Tap the coin and heads or tails comes up 50/50
A coin flip is the oldest way to settle a choice between two options without favoring either one. When you tap the coin or the flip button here, your browser's cryptographic random generator picks heads or tails at that moment, 50% each, and the coin spins to land on that side. If you name the two sides, say "Pizza" and "Tacos", the result shows that name in large type, so you can settle a menu or a turn order right away.
It also does more than a single flip. Flip 10 up to 10,000 times at once and the tool draws a curve of the heads ratio settling toward 50%, plus bars showing how many times the same side repeated. If you ever wondered "heads came up six times in a row, is that suspicious?", it answers with the probability of that run for a fair coin.
Why flip a coin at all?
A coin flip looks like leaving things to luck, but people use it for three practical reasons.
- A start nobody can complain about: no one can pick the result, so deciding order or sides causes no argument. That is why the official rules of soccer, cricket and tennis settle the start of a match with a coin. The rules table below shows what each sport decides.
- Finding out what you want between two similar options: a 2019 study (Jaffé et al.) reported, across two experiments, that once the coin pointed to one option, people felt more strongly about it and had a stronger sense of suddenly knowing what they wanted. The authors describe the coin as a magnifying glass for feelings rather than a replacement for the decision. If the result leaves you disappointed, you were hoping for the other side.
- Seeing probability with your own eyes: one coin shows both the law of large numbers and the fact that runs are longer than they feel. Flipping by hand 10,000 times would take hours; here it takes one tap.
How to use it
- Name the sides (optional): type your two options into the heads and tails cards. If you leave them empty, the sides are called "Heads" and "Tails". Press Enter in a name field to flip right away.
- Flip: tap the coin in the middle or press the flip button. The coin rises for about a second and falls, and the result area shows the name (or the side) and which flip it was. The card of the side that came up last gets a darker border.
- Flip many times: press 10, 100, 1,000 or 10,000 to flip that many times at once; the coin lands on the final result. The running total counts up to 1,000,000 flips.
- Read the log: the flip log piles up the most recent results, oldest first, and underlines the run that is still going. The ratio curve and the run-length bars below change along with it.
- Showing it to a group: Full screen shows only the coin, the two cards and the flip buttons in large size. Press Space to flip and Esc to leave. Copy link copies an address that contains both names; Copy log copies the counts, ratios, longest run and the recent sequence.
The heads ratio settles near 50%, but not exactly on it
Even a fair coin swings a lot when you flip it only a few times. Getting 7 heads in 10 flips is common, and it does not mean the coin is a 70% coin. The table below gives the range the number of heads falls into with better than 95% probability for n flips of a fair coin, calculated exactly from the binomial distribution. At most 2.5% is cut from each end, so the real probability of landing inside is a little above 95%. The gray band in the workspace is this range.
| Flips | Heads range | Heads ratio range | Chance of landing inside |
|---|---|---|---|
| 10 | 2–8 | 20.0–80.0% | 97.9% |
| 20 | 6–14 | 30.0–70.0% | 95.9% |
| 50 | 18–32 | 36.0–64.0% | 96.7% |
| 100 | 40–60 | 40.0–60.0% | 96.5% |
| 1,000 | 469–531 | 46.9–53.1% | 95.4% |
| 10,000 | 4,902–5,098 | 49.0–51.0% | 95.1% |
| 100,000 | 49,690–50,310 | 49.7–50.3% | 95.0% |
Two things stand out. First, the width of the ratio range shrinks with the square root of the number of flips. The ±10 percentage points at 100 flips become ±1 point at 10,000, so cutting the width to a tenth takes 100 times as many flips. Second, the gap in counts actually grows. At 100 flips heads and tails can differ by as many as 20, and at 10,000 flips by as many as 196. So the accurate statement is not "heads and tails even out in number" but "the ratio gets closer to 50%".
If your record leaves the gray band, the readout line says so. For a fair coin this happens at most about once in 20 tries, so one excursion outside the band does not mean the random generator is broken.
Runs are longer than you would expect
People tend to think random flips should alternate often, but real random records contain long runs. The table below gives the longest run of the same side in n flips of a fair coin, counting runs of heads and runs of tails alike.
| Flips | Longest run (typical) | Chance of a run of 5 or more | 7 or more | 10 or more |
|---|---|---|---|---|
| 10 | 3 | 21.7% | 3.9% | 0.2% |
| 20 | 4 | 45.8% | 11.5% | 1.2% |
| 50 | 6 | 82.1% | 30.9% | 4.1% |
| 100 | 7 | 97.2% | 54.2% | 8.7% |
| 1,000 | 10 | >99.9% | >99.9% | 62.4% |
"Typical" is the shortest length that the longest run stays at or below with probability of at least one half (the median). In 100 flips, a run of 7 or more happens more than half the time, and a run of 5 is almost certain. In the workspace, "How long did the same side repeat?" works out the chance of a run at least as long as your longest one, and the vertical tick beside each bar shows the count a fair coin is expected to give for that length. In 100 flips you can expect about 25.5 runs of length 1 (the side changes right away), 12.6 runs of length 2 and 6.3 runs of length 3; each extra step roughly halves the count.
