This coin flip simulator flips a fair digital coin as many times as you like, up to 100,000, and shows what random flips really look like: streaks, the gap between heads and tails, and four “systems” that try to call the next flip. There are no chips and no bets, so you can run it as long as you want.
The point is independence. A fair coin has no memory, and the longer you flip, the clearer it becomes. Streaks are common, the gap between heads and tails grows, and every system for calling the next flip lands near 50%.
How does this coin flip simulator work?
Press Flip once, or Flip 10, 100 or 1,000 times. The coin uses your browser’s secure random number generator, so heads and tails are each exactly 50% on every flip. The panel then shows counts, the longest streak so far, and how that streak compares with what the maths expects.
- Streaks: your current and longest run of the same side, and the exact chance of a run that long or longer in that many flips.
- The gap: the difference between heads and tails, and the typical size of that gap for your number of flips.
- After a streak: a table showing how often the next flip matched a streak of 1, 2, 3 or more.
- Four systems: always heads, repeat the last flip, call the opposite of the last flip, and call that a streak of 3 or more will end. Each is scored before every flip.
Nothing is saved to your browser or sent anywhere. Reset starts again with the same fair coin.
Is a coin flip really 50/50?
A fair digital coin is exactly 50/50 on every flip. A real coin is very close but not exact: in a 2023 study of 350,757 flips, coins landed on the same side they started 50.8% of the time. Heads came up 50.01%. This simulator uses a random number generator, so it has no such bias.
The reason is physics. A coin that is flipped with a lot of spin and a little wobble tends to land as it started. Diaconis, Holmes and Montgomery worked this out in 2007 and put the same-side chance near 51% for natural flips. A bias of that size changes nothing in a single decision, and it is not a rule you can use to win anything.
How long a streak should you expect in a run of coin flips?
The longest streak in n fair flips is about log base 2 of n. In 100 flips the average longest run is about 7, and a run of 6 or more happens in about 81% of 100-flip sequences. Streaks look suspicious to people but are a normal sign of randomness.
| Flips | Run of 4+ | Run of 5+ | Run of 6+ | Run of 7+ | Run of 8+ | Run of 10+ | Average longest run |
|---|---|---|---|---|---|---|---|
| 10 | 46.5% | 21.7% | 9.4% | 3.9% | 1.6% | 0.20% | 3.7 |
| 20 | 76.8% | 45.8% | 23.7% | 11.5% | 5.4% | 1.2% | 4.7 |
| 50 | 98.1% | 82.1% | 54.4% | 30.9% | 16.2% | 4.0% | 6.0 |
| 100 | 100.0% | 97.2% | 80.7% | 54.2% | 31.5% | 8.7% | 7.0 |
| 200 | 100% | 99.9% | 96.5% | 79.9% | 54.2% | 17.2% | 8.0 |
| 500 | 100% | 100% | 100.0% | 98.3% | 86.3% | 38.4% | 9.3 |
| 1000 | 100% | 100% | 100% | 100.0% | 98.2% | 62.4% | 10.3 |
Read one row to see how streaks scale. In 20 flips, a run of 5 or more happens almost half the time (45.8%). In 1,000 flips, a run of 10 or more happens 62% of the time. A specific run of 10 heads starting on a given flip is 1 in 1,024, but you get many chances to start one.
What is the gambler’s fallacy?
The gambler’s fallacy is the belief that a streak makes the opposite result more likely next, as if the coin had to even things out. It does not. After five heads, the chance of heads is still 50%, because each flip is independent. The simulator’s After a streak table shows this directly.
A famous example happened at a Monte Carlo casino in August 1913, when, by the usual account, the ball landed on black 26 times in a row at roulette while players kept backing red. By our arithmetic a run of 26 blacks has about 1 chance in 137 million of starting on a given spin, or 1 in 68 million for either color. A streak that long is rare, but it does not make the next spin due to change.
Researchers have found the same thinking outside casinos. A 2016 study of asylum judges, loan officers and baseball umpires found decisions that tended to switch after a run of similar ones, as if the run had to end.
Does the gap between heads and tails close over many flips?
The share of heads moves toward 50%, but the count gap between heads and tails does not close. It grows, slowly. The typical gap after n flips is about 0.8 times the square root of n, so it grows roughly as the square root of the flips, while the share drifts toward 50%.
| Flips | Typical gap between heads and tails | Typical share of heads |
|---|---|---|
| 10 | 2.5 | about 62.6% or 37.4% |
| 100 | 8 | about 54.0% or 46.0% |
| 1,000 | 25 | about 51.3% or 48.7% |
| 10,000 | 80 | about 50.4% or 49.6% |
| 100,000 | 252 | about 50.13% or 49.87% |
This is the law of large numbers in action, and it is the opposite of “the coin makes up for it”. After 1,000 flips a gap of 25 is normal. The coin does not correct past flips. Later flips just make the early gap a smaller share of a bigger total.
Example: exactly 50 heads in 100 flips happens only 7.96% of the time. Most 100-flip runs finish with a split like 55 to 45 or 42 to 58.
Can any system predict the next coin flip?
No. The simulator tests four common calling systems against the same fair coin, and every one lands near 50% because each flip is independent. A system can change the pattern of your calls, but not the chance that any call is right.
Betting systems built on this idea fail for the same reason. The Martingale, which doubles the bet after each loss, relies on the idea that a win must be near. On a fair coin it is a fair game with a risk of a very large loss. On a game with a house edge, such as roulette, it also pays the edge. Six losses in a row on a fair coin happen 1 time in 64, and the stake needed grows to 63 times the first bet.
How does an online coin flip pick heads or tails?
A good online coin flip uses a random number generator to pick one of two outcomes with equal chance. This page uses the secure random generator built into your browser, with rejection sampling so that no value is favored. It does not look at your earlier flips or at how you called.
Be careful with coin-flip games for money. The odds of a fair coin flip are 50/50, but any site that pays less than double on a correct call has a house edge, and the edge costs you on average in the same way as in roulette. Chancepedia does not link to operators.
Does flipping a coin help with decisions or gambling?
A coin flip is a fair way to break a tie when both choices are acceptable. It does not help with gambling, where the odds are fixed by the game. The simulator is a quick way to see why a hot streak is not evidence that a game is changing in your favor.
Pure luck games feel as if they have patterns because our minds look for them. If you notice yourself looking for patterns in gambling outcomes, or betting because something feels due, take a break and read the Safer play toolkit. Free confidential help is on Get help.
What should you try next?
- Flip 100 times five times and note the longest streak each time. Compare with the table above.
- Flip 1,000 times and look at the After a streak table. Does a streak of 5 change what comes next?
- Compare the four systems after 1,000 flips. Which one is best?
- Work out dice and card chances with the dice probability calculator.
How to read your session
The panel shows counts, the current and longest streak, and the exact chance of a streak that long in that many flips. The After a streak table shows how often the next flip matched a streak of each length. All of these settle near 50% when counts are large.
How it is calculated
Heads and tails are each 50% on every flip. The chance that the longest run in n flips is at least k comes from the run recurrence u(t) = u(t-1) - 2^-(k+1) x u(t-k-1), which counts every sequence exactly. The typical gap between heads and tails is the square root of (2n / pi). The average longest run is about log base 2 of n.
Worked example
Worked example
In 100 fair flips: average longest run about 7.0, a run of 6 or more in 80.7% of sequences, a run of 10 or more in 8.7%, and exactly 50 heads in 7.96%.
Limits
The simulator is a fair digital coin. Real coins are very slightly biased toward the starting side (about 50.8% in one large study). Results are random and vary each time. The limit is 100,000 flips per session.