Maxi Calculator

Coin Toss Streak Calculator

Analyze probabilities of consecutive outcomes in coin tosses

Coin Toss Streak Calculator

Enter the length of the streak you want to analyze

Select which outcome you want to track streaks for

Enter the probability of getting your target outcome (0.5 for a fair coin)

Enter the number of trials to simulate (minimum 1000)

Table of Contents
How the Calculator Works

This calculator analyzes the probability of getting consecutive outcomes (streaks) in a series of coin tosses:

  • Enter the length of the streak you want to analyze (e.g., 3 for three consecutive heads)
  • Choose whether you want to analyze streaks of heads or tails
  • Set the probability of getting your target outcome on each toss (0.5 for a fair coin)
  • The calculator provides:
    • Exact probability of getting the specified streak
    • Probability of getting at least that long of a streak
    • Expected number of tosses needed to see such a streak
    • Simulated probability based on multiple trials for verification
Understanding Streak Probability

Streak probability in coin tosses follows specific mathematical principles:

  • For a streak of length k, you need k consecutive successes
  • The probability of a streak is affected by:
    • The length of the desired streak
    • The probability of success on each individual toss
    • Whether you're looking for an exact or minimum streak length
  • The expected waiting time follows a geometric distribution pattern
  • Longer streaks are exponentially less likely than shorter ones
Applications and Uses

Streak analysis has various practical applications:

  • Analyzing patterns in random sequences
  • Testing for randomness in data
  • Understanding the likelihood of rare events
  • Studying the gambler's fallacy
  • Educational demonstrations of probability concepts
Frequently Asked Questions

Why is the probability of a long streak so low?

The probability decreases exponentially with streak length because each additional toss must be successful while maintaining the previous successes. For a fair coin, each additional required success halves the probability.

What's the difference between exact and at-least probabilities?

Exact probability tells you the chance of getting exactly the specified streak length, while at-least probability includes the chance of getting that length or longer. The at-least probability is always greater than or equal to the exact probability.

Why does the simulated probability differ from the theoretical one?

The simulation uses random sampling to estimate probabilities, so there will always be some variation from the theoretical value. The more trials you run, the closer the simulated probability will tend to be to the theoretical value.