias of about 0.8 percentage points toward the face it started on, because of how the coin precesses in the air.
1 in 1,024, or about 0.098 %. That is one half multiplied by itself ten times. Note this is the probability before you begin; once nine heads have landed, the tenth flip is still 50/50.
No. That is the gambler’s fallacy. Coin flips are independent, so no amount of history changes the next outcome. The law of large numbers makes the ratio converge on half, not the running difference.
Let one party call the side while the coin is in the air, so neither can control the starting face. That removes the small same-side bias entirely, which is exactly why cricket and football tosses are done this way.
A properly seeded pseudorandom generator is statistically indistinguishable from a fair coin for this purpose, and browsers expose a cryptographically secure generator through the Web Crypto API. It is more even-handed than a physical flip, which has a measurable same-side bias.
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