Seeing a run and feeling that "the other side is due" is called the gambler's fallacy. The coin has no memory of earlier flips, so even after five heads in a row the next flip is still 50% heads and 50% tails. Whenever a run reaches 3 or more, the workspace prints this fact in one line under the result.
Is a real coin flipped by hand also 50/50?
Unlike a computer's random numbers, a coin flipped by hand obeys physics. In 2007 Diaconis, Holmes and Montgomery proposed a model in which the coin's spin axis wobbles slightly, so that even with a vigorous flip the side that started facing up lands up about 51% of the time. To test that prediction, a team led by Bartoš, 48 people in all, flipped 44 kinds of coins 350,757 times, and the results appeared in the Journal of the American Statistical Association in 2025.
| Record | Flips | Result | Heads ratio |
|---|---|---|---|
| ① John Kerrich (1946 book) | 10,000 | 5,067 heads | 50.67% |
| ② Karl Pearson (1897 book) | 24,000 | 12,012 tails | 49.95% |
| ③ Bartoš et al., 48 people (2025) | 350,757 | 175,421 heads | 50.01% |
The numbers match the numbered dots on the workspace's ratio curve. In all three records the heads ratio was close to one half, but in the Bartoš study the coin landed on the same side it started on 50.8% of the time (95% credible interval 50.6–50.9%), in line with the Diaconis model. The bias differed a lot from person to person and tended to shrink with more flips. It is small, but if you bet with a friend you can remove it by not looking at which side is up before the flip, or by having the other person call it while the coin is in the air. The random numbers in this tool have no starting side, so this bias cannot occur.
Which side is heads?
The convention for which side of a coin is called heads differs from country to country and from coin to coin. Many people take the side with the portrait or main picture to be heads, but others go by the side with the number. When you toss a real coin, agree on which side counts as heads before you throw. The coin in this tool does not use any real currency design; it tells the two sides apart with the labels "H" and "T" and the names you type.
What a coin toss decides in sports
| Sport · rule | Who tosses | What the winner chooses |
|---|---|---|
| Soccer · IFAB Laws of the Game, Law 8.1 | The referee | The goal to attack in the first half, or the kick-off. The other team gets the remaining choice, and in the second half the teams swap ends, with the team that chose the goal taking the kick-off. A new toss is also made before extra time. |
| Cricket · MCC Laws 13.4 and 13.5 | The two captains (on the field, with an umpire present, 30 to 15 minutes before the start) | Whether to bat or to field. Once the decision has been told to the opposing captain and the umpires, it cannot be changed. |
| Tennis · ITF Rules of Tennis, Rule 9 | A toss before the warm-up | One of serve or receive, which end to start from, or to let the opponent choose. The opponent then makes the remaining choice. |
In all three sports the toss only decides who gets to choose; what to choose is the winner's judgment. The side that knows the conditions, such as wind, sun or the advantage of going first, is the one that makes use of that right.
How this tool decides the result
When you press flip, the tool asks Web Crypto's crypto.getRandomValues for random bytes and calls the result heads if the lowest bit is 1 and tails if it is 0. Of the 256 values a byte can take, exactly 128 are odd and 128 are even, so heads and tails are exactly equally likely. Flipping many times works the same way, drawing as many bytes as needed. The result is fixed the instant you press; the spinning coin is an animation timed to land on that side, so the speed or height of the spin tells you nothing about the outcome. If your device has "reduce motion" turned on, the coin does not spin and simply shows the resulting side.
The 95% range adds up exact binomial probabilities, and the probability of the longest run is computed with a recurrence over the state "is this flip the same side as the one before". Neither is an approximation, which is why the tables above match the values in the workspace.
Common misconceptions
- "In 10 flips you should get exactly 5 of each": the chance of exactly 5 heads in 10 flips is only 24.6%. Anything from 3 to 7 is normal, and 2 or 8 is not rare.
- "A run just happened, so the other side is next": that is the gambler's fallacy. The next result is always 50%.
- "I don't like that result, let's make it best of three": changing the rules after seeing the result removes the fairness. Decide how many flips there will be before you flip. And if the result disappointed you, that feeling is already your answer.
- "Computer random numbers are fake and biased": the Web Crypto numbers this tool uses are of the quality used for cryptography. Flip many times and you can watch the ratio settle toward 50% within the ranges in the table.
Limits and cautions
- Results and the log exist only on this browser screen and are not stored on a server. Nobody can prove who got what and when, so this is not suited to jobs that must prove fairness, such as a prize draw.
- A name can be up to 20 characters per side, and control characters such as line breaks are removed. Names are put into the link address as they are, so do not type personal information.
- The running total counts up to 1,000,000 flips. Copy log includes the sequence for only the last 1,000 flips.
- On a very old browser without Web Crypto, the tool falls back to Math.random, which is not a cryptographic random generator.
- The same-side bias of a real hand-flipped coin (about 50.8%) is not imitated. This tool is always a perfectly fair coin.
- Use a coin to settle a choice between two similar options, and do not leave decisions with large consequences, such as money, health or legal matters, to it.
