You expect 50 heads, but anything from about 40 to 60 is completely ordinary, and exactly 50 happens less than one run in twelve. Flip a coin, free, drawn from a genuine cryptographic random source, and see where your own 100 land.
The short answer, with numbers
100 flips is a binomial distribution with n = 100 trials and p = 0.5, the probability of heads on any single flip. Mean = n × p = 50. Standard deviation = √(n × p × q), where q is the probability of the other outcome, 1 − p = 0.5: √(100 × 0.5 × 0.5) = √25 = 5.
Computing the exact binomial probabilities (not the rounded normal-distribution shortcut) for how often the real count of heads falls in each band around that mean:
| Range | Exact probability |
|---|---|
| 45–55 heads | 72.9% |
| 40–60 heads | 96.5% |
| 35–65 heads | 99.8% |
These are close to, but not identical to, the classic “68/95/99.7” rule taught for a continuous normal curve, the small difference comes from the fact that a head count is a whole number, and an inclusive range like “45 to 55” actually covers slightly more area than exactly one standard deviation once you account for that.
The practical takeaway from the table: a result like 43 heads or 57 heads, both a full seven away from the expected 50, is still comfortably inside the 40–60 band that shows up in roughly 96.5% of runs. It’s only once a result drifts out past that band, below 40 or above 60, that it starts becoming genuinely unusual rather than just “a bit off from the middle.”
What are the odds of exactly 50 heads?
P(exactly 50) = C(100, 50) ÷ 2¹⁰⁰ ≈ 0.0796, about 8%. Worth sitting with the two facts side by side: 50 heads is the single most likely individual outcome of the 101 possible results (0 through 100 heads), and it still happens less than one time in twelve. Every other specific outcome is even less likely on its own, the “most likely” result is still an underdog against “everything else combined.” This is the same reason lottery jackpot numbers feel implausible even though every single combination is exactly as unlikely as every other, no individual outcome in a spread-out distribution needs to be common for the distribution itself to have a clear, predictable shape.
How unusual is 60 heads?
Computed exactly as the sum of the binomial probabilities from 60 heads through 100, not estimated: P(60 or more) ≈ 2.8%, roughly 1 in 35. That’s a genuinely unusual result but well within the range a fair coin produces regularly, not evidence of anything. P(70 or more) ≈ 0.004%, about 1 in 25,000, drops into “now start asking questions” territory, a run that lopsided from a fair coin is rare enough that a biased coin or a biased flip becomes the more likely explanation.
The longest streak you should expect
In 100 flips, the longest run of the same side (heads-heads-heads… or tails-tails-tails…) is typically around six or seven, following the rough rule that the expected longest streak in n flips is about log₂(n): log₂(100) ≈ 6.6. This is the basis of a genuinely useful classroom demonstration: ask a group to fake 100 coin flips on paper without actually flipping anything, and their invented sequences almost never contain a run of seven or more, people writing “randomly” instinctively break up long streaks because a long run doesn’t feel random, even though real random sequences produce one almost every time. Spotting the absence of a long streak is often the fastest way to catch a faked sequence.
The same instinct that makes people avoid writing long streaks when faking a sequence, “that doesn’t look random,” is the gambler’s fallacy working in reverse, the mistaken belief that a fair process needs to actively avoid repeating itself to stay fair. A genuinely random sequence has no memory at all, the coin doesn’t know it’s already come up heads six times in a row, and the seventh flip is exactly 50/50 regardless of what came before it. Streaks aren’t a sign randomness is breaking down, they’re a normal, expected feature of it.
What about 1,000 flips?
Same shape, tighter as a percentage of the total. Mean = 500, standard deviation = √(1000 × 0.25) = √250 ≈ 15.8, and the exact probability of landing between 468 and 532 heads is about 96.0%. That’s a wider absolute gap than the 40–60 band at 100 flips, 64 heads wide instead of 20, but a much narrower one as a percentage of the total, 46.8–53.2% of 1,000 flips versus 40–60% of 100. This is the law of large numbers in action: it tightens the proportion of heads toward 50%, not the raw head count’s distance from the halfway mark, which actually grows in absolute terms as you flip more.
Are real coins actually 50/50?
Almost, not quite. Diaconis, Holmes and Montgomery’s 2007 physics model of a tossed coin predicted a “dynamical bias,” a coin tends to land on the same side it started on slightly more often than chance, driven by precession, a wobble in the spin axis, rather than anything about the coin’s weighting. Their model predicted roughly a 51% same-side bias for a naturally tossed coin. Bartoš et al.’s 2023 study of 350,757 real flips empirically confirmed it, finding a same-side bias of about 50.8%, close to the physics model’s prediction and clearly real, if small.
That bias is a property of the physical toss, the wobble and the starting position, not the coin itself, and it has nothing to do with digital random number generation. It’s also small enough that it only shows up reliably across hundreds of thousands of flips, a 50.8% bias means roughly 508 same-side outcomes per 1,000 flips instead of an even 500, a gap invisible in any single game or classroom demonstration and only detectable once you’re pooling results across a genuinely enormous sample. A digital flip a coin result, drawn from a cryptographic random source, has no spin, no wobble and no starting side to be biased toward in the first place, there’s no physical mechanism for the same kind of bias to act through.
How to actually run 100 flips
Being straightforward about how this works today: go flip a coin and you’ll find it does one flip at a time, keeping a running heads, tails and total tally for the session, which resets if you reload the page. A hundred flips means a hundred taps, which is genuinely the point for a classroom demonstration, watching the running tally settle toward the expected spread as you go is more instructive than a single instant result. A dedicated flip a coin 100 times page that runs the full batch at once is on the roadmap, this page will link to it properly once it exists.
FAQ
How many heads should I get in 100 flips?
Expect somewhere around 50, but anything from about 40 to 60 is completely ordinary. The exact math, mean 50 with a standard deviation of 5, is worked through above.
What are the odds of exactly 50 heads?
About 8%, computed exactly as C(100,50) divided by 2 to the power 100. It’s simultaneously the single most likely outcome and something that happens less than one run in twelve.
Is 60 heads out of 100 suspicious?
Not really, the exact probability of 60 or more heads is about 2.8%, roughly a 1-in-35 event. 70 or more is a different story, about 1 in 25,000, that’s genuinely worth a second look.
What’s the longest streak in 100 flips?
Typically around six or seven, following the rough rule that the expected longest run in n flips is about log base 2 of n. A “faked” sequence of 100 flips almost never contains a run that long, which is exactly how you can spot one.
Is a real coin toss really fair?
Almost, but not perfectly. Physical coins have a slight, real bias toward landing on the side they started on, measured at about 50.8% in the largest study to date, driven by the physics of the toss rather than the coin itself. A digital flip drawn from a cryptographic random source has no physical toss to be biased in the first place.
Ready to actually go see your own 100? Flip a coin, free, no signup, drawn from a genuine cryptographic random source with a running tally as you go. For a number-based random pick instead, the dice roller covers that, and the random name picker handles anything with more than two possible outcomes.