Coin Flip Streak Probability Calculator
The chance of seeing a run of k heads (or tails) in a row somewhere within n coin flips — exact probability, the expected longest streak and flips needed for a 50% chance.
How it works
P(no run of k in n) via the recursion over the current run length rᵢ ∈ {0…k−1}; P(run) = 1 − P(no run); E[longest] = Σⱼ P(run ≥ j)
Streaks are far more common than intuition says: in 100 fair flips a run of six heads appears about 54% of the time and a run of seven about 32%, and the longest run is usually 6–7. That is why real sequences look “too clumpy” to people asked to fake them. The recursion tracks the probability of every possible current run length after each flip, which gives exact answers without simulation and works for biased coins too — set the probability to a hitter’s batting average or a shooter’s make rate to see how ordinary hot streaks are.
Worked example
100 flips, run of 7: probability 31.8%, expected longest run about 6. A run of 10 has a 50% chance of appearing by about 1,420 flips.
Frequently asked questions
Heads or tails — does it matter?
The result is for one named outcome. For “either heads or tails k in a row” use k−1 with the same n, roughly doubling the chance.
Is the hot hand real?
Runs this common arise from pure chance; genuine streakiness has to be shown over and above this baseline.
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This calculator is for educational purposes. Double-check important results before acting on them.