Find the probability of getting a run of heads or tails in a series of coin flips
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Flip a coin 100 times. How likely is it that you’ll see five heads in a row? The answer might surprise you, it’s far more common than intuition suggests. Streaks are a natural part of random sequences, and understanding their probability helps explain why we often see “runs” in everything from sports to financial markets. But calculating the probability of a streak isn’t as simple as multiplying a few coin flips together, you have to account for the overlapping nature of streaks in a sequence.
This coin toss streak calculator does the heavy lifting for you. Enter the number of tosses and the target streak length, the tool computes the probability of getting at least one streak, the “1 in X” odds, and the expected number of streaks. Choose whether you’re looking for heads or tails, and the calculator handles the rest. Whether you’re a statistics student studying runs in random sequences, a gambler analyzing betting patterns, or just curious about how streaks work, this calculator delivers accurate results instantly. All calculations run locally in your browser, keeping your data private.
Select your target side: Heads or Tails using the radio buttons at the top of the calculator.
Enter the total number of coin tosses using the first input field, this is the length of the sequence.
Enter the streak length you’re interested in the number of consecutive heads or tails in a row.
Review the probability of at least one streak, the “1 in X” odds, and the expected number of streaks.
Use the Copy button to save results or Share to send them to others.
The calculator applies a dynamic programming algorithm to compute the probability of at least one streak of length k in a sequence of n independent fair coin flips. This approach tracks the current streak length state and propagates probabilities forward.
Formula: P = 1 − (Probability of no streak of length k)
The probability of at least one streak is the complement of the probability that no streak of length k occurs. The DP algorithm maintains a state vector where each element represents the probability of being in a streak of a certain length (0 to k−1), and updates it for each toss.
Formula: Expected Number of Streaks ≈ (n − k + 1) × p^k
For a fair coin, the probability of a specific streak of length k starting at a given position is p^k = (1/2)^k. There are (n − k + 1) possible starting positions, so the expected number of streaks is approximately (n − k + 1) × (1/2)^k. This is an approximation because streaks can overlap, but it’s useful for understanding the scale.
Consider flipping a fair coin 100 times. What’s the probability of getting at least one run of 5 consecutive heads?
Step 1: Identify the known values
n = 100 tosses
k = 5 consecutive heads
p = 0.5 (fair coin)
Step 2: Calculate using the DP algorithm
The probability of at least one streak of 5 heads is approximately 96.85%.
Step 3: Determine the “1 in X” odds
1 / 0.9685 ≈ 1.03 — about 1 in 1.03, meaning the streak is almost guaranteed.
Step 4: Calculate the expected number of streaks
Expected = (100 − 5 + 1) × 0.5⁵ = 96 × 0.03125 = 3.00
Interpretation: In 100 tosses of a fair coin, there’s about a 96.9% chance of seeing at least one run of 5 heads. You’d expect to see about 3 such streaks on average. The probability is high because even though each specific 5-head streak has only a 3.125% chance, there are 96 possible starting positions, and the events overlap.
The probability of getting at least one run of 5 consecutive heads in 100 tosses is approximately 96.9%. This means it’s almost guaranteed to happen.
You need about 30 tosses for a 50% chance of at least one 5-head streak. At 100 tosses, it’s over 96%. The calculator lets you explore the exact probability for any n.
The expected longest run in 100 tosses is approximately 6.6. This means you’d typically see a run of 6 or 7 heads or tails. For 1,000 tosses, it’s about 10.
Streaks overlap when a streak of length k can start at multiple positions that share some of the same flips. For example, in a sequence of 6 heads, there are two overlapping 5-head streaks. This overlap makes streaks more likely than a simple independence assumption would suggest.
The probability of at least one 10-head streak in 100 tosses is about 4.4%. This is rare but not impossible, you’d expect to see it about once every 23 runs of 100 tosses.
For a fair coin, the probability of a heads streak and a tails streak are identical. The calculator lets you choose either side, but the probabilities are the same.
The calculator assumes a fair coin (p = 0.5). For a biased coin, the DP algorithm can be adapted by changing p, but the calculator currently only supports a fair coin. The principles are the same, the probability of a streak increases with p for the target side.
People often underestimate the probability of streaks because they think in terms of independent events rather than overlapping sequences. The calculator shows the true probability, helping you understand that streaks are a natural part of random sequences.
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