The odds of flipping heads several times in a row are 1 in 2 multiplied by itself once per flip. Two heads is 1 in 4 (25%), three is 1 in 8 (12.5%), five is 1 in 32, and ten in a row is 1 in 1,024. But there's a twist: if you flip a coin a lot of times, long streaks somewhere in the sequence are far more likely than those numbers suggest. Here's how both halves of that work.
Each flip of a fair coin is independent. The coin doesn't remember the last flip, so every toss is a fresh 50/50. To get the chance of several specific results in a row, multiply the individual chances together.
For three heads: ½ × ½ × ½ = ⅛, or 12.5%. The general formula is (½)ⁿ, where n is the number of flips. Every extra head halves the probability, which is why the numbers shrink so fast:
| Heads in a row | Probability | Odds (1 in …) |
|---|---|---|
| 1 | 50% | 2 |
| 2 | 25% | 4 |
| 3 | 12.5% | 8 |
| 4 | 6.25% | 16 |
| 5 | 3.125% | 32 |
| 6 | 1.5625% | 64 |
| 7 | 0.78% | 128 |
| 8 | 0.39% | 256 |
| 10 | 0.098% | 1,024 |
| 15 | 0.0031% | 32,768 |
| 20 | 0.0001% | 1,048,576 |
The same table works for tails, or for any specific sequence. Heads-tails-heads-tails-heads is exactly as unlikely as five heads: 1 in 32. A streak just looks more special to us.
No, and this is the mistake that has cost gamblers the most money. It's called the gambler's fallacy. After five heads, the next flip is still 50/50. The coin has no way to "balance out."
The confusion comes from mixing up two questions. Before you start, the chance of six heads in a row is 1 in 64. But once five heads have already happened, only the sixth flip is still uncertain, and that's a coin flip. The famous example is a Monte Carlo roulette table in 1913, where black came up 26 spins running and players lost fortunes betting that red was "due."
Over thousands of flips, the percentage of heads does settle near 50%. That's the law of large numbers. It doesn't happen because tails catch up. It happens because early streaks get swamped by the sheer volume of flips that follow.
Here's where intuition goes badly wrong. Five heads in a row starting from a particular flip is 1 in 32. But if you flip 100 times, there are dozens of places a streak could start, and the chances pile up. We ran the numbers exactly:
| Streak of at least … | In 20 flips | In 100 flips |
|---|---|---|
| 3 heads in a row | 78.7% | 99.97% |
| 5 heads in a row | 25.0% | 81.0% |
| 6 heads in a row | 12.2% | 54.6% |
| 7 heads in a row | 5.8% | 31.8% |
| 10 heads in a row | 0.59% | 4.4% |
So in 100 flips, you're more likely than not to see at least six heads in a row somewhere, and a run of five is close to a sure thing. Count streaks of either side and it's more lopsided still: the chance of a run of 6 or more heads or tails in 100 flips is about 81%.
Statistics teachers use this as a party trick. Half the class flips a real coin 100 times, the other half writes down a made-up sequence. The teacher can usually pick out the fakes because they don't have any long streaks. People think randomness looks evenly mixed. Real randomness is clumpy.
About 24.6%. There are 1,024 possible sequences of ten flips, and 252 of them contain exactly five heads. You can pull those numbers straight from row 10 of Pascal's triangle. The next most likely results are 4 or 6 heads, at about 20.5% each. Getting all ten the same way is 1 in 512 once you count both all-heads and all-tails.
Close, but not quite. In 2007, statistician Persi Diaconis and his colleagues showed that a flipped coin slightly favors the side facing up when it's tossed, because of how it wobbles in the air. A 2023 study put that to the test with 350,757 real flips by 48 people and found coins landed on the same side they started about 50.8% of the time.
That edge is tiny. For deciding who goes first, it doesn't matter. But if you ever want a perfectly fair call, have someone else flip, or don't look at which side is up before the toss. And coins landing on their edge? It happens, but for a US nickel the commonly cited estimate is around 1 in 6,000 flips, from a 1993 physics model. It's not something to plan around.
A coin has two outcomes and a die has six, so the same logic just uses sixths. Rolling a 6 is 1 in 6. Two sixes in a row is 1 in 36. With two dice added together, the totals aren't equally likely, because some can be made more ways than others:
| Two-dice total | Ways to roll it | Probability |
|---|---|---|
| 2 or 12 | 1 | 2.8% each |
| 3 or 11 | 2 | 5.6% each |
| 4 or 10 | 3 | 8.3% each |
| 5 or 9 | 4 | 11.1% each |
| 6 or 8 | 5 | 13.9% each |
| 7 | 6 | 16.7% |
That's why 7 is the key number in craps. You can check the spread yourself with the dice roller, or use the random number generator for anything that isn't a coin or a standard die.
For a specific streak, use (½)ⁿ: three heads is 1 in 8, ten is 1 in 1,024. Each flip is still 50/50 no matter what came before. And over a long session, streaks of five, six or seven aren't a sign anything's rigged. They're exactly what a fair coin does.
Flip once or run hundreds of tosses and watch the streaks and heads-to-tails split for yourself.
Coin Flip →1 in 8, or 12.5%. Each flip is a 1 in 2 chance, so you multiply ½ × ½ × ½.
1 in 1,024, or about 0.098%. The chance of ten of the same side in a row (all heads or all tails) is 1 in 512.
No. Each flip is independent, so the next toss is still 50/50. Believing tails is due is known as the gambler's fallacy.
Much more often than people expect. In 100 fair flips, there's about an 81% chance of at least 5 heads in a row somewhere and about a 55% chance of at least 6 in a row.
Very nearly. Research found a coin lands on the same side it started about 50.8% of the time because of how it wobbles in the air. For everyday decisions, that difference doesn't matter.