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Coin Flip Streak Probability Calculator — result sheet
Calculate the probability of seeing at least one run of consecutive heads in fair coin flips.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: Probability of at least one run = 1 − probability of avoiding the selected run across all flips.
A finite-state recurrence counts paths that have not yet reached the requested heads streak, avoiding a simulation estimate.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Number of flips — minimum 1; maximum 1000
- Heads in a row — minimum 1; maximum 1000
Worked example
| Input | Value |
|---|---|
| Number of flips | 10 |
| Heads in a row | 3 |
Probability of at least one three-head streak ≈50.78%.
Assumptions and limits
- Flips are fair, independent, and recorded in order.
- The streak is consecutive heads and may begin at any position.
- Biased coins, stopping rules, overlapping event costs, and physical procedures are not modeled.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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