As of The probabilities in this article were calculated for a fair coin (heads 1/2, independent flips) from the binomial distribution and a recurrence for run lengths. The cited studies and the match rules (IFAB 2026/27, MCC 2026 edition, ITF 2026 edition) were checked against the original documents on 2026-10-22.
Sources
- 01Bartoš, F. et al. (2025). Fair coins tend to land on the same side they started: Evidence from 350,757 flips. Journal of the American Statistical Association 120 (arXiv 2310.04153)350,757 flips of 44 coins by 48 people, same side 50.8% (95% credible interval 50.6–50.9%), 175,421 heads (50.01%), quotes the Pearson and Kerrich records
- 02Diaconis, P., Holmes, S. & Montgomery, R. (2007). Dynamical Bias in the Coin Toss. SIAM Review 49(2), 211–235A vigorously flipped coin lands on its starting side with probability about 0.51
- 03Jaffé, M. E., Reutner, L. & Greifeneder, R. (2019). Catalyzing decisions: How a coin flip strengthens affective reactions. PLOS ONE 14(8), e0220736Two experiments: when the coin points to an option, emotional reactions to that option get stronger
- 04IFAB Laws of the Game, Law 8: The Start and Restart of Play8.1: the referee tosses a coin, the winner chooses the goal to attack or the kick-off, the team that chose the goal takes the second-half kick-off, and a new toss is made before extra time
- 05MCC Laws of Cricket 2017 Code 4th Edition (2026), Law 13 Innings13.4: captains toss on the field in the presence of an umpire to choose the innings (30 to 15 minutes before the start); 13.5: the decision cannot be changed once notified
- 06ITF Rules of Tennis 2026, Rule 9 Choice of Ends and ServiceToss before the warm-up; the winner chooses serve or receive, an end, or to let the opponent choose
- 07MDN: Crypto.getRandomValues()The Web Crypto function that fills an array with cryptographically strong random values
Frequently asked questions
Is this coin flip really 50/50?
Yes. The moment you press Flip, the tool draws one byte from your browser's cryptographic random generator (Web Crypto's crypto.getRandomValues) and calls it heads if the lowest bit is 1 and tails if it is 0. Among the values 0 to 255, exactly 128 are odd and 128 are even, so there is no bias, and each flip is drawn fresh, so heads and tails are 50% each regardless of earlier results. The coin graphic is an animation that spins to land on the chosen side.
Heads came up 5 times in a row. Is that strange?
Not at all. The chance that the first five flips are all the same side is 1 in 16 (6.25%), and in 100 flips the chance of at least one run of 5 or more is 97.2%. The longest run in 100 flips is typically 7. The "How long did the same side repeat?" panel works out the chance of a run as long as your longest one straight from your record.
After 5 heads in a row, is tails more likely next?
No. A coin does not remember earlier results, so the next flip is still 50% heads and 50% tails. Believing the other side is due after a run is called the gambler's fallacy. The ratio moves toward 50% with more flips not because the coin pays back the earlier imbalance, but because the early imbalance gets diluted among the many new results.
Is a real coin flipped by hand also 50/50 for heads and tails?
Heads and tails themselves are close to even, but the side that was facing up before the flip lands up slightly more often. In a study where 48 people flipped coins 350,757 times (Bartoš et al., Journal of the American Statistical Association, 2025), heads came up 50.01% of the time, but the coin landed on its starting side 50.8% of the time. That agrees with the roughly 51% predicted by the 2007 physical model of Diaconis and colleagues. To keep it fair, don't look at which side is up before the flip, or have the other person call it in the air.
Which side of a coin is heads?
It depends on the country and the coin. Many people take the side with the portrait or main picture to be heads, others go by the side with the number. When you flip a real coin with someone, agree on which side counts as heads first. This tool uses no real coin designs and tells the sides apart with the labels H and T and the names you type.
How many flips until the heads ratio gets close to 50%?
Even for a fair coin, the heads ratio stays within 40-60% at 100 flips, 46.9-53.1% at 1,000 flips and 49.0-51.0% at 10,000 flips, each with better than 95% probability. The width of the range shrinks with the square root of the number of flips, so cutting it to a tenth takes 100 times as many flips. The gray band on the ratio curve is that range, and you can check it with the flip-many buttons.
What do soccer, cricket and tennis decide with a coin toss?
In soccer, under Law 8 of the IFAB Laws of the Game, the referee tosses the coin and the winner chooses the goal to attack in the first half or the kick-off. In cricket, under MCC Laws 13.4 and 13.5, the two captains toss and the winner decides whether to bat or field, and the decision cannot be changed once announced. In tennis, under ITF Rule 9, a toss before the warm-up lets the winner choose serve or receive, an end, or to let the opponent choose.
Are my flips or the side names saved?
No. The flip log stays on this screen, is never sent to a server, and disappears when you reload. To keep it, use Copy log to copy the counts, ratios, longest run and the sequence of the last 1,000 flips. The side names can go into the address with Copy link, and opening that link lets you flip with the same names right away. Results are not put in the link.