Flip a Coin
Flip a coin for heads or tails, or flip up to 1,000 at once and see how the split and the longest run compare with chance.
Your flip
- Chance of each face
- exactly 1 in 2
How the Flip a Coin works
A virtual coin flip, or virtual coin toss, is heads or tails, each with probability exactly one half. Flip up to 1,000 coins at once to get the counts, the longest run, and how likely that result was.
Many flips at once is where intuition breaks down. The chance of exactly your count of heads, of that many or more, and of a split at least as uneven in either direction all come from the binomial distribution with p = 1/2. In 100 flips, 60 or more heads happens 2.84% of the time.
Runs surprise people more than counts do. In 100 fair flips a run of seven or more of either face turns up 54.2% of the time. The expected longest run grows like log2(n) plus about a third, so 1,000 flips average a longest run of 10.3. People who write a sequence by hand to look random switch faces too often and leave runs far shorter than these, which is why a long streak in a real sequence looks suspicious and is not.
Flip a Coin FAQ
Is this coin flip fair?
Yes. Each flip comes from your browser's cryptographically secure random generator, with heads and tails exactly equally likely. Nothing about earlier flips affects the next one.
What are the odds of 10 heads in a row?
1 in 1,024, or about 0.098%, counted from before the first flip. Each flip is a half, so ten in a row is (1/2)^10. Once nine heads have happened, the tenth is still exactly 1 in 2.
How many heads should I get if I flip a coin 100 times?
50 on average, but exactly 50 only 7.96% of the time. 96.5% of results fall between 40 and 60 heads. A result of 60 or more of either face happens 5.69% of the time, so it is uncommon without being a sign that anything is wrong.
Is a real coin 50/50?
Close, though measurably off. Diaconis, Holmes and Montgomery (2007) predicted that a flipped and caught coin lands on the side it started on about 51% of the time, because it wobbles as it spins. František Bartoš and colleagues (2023) measured 50.8% same side over 350,757 flips. The bias follows the starting face, so heads and tails are only favored depending on which was up at the start.
Can a coin land on its edge?
A real one can, rarely. Murray and Teare (Physical Review E, 1993) modeled a US nickel and estimated about 1 landing on edge in 6,000 tosses. This generator has two outcomes only.
Why are the runs so long when I flip many coins?
Because long runs are normal. In 100 fair flips the longest run of either face averages about 7, and a run of six or more turns up in 80.7% of sequences. The result shows the chance of a run at least as long as yours.