Coin Flip Streak Calculator
Calculate the probability of exact, at least, or at most consecutive heads streaks in coin toss sequences with distribution breakdown.
What Are Streaks in Coin Flips?
A streak (or run) in coin flipping is a sequence of consecutive identical outcomes, such as three heads in a row. Unlike standard binomial probability, which counts total heads regardless of order, streak probability depends on the arrangement of results.
Types of Streak Probability
- Exactly: The longest streak of heads equals a specific length.
- At least: The longest streak of heads is greater than or equal to a given length.
- At most: The longest streak of heads does not exceed a given length.
How This Calculator Works
Enter the total number of coin flips, the streak length you are interested in, and the streak type. The calculator uses dynamic programming to count valid sequences and returns the probability, percentage, and odds (1 in N). For up to 20 flips, a full distribution of longest-streak probabilities is shown.
Example: Three Coin Flips
With 3 flips, there are 8 equally likely outcomes. The probability of a longest streak of exactly 2 heads is 2/8 = 25%. The probability of at least 2 consecutive heads is 3/8 = 37.5%.
Frequently Asked Questions
How is streak probability different from binomial probability?
Binomial probability counts how many heads appear in total, regardless of order. Streak probability cares about consecutive runs, so HHT and HTH give different streak results even with the same head count.
What does "at least k consecutive heads" mean?
It means the longest run of heads in the sequence is k or more. For example, HHH contains a streak of at least 2 because it also has three consecutive heads.
Can I calculate tails streaks?
By symmetry, the probability of a heads streak of length k equals the probability of a tails streak of length k on a fair coin.
Why is the streak distribution not symmetric?
The distribution of the longest streak length is not symmetric around the middle because short streaks are more common than very long ones, especially with fewer flips.
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