What does "at least one streak" mean?

It means the sequence of n flips contains at least one run of k (or more) consecutive identical outcomes. Overlapping runs count only once toward the streak threshold — we just need one to appear.

How is this different from a simulation?

A simulation approximates the answer by running thousands of random trials. This calculator uses an exact Markov-chain recurrence that tracks every possible state, so the result is mathematically exact — no sampling error.

Why does the probability rise so fast with more flips?

With more flips you get more independent "windows" for a streak to start. Even a streak of 6 heads becomes more likely than not somewhere around 100 flips.

What is the "expected number of streaks"?

This is the average number of non-overlapping streak occurrences you would observe if you repeated the n-flip experiment many times. A value of 0.5 means you expect to see one streak about every other experiment.

Does "either outcome" double the probability?

Not exactly, because the events overlap. The calculator handles this correctly using inclusion-exclusion so it never exceeds 100%.

Is the coin assumed fair?

Yes — each flip is 50/50. A future version may support biased coins. For now all probabilities assume p = 0.5.

Coin Flip Streak Probability Calculator

Name: Coin Flip Streak Probability Calculator
Availability: InStock
Author: Nham Vu

Enter the number of flips and desired streak length to find the exact probability of at least one consecutive run, plus the expected streak count.

Parameters

Number of flips (n)

1 – 10,000

Streak length (k)

1 – 100 (must be ≤ n)

Count streaks of

Either outcome (heads or tails) Heads only Tails only

At Least One Streak

—

No Streak

—

Expected Streaks

—

per experiment

Streak probability 0%

0% (impossible) 100% (certain)

How probability grows with flip count

Flips (n)	P(at least one streak)	Expected streaks

Set your parameters and click Calculate

Results use exact Markov-chain math — no simulation

Summary

Enter the number of flips and desired streak length to find the exact probability of at least one consecutive run, plus the expected streak count.

How it works

Set the number of flips (n) and the streak length (k) you want to detect.
Choose whether to count heads streaks, tails streaks, or either outcome.
The tool builds a Markov chain where each state tracks the current run length toward k.
It evolves the probability distribution across all n flips without any approximation.
Results show P(at least one streak), probability of zero streaks, and expected streak count.

Use cases

Verify gambling intuitions — how likely is 5 heads in a row over 20 flips?
Teach probability and Markov chains with a concrete, interactive example.
Analyze streaks in sports win/loss records under the null hypothesis of equal skill.
Assess quality-control run rules: how often does a 7-in-a-row alarm trigger by chance?
Settle probability debates at card game tables or in statistics classes.
Explore how streak probability scales with flip count and streak length.

Frequently Asked Questions

Last updated: 2026-07-22 · Reviewed by Nham Vu