Coin Flip Streak Tracker – Visualize Randomness

The probability of getting 5 consecutive heads in 5 flips is (1/2)⁵ = 1/32 ≈ 3.125%. However, in a long sequence of flips, the chance of encountering a streak of 5 heads at some point is much higher. For example, in 100 flips, the probability of seeing at least one streak of 5+ heads exceeds 80%. Streaks are a natural part of random sequences and do not indicate any bias.

The Gambler's Fallacy is the mistaken belief that past events affect future probabilities in independent random events. For example, after seeing 5 tails in a row, someone might think "heads is due" — but the probability of heads on the next flip is still exactly 50%. Each coin flip is independent; the coin has no memory. This tool helps visualize that long streaks occur naturally in truly random sequences.

The Law of Large Numbers states that as the number of trials increases, the observed ratio of heads (or tails) will tend to converge toward the theoretical probability of 50%. However, this convergence is not smooth — you'll see fluctuations and streaks along the way. Watch the running ratio chart above as you flip more coins; notice how it gradually stabilizes around the 50% line, even though short-term swings can be dramatic.

In 100 coin flips, the expected longest streak is about 6 to 7 flips. Streaks of 8+ are less common but still occur regularly. In 1,000 flips, you can expect a longest streak of around 9 to 10. This follows from extreme value theory: the expected longest streak in N flips is approximately log₂(N). Use this tracker to see how long your streaks get — you might be surprised!

No. Each coin flip is an independent event with a fixed 50% probability for each side (assuming a fair coin). No matter what pattern or streak you've observed, the next flip is unaffected. This independence is what makes coin flips a classic example of true randomness. Any apparent "patterns" are just the human brain's tendency to find order in random data — a phenomenon called apophenia.

Theoretical probability is the expected likelihood based on the nature of the event — for a fair coin, it's exactly 50% heads. Empirical probability is what you actually observe from experiments. With a small number of flips, the empirical result can deviate significantly from 50%. As you increase the number of flips (using the batch buttons above), the empirical probability should gradually approach the theoretical value — a powerful demonstration of probability theory in action.