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
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:
- Bernoulli Trials: Each pull is an independent trial with a base success probability
- Cumulative Probability: Probability of success within N attempts
- Pity Systems: Guaranteed success after threshold (affects distribution)
- 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:
- Probability Modeling: Bernoulli trials, geometric distributions, modified distributions with pity
- Cumulative Calculations: Probability of success within N attempts
- Monte Carlo Simulation: Simulating many pulls to generate distributions
- 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