Coin Flip Streak Calculator

Find the exact probability of getting a streak of consecutive heads (the same outcome) within a set number of coin flips, for a fair or biased coin.

Quick Facts

Method
Exact run-length recurrence (dynamic programming)
Counts every sequence with a run of r or more heads — no approximation.

Your Results

Calculated
P(streak of r+ heads)
-
Chance it happens at least once in n flips
Odds
-
Roughly 1 in this many runs
P(no such streak)
-
Complement — the streak never occurs
Expected longest run
-
Average length of the longest head-streak

Ready

Enter the number of flips, the streak length, and the per-flip head probability.

What this calculator finds

A "streak" (or run) is a block of consecutive flips that all land the same way — for example five heads in a row. This tool answers a precise question: given n flips of a coin that lands heads with probability p, what is the chance of seeing at least one run of r or more consecutive heads somewhere in those flips? By symmetry, the same numbers apply to a run of tails when the coin is fair; for a biased coin, set p to the probability of the outcome whose streak you care about.

Why it is not simply (1/2)ʳ

A common mistake is to compute (1/2)ʳ and stop. That is the probability of a specific block of r heads at one fixed starting position — for r = 5, that is 1/32 ≈ 3.125%. But in a sequence of n flips a run of length r can begin at many different positions, and those windows overlap, so you cannot just multiply or add them. The correct probability of getting such a run anywhere in n flips is larger. For 10 fair flips and r = 5 the true answer is 11/32 of a naive guess away from intuition: exactly 0.109375 (10.9375%), which is 112 of the 1024 possible sequences.

The exact method

This calculator uses a run-length recurrence (a small dynamic program), which gives the exact probability rather than an approximation. It tracks the length of the current trailing head-run after each flip. Each flip, a head extends the run and a tail resets it to zero; as soon as the run reaches r, that sequence is counted as a success. Summing the probability mass that reaches the "r" state gives P(streak). The chance that no such streak occurs is simply the complement, 1 − P(streak).

Expected longest streak

The calculator also reports the expected length of the longest head-run, computed as E[L] = Σr≥1 P(longest run ≥ r). For 10 fair flips the expected longest head-run is about 2.80; for 100 fair flips it rises to roughly 6. A useful rule of thumb for a fair coin is that the longest run of heads in n flips is close to log₂(n): log₂(100) ≈ 6.64, which is why long sequences almost always contain a surprisingly long streak.

Reference points for a fair coin (p = 0.5)

  • 5+ heads in 10 flips: 0.109375 (about 1 in 9).
  • 3+ heads in 10 flips: 0.5078125 (just over even odds).
  • 5+ heads in 100 flips: about 0.8101 — a 5-streak is the norm, not the exception, over 100 flips.
  • 7+ heads in 100 flips: about 0.3175.
  • At least 1 head in 10 flips (r = 1): 1 − 0.5¹⁰ = 0.999023.

Frequently Asked Questions

What is the chance of 5 heads in a row within 10 flips of a fair coin?
Exactly 10.9375%. Of the 1024 equally likely sequences of 10 fair flips, 112 contain a run of five or more consecutive heads, and 112 ÷ 1024 = 0.109375. That is far higher than (1/2)⁵ = 3.125%, because a 5-run can start at any of several positions in the sequence.
Does it work for tails, or for a biased coin?
Yes. For a fair coin the streak probability for tails equals that for heads by symmetry, so leave p at 0.5. For a biased coin, enter the per-flip probability of the specific outcome whose streak you want — for example 0.3 if you are asking about a run of an event that happens 30% of the time.
Why can a long streak appear "against the odds"?
Because each independent flip has no memory. A run of heads does not make tails "due" — the gambler's fallacy. Over many flips, long runs are actually expected: in 100 fair flips the longest head-run is about 6 on average, and seeing at least a 5-run happens roughly 81% of the time. Streaks are a normal feature of randomness, not evidence of a rigged coin.

Related calculators