About Coin Flips
A coin flip is the oldest and simplest form of randomisation — a binary decision where two outcomes have equal probability. Its appeal is partly mathematical (each flip is a clean 50/50) and partly social: a coin toss feels fair, takes a second, and settles a dispute without negotiation. It has been used for centuries to resolve everything from the outcome of cricket matches to who pays for dinner.
This tool simulates a fair coin with a real 3D flip animation, tracks your flip history and stats, and supports best-of-N series — all in your browser, with no data ever leaving your device.
The mathematics of a coin flip
Each flip is an independent event with exactly two possible outcomes, each with probability 0.5. Because the flips are independent, past results do not influence future ones — a coin has no memory. This has a few consequences that surprise people:
| Situation | Probability | Interpretation |
|---|---|---|
| Next flip is heads | 50% | Always, regardless of history |
| Two heads in a row | 25% | 0.5 × 0.5 |
| Five heads in a row | 3.125% | Uncommon but far from impossible |
| Five heads, then heads again | 50% | The five heads are already history |
| At least 5 heads in 10 flips | ~62% | Symmetry includes the "5 heads, 5 tails" case |
The gambler's fallacy is the belief that past results change future probabilities. After ten tails in a row, a "hot" side is not due — the next flip is still 50/50. Real randomness is clumpy. Streaks, clusters and apparent patterns are not just possible; they are expected.
Are real coins fair?
Almost. Physical coins have tiny biases due to asymmetries in the design — the head side of a US penny, for example, is slightly heavier. Studies on spinning and tossing coins have measured biases of less than 1% in most cases, which is undetectable in everyday use. Interestingly, a 2007 study by Bartos and colleagues found that when a coin is spun on a table, it is slightly more likely to land on the side that was initially facing up. For a normal toss, this effect is negligible.
This tool is mathematically fair: every flip has exactly 50% probability for each side, with no bias at all.
What does "best of N" mean?
A best-of-N series reduces the effect of luck by requiring a majority of wins rather than a single flip. Common formats:
| Series | First to | Win probability (fair coin) |
|---|---|---|
| Single flip | 1 | 50% |
| Best of 3 | 2 | 50% |
| Best of 5 | 3 | 50% |
| Best of 7 | 4 | 50% |
The probability that each side wins is still 50% — the coin is fair. What best-of-N reduces is the variance: in a best-of-7, a lucky streak of 4 flips is much less likely to decide the outcome than a single lucky flip in a one-flip decision. Best-of-N is standard in sports playoffs (MLB World Series, NBA Finals, best-of-7 hockey series) for exactly this reason.
Common use cases
Settling disputes
Who pays, who goes first, who wins the coin toss.
Games & decisions
Simple binary choices where 50/50 is required.
Teaching probability
Demonstrate independence and the gambler's fallacy.
Simulation & testing
Random binary data for experiments and code.
Sports & tournaments
Choose sides, brackets and starting positions.
Group decisions
Best-of-7 to decide between two options.
Privacy
This coin flip runs entirely in your browser. Every flip uses Math.random() locally, and your history and stats are stored only in your browser's localStorage. Nothing is transmitted, stored or logged on any server. Clear your browser data and the history is gone.