Coin Flip Probability Calculator
Work out real coin-flip odds — the chance of a streak of heads, all heads, or no heads at all, for any number of flips and any coin bias.
How it works
P(all heads) = p^n · P(no heads) = (1−p)^n · P(streak of k) = 1 − P(no run of k), computed with a run-length dynamic program · expected heads = n × p
A fair coin has a 50% chance of heads each flip, but people badly underestimate how likely a streak becomes over many flips. The chance of all heads is simply p multiplied by itself for every flip, and no heads is the same with tails. The streak probability is trickier — it uses a dynamic program that tracks the current run length flip by flip, so it correctly counts every way a run of k heads could appear anywhere in the sequence.
Worked example
With 10 flips of a fair coin, the chance of getting at least one run of 3 heads in a row is about 51% — better than even, which surprises most people. Yet all 10 heads is only (0.5)^10 ≈ 0.098%, roughly 1 in 1,024.
Frequently asked questions
Why is a streak more likely than I’d guess?
Because the run can start at many positions across the flips. Each individual streak is unlikely, but with ten or more flips there are lots of chances for one to appear, so the combined probability climbs quickly.
Can I use a biased coin?
Yes — set the “chance of heads” away from 50%. The all-heads, no-heads and streak odds all adjust for the bias you enter.
Does this give a random flip result?
No. It reports exact probabilities, which are the same every time, rather than simulating a single random outcome.
Related calculators
For fun and learning — the probabilities are exact, but real coins and dice can never be perfectly fair.