The chart
These figures assume a fair coin, where heads and tails are each 50%. Tails works exactly the same way as heads, so "all heads" has the same probability as "all tails".
| Flips | All heads | Odds of all heads | At least one head | Exactly half heads |
|---|---|---|---|---|
| 1 | 50.0% | 1 in 2 | 50.0% | – |
| 2 | 25.0% | 1 in 4 | 75.0% | 50.0% |
| 3 | 12.5% | 1 in 8 | 87.5% | – |
| 4 | 6.25% | 1 in 16 | 93.8% | 37.5% |
| 5 | 3.12% | 1 in 32 | 96.9% | – |
| 6 | 1.56% | 1 in 64 | 98.4% | 31.2% |
| 7 | 0.78% | 1 in 128 | 99.2188% | – |
| 8 | 0.39% | 1 in 256 | 99.6094% | 27.3% |
| 9 | 0.20% | 1 in 512 | 99.8047% | – |
| 10 | 0.0977% | 1 in 1,024 | 99.9023% | 24.6% |
| 11 | 0.0488% | 1 in 2,048 | 99.9512% | – |
| 12 | 0.0244% | 1 in 4,096 | 99.9756% | 22.6% |
| 13 | 0.0122% | 1 in 8,192 | 99.9878% | – |
| 14 | 0.0061% | 1 in 16,384 | 99.9939% | 20.9% |
| 15 | 0.0031% | 1 in 32,768 | 99.9969% | – |
| 16 | 0.0015% | 1 in 65,536 | 99.9985% | 19.6% |
| 17 | 0.000763% | 1 in 131,072 | 99.9992% | – |
| 18 | 0.000381% | 1 in 262,144 | 99.9996% | 18.5% |
| 19 | 0.000191% | 1 in 524,288 | 99.9998% | – |
| 20 | 0.000095% | 1 in 1,048,576 | 99.9999% | 17.6% |
How to read it
- All heads is one outcome out of 2n, where n is the number of flips. Each extra flip halves the chance.
- At least one head is 100% minus the chance of all tails. It climbs quickly towards certainty.
- Exactly half heads is the number of ways to choose half the flips to be heads, divided by 2n. It only applies to an even number of flips.
Why "exactly half" gets less likely
With 2 flips, you get one head and one tail half the time. With 20 flips, exactly 10 heads happens about 17.6% of the time. The proportion of heads gets closer to 50% as you flip more, but hitting the exact count gets harder. A split such as 9 heads and 11 tails is just as normal as 10 and 10.
The odds of a streak
The chart shows the chance of one specific run starting from your first flip. Streaks that can start anywhere in a longer sequence are more common than people expect. For any run length and number of flips, use the coin flip odds calculator.
Past flips don't change the next one
If you have flipped five heads, the next flip is still 50/50. The chance of six heads in a row is low before you start, but once five have happened, the sixth is just one more flip. This is the idea behind the gambler's fallacy.
Try it yourself
Flip up to six coins at once on our coin flip page, or use the best of 3 coin flip to see how a short series plays out.
Last updated 2026-10-18.