Gaming

Gacha Probability Calculator

Calculate your odds of pulling a specific character or item. Enter the drop rate, number of pulls, and optional pity system to see exact probabilities.

Quick Answer

With a 0.6% drop rate and 90 pulls, you have a ~41.8% chance of getting at least one copy (without pity). With a pity system at 90 pulls, you are guaranteed. Use the calculator below for your specific banner.

Pity System

Probability Results

Chance of at least 1 copy100.00%
0 Copies
0.00%
Exactly 1 Copy
31.61%
2+ Copies
68.39%
Expected Pulls for 1 Copy
90
Median Pulls (50% Chance)
116

About This Tool

The Gacha Probability Calculator is a free tool for mobile and online gamers who want to understand their real odds before spending premium currency. Gacha games use randomized loot-box-style mechanics where players spend in-game currency (or real money) to "pull" for characters, weapons, or items. Each pull has a stated drop rate, but human intuition is notoriously bad at understanding probability, especially for rare events. This calculator turns abstract percentages into concrete numbers you can plan around.

The Mathematics Behind Gacha Pulls

Each gacha pull is modeled as an independent Bernoulli trial with a fixed success probability (the drop rate). The probability of getting at least one success in N trials follows the formula P(at least 1) = 1 - (1 - rate)^N. This is derived from the complement rule: the probability of getting zero successes in N independent pulls is (1 - rate)^N, and the probability of the opposite event (at least one success) is one minus that. For example, with a 0.6% drop rate and 100 pulls, the probability of zero successes is (0.994)^100 = 54.8%, so the probability of at least one success is 45.2%.

Understanding Pity Systems

Most modern gacha games implement a pity system to prevent extremely long dry streaks. A hard pity guarantees the rare drop after a fixed number of pulls (e.g., 90 in Genshin Impact). A soft pity gradually increases the drop rate as you approach the hard pity threshold, making it increasingly likely you will get the item before reaching hard pity. In Genshin Impact, the base 5-star rate of 0.6% starts increasing around pull 74, reaching roughly 32% per pull by pull 89. The average 5-star arrives around pull 62, well before the 90-pull hard pity.

Expected Value vs. Worst Case

The expected number of pulls to get one copy follows the geometric distribution: E(X) = 1/rate. For a 0.6% rate, the expected value is about 167 pulls. However, this is an average across infinite attempts. In practice, you could get lucky on pull 1 or unlucky and need the full 90 (with pity). Planning for the worst case (hard pity) is financially safer than relying on the average. If you budget for 90 pulls and get the character earlier, the leftover currency carries forward to the next banner. This calculator shows both the expected value and the specific probability for your chosen number of pulls.

The 50/50 and Guarantee System

Many gacha games add a second layer of randomness: even when you hit the rare tier, the item might not be the one you want. Genshin Impact's 50/50 system means your first 5-star has a 50% chance of being the featured character and a 50% chance of being a non-featured standard 5-star. If you lose the 50/50, your next 5-star is guaranteed to be the featured character. This effectively means the true worst case for a guaranteed featured character is 180 pulls (two full pity cycles). This calculator handles the raw drop rate; for 50/50 systems, consider doubling the pulls for a worst-case estimate.

How to Use This Calculator for Budget Planning

To plan your spending, enter the banner's drop rate and the number of pulls you can afford with your saved currency. If the probability of at least one copy is below your comfort threshold (most players aim for 80-90% confidence), you know you need to save more before pulling. For paid currency, divide the real-money cost per pull by the probability to estimate your expected cost. Remember that gacha spending can add up quickly: at $2 per pull in a typical game, 90 pulls costs $180, and 180 pulls for a guaranteed featured character costs $360. Always set a budget before pulling and never chase losses.

Common Drop Rates Across Popular Games

Genshin Impact and Honkai: Star Rail use a 0.6% base rate for the highest rarity with soft pity at 74 and hard pity at 90. Fate/Grand Order has a 1% rate for 5-star servants with no pity system, making it one of the least generous major gacha games. Blue Archive offers 2.5% for 3-star characters with a 200-pull pity. Arknights has 2% for 6-star operators with a pity system that increases rates after 50 pulls without a 6-star. Knowing your game's specific rates and pity mechanics is essential for making informed pulling decisions.

Frequently Asked Questions

How is gacha probability calculated?
The probability of getting at least one copy in N pulls with a drop rate of R% is: P = 1 - (1 - R/100)^N. This uses the complement rule: instead of calculating the complex 'at least one' probability directly, we calculate the simpler probability of getting zero copies and subtract from 1. Each pull is an independent event with the same probability, making this a binomial distribution problem.
What is a pity system in gacha games?
A pity system guarantees a rare drop after a certain number of unsuccessful pulls. For example, Genshin Impact guarantees a 5-star character within 90 pulls (with soft pity increasing rates around pull 74). Honkai: Star Rail uses 90 pulls for standard and 80 for limited banners. The pity counter usually resets when you get the rare item. Some games have 'hard pity' (guaranteed at X pulls) and 'soft pity' (increased rates starting at Y pulls).
How many pulls do I need for a 50% chance?
The median number of pulls for a 50% chance is ceil(ln(0.5) / ln(1-rate)). For a 0.6% drop rate (common in gacha games), you need about 115 pulls for a 50% chance. For a 90% chance, you need about 383 pulls. This means even with hundreds of pulls, there is no certainty without a pity system. The pity system exists specifically to prevent extreme bad luck streaks.
What are typical gacha drop rates?
Genshin Impact: 0.6% for 5-star characters (1.6% with soft pity factored in). Honkai: Star Rail: 0.6% base for 5-star. Fate/Grand Order: 1% for 5-star servants. Blue Archive: 2.5% for 3-star students. Arknights: 2% for 6-star operators. Most games are required by law (in some countries) to disclose exact drop rates. Always check the in-game details page for the official rates of any specific banner.
Does the 50/50 system affect my odds?
Many gacha games use a 50/50 system where even if you pull a rare item, there is only a 50% chance it is the featured character. If you lose the 50/50, your next rare pull is guaranteed to be the featured character. This effectively doubles the expected pulls needed: in Genshin Impact, the average to guarantee the featured 5-star is about 160 pulls (worst case 180). This calculator focuses on raw drop rates; multiply expected pulls by 2 for 50/50 systems.

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