Coin Flip Streak Calculator

Calculate the probability and expected length of consecutive heads or tails streaks in a series of coin flips.

P(STREAK ≥ k)
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Expected Max Streak
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P(any streak ≥ k)
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Simulated P
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Avg Max Streak
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About Coin Flip Streaks

Streaks in coin flipping are surprisingly common and often longer than people expect. Humans tend to underestimate the likelihood of long runs, which leads to the "hot hand fallacy" in sports and gambling. Understanding streak probability is essential for evaluating randomness.

In n fair coin flips, the expected length of the longest streak is approximately log2(n). With 100 flips, expect a streak of about 7. With 1000 flips, about 10.

Expected Maximum Streak

E[longest run] ≈ log2(n) for fair coin
E[longest run] ≈ -log(n) / log(p) for biased coin

Expected Streaks by Number of Flips

FlipsExpected Max Streak
10~3.3
50~5.6
100~6.6
1000~10.0

FAQ

Is a streak of 10 heads suspicious?

In 20 flips, very suspicious (P ≈ 0.04%). In 10,000 flips, completely expected. Context (total flips) matters enormously when evaluating streaks.

What is the hot hand fallacy?

The belief that a person who has experienced success has a greater chance of further success. While recent research suggests a small hot hand effect may exist in some sports, much of what people perceive as hot streaks is consistent with random variation.