How it works
Choose k heads in a row to find the chance of a streak of at least k consecutive heads somewhere in n flips. Streaks are far more common than people expect: in just 10 fair flips there is about a 51% chance of seeing 3 or more heads in a row.
Choose at least k heads total for the binomial probability of k or more heads anywhere in the sequence, regardless of order.
The streak probability is computed exactly by tracking the length of the current run of heads after each flip. Set the chance of heads below or above 50% to model a biased coin or any yes/no event.
Formula
Total: P(X ≥ k) = Σ C(n, j) pʲ(1 − p)ⁿ⁻ʲ for j = k…n · Streak: Markov chain on current run length
Questions people ask
What are the odds of 10 heads in a row?
If you flip exactly 10 times, it is 0.5¹⁰ = 1 in 1,024. Over a longer series the chance of a 10-streak somewhere rises; in 1,000 flips it is about 38%.
After 5 heads, is tails more likely?
No. Coin flips are independent, so the next flip is still 50/50. Believing otherwise is the gambler’s fallacy.
Why are streaks so common?
There are many starting points for a streak in a long sequence, and each one is another chance for it to happen. People tend to underestimate this when judging whether a sequence looks random.