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Probability

Gacha Calculator

Learn the expected number of pulls to get the amount of SSR copies to budget your spending, or to maximize revenue as a gacha creator.

What Is This About?

This comprehensive suite of interactive calculators helps you understand gacha systems and general gacha mechanics analysis. Gacha games use probability-based reward systems where players spend currency to obtain rare items or characters.

The Challenge: Understanding Gacha Probability

Gacha systems are complex probability models:

  • Base Rates: Low probability (0.5-1%) for rare items
  • Pity Systems: Guaranteed rewards after certain thresholds
  • Soft Pity: Increasing rates before hard pity
  • 50/50 Mechanics: Chance to get event-limited vs standard items

Understanding these mechanics helps players budget spending and helps game designers optimize monetization.

Who Is This For?

This calculator is designed for:

  • Gacha Game Players: Budgeting spending and understanding pull probabilities
  • Game Developers: Designing and balancing gacha systems
  • Data Analysts: Understanding probability distributions in gaming
  • Anyone Learning Probability: Practical application of cumulative probability and distributions
  • Gacha Game Designers: Optimizing revenue through probability mechanics

Cumulative Probability Chart

This chart shows how many attempts you need to reach specific probability thresholds for obtaining target copies.

Help

Suppose you intend to C6 a limited character from Genshin Impact, you will read the green line "Bernuolli + Pity adjust".

At default settings, it works out to ~1300 rolling attempts to have a 95% chance of maxing out your character.

Basic Parameters

Pity System

Bernoulli System

Chart Information

This chart shows the required amount of attempts to reach a cumulative probability of obtaining 1 target copies of a limited character you intend to pull. Each line represents a different gacha system configuration:

  • Base: Standard gacha with 0.5% base rate

SSR Count Distribution

This histogram shows the distribution of expected counts of the SSR you want from a given number of attempts.

Basic Parameters

Pity System

Bernoulli System

Statistics

Base:Expected SSR: 4.89, Variance: 4.56

SSR

  • Pity Peak: 90
  • Pity Start: 75
  • Bernuolli Probability: 50

Weapon

  • Pity Peak: 80
  • Pity Start: 65
  • Bernuolli Probability: 75

SSR

  • Pity Peak: 80
  • Pity Start: 70
  • Bernuolli Probability: 50

Weapon

  • Pity Peak: 80
  • Pity Start: 70
  • Bernuolli Probability: 100

How to Do This Properly on Your Own

Understanding Gacha Probability Models

Gacha systems use several probability concepts:

  1. Bernoulli Trials: Each pull is an independent trial with a base success probability
  2. Cumulative Probability: Probability of success within N attempts
  3. Pity Systems: Guaranteed success after threshold (affects distribution)
  4. 50/50 Mechanics: Conditional probability for event-limited items

Key Calculations

  • Expected Pulls: Average number of pulls needed for success
  • Cumulative Probability: P(success within N pulls) = 1 - (1 - p)^N (simplified, before pity)
  • Distribution Analysis: Histogram of outcomes across many simulations

Implementation Notes

  • Pity systems modify the probability distribution (not simple geometric)
  • Soft pity increases rates gradually before hard pity
  • 50/50 mechanics require tracking state (limited vs standard)

Has This Helped You?

If you found this gacha calculator useful:

  • Share it with your gaming community or on social media
  • Bookmark this page for future reference
  • Write backlinks to this page when referencing gacha probability analysis

This calculator provides insights into:

  • Pull budgeting and spending planning
  • Probability distributions in gacha systems
  • Pity system mechanics
  • Expected value calculations

For Those Who Want to Do It Properly Themselves

Ready to build your own gacha probability calculator? The core concepts involve:

  1. Probability Modeling: Bernoulli trials, geometric distributions, modified distributions with pity
  2. Cumulative Calculations: Probability of success within N attempts
  3. Monte Carlo Simulation: Simulating many pulls to generate distributions
  4. State Tracking: Handling 50/50 mechanics and pity counters

You can reference the chart components to understand how to:

  • Calculate cumulative probabilities with pity systems
  • Generate probability distributions
  • Visualize expected outcomes