Coin flip streak probability calculator
Is 5 heads in a row within 20 flips rare? The tool gives the exact chance and the average number of flips until the streak appears.
Loading the tool…
Processing and privacy: The result is calculated inside your browser and your data is not sent to any server.
How to use it
- Enter number of flips n, streak length k, streak of and chance of heads.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Dynamic programming over the current run length after each flip with heads chance p; the answer is 1 minus the chance the run never reaches k. Mean flips to k heads in a row = (1 - p^k) ÷ ((1 - p) × p^k).
Example
Inputs: Number of flips n = 20, Streak length k = 5, Streak of = Heads only, Chance of heads = 0.5. Result: Chance of at least one streak: 0.2498703003; As a percentage: 24.98703%; Chance of no streak: 0.7501296997.
Limits and caveats
- Assumes independent flips with a fixed chance of heads.
- Up to 2000 flips.
Questions about this tool
Is 3 heads in a row within 10 flips rare?
No, the chance is about 50.8%, roughly every other try.
How many flips does 5 heads in a row take on average?
With a fair coin the average is 2^(k+1) - 2 = 62 flips.
What is the difference between heads only and either side?
Either side counts k identical faces in a row, heads or tails, so the chance is higher.