Gacha Probability Calculator
Free Gacha probability tool for odds & chance. Enter your details to get instant, tailored results and guidance. Includes formulas and worked examples.
Gacha Probability Calculator
Calculator
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Formula: P(at least 1) = 1 - (1 - r)^n
Worked example — 38.2% chance in 80 pulls | 100% with pity at 90 | Expected: 167 pulls
Formula
P(at least 1) = 1 - (1 - r)^n
Where r is the drop rate (as a decimal) and n is the number of pulls. For multiple copies, the binomial distribution is used: P(exactly k) = C(n,k) x r^k x (1-r)^(n-k). Pity systems guarantee a drop within a fixed number of pulls regardless of probability.
Worked Examples
Example 1: Featured 5-Star Character (0.6% rate)
Problem:Calculate probability of getting a featured 5-star character with 0.6% rate in 80 pulls, 90-pull pity.
Solution:Drop rate: 0.6% = 0.006 Probability per pull of NOT getting: 0.994 P(at least 1 in 80) = 1 - 0.994^80 = 1 - 0.618 = 38.2% Expected pulls: 1/0.006 = 167 50% chance at: 115 pulls 90% chance at: 383 pulls With 90-pull pity: guaranteed by pull 90
Result:38.2% chance in 80 pulls | 100% with pity at 90 | Expected: 167 pulls
Example 2: SSR Card in Mobile Game (3% rate)
Problem:What are the odds of pulling at least 2 SSR cards with 3% rate in 50 pulls? Cost is $3/pull.
Solution:Drop rate: 3% = 0.03 P(exactly 0) = 0.97^50 = 21.8% P(exactly 1) = C(50,1) x 0.03^1 x 0.97^49 = 33.7% P(at least 2) = 1 - 21.8% - 33.7% = 44.5% Expected SSR cards: 50 x 0.03 = 1.5 Total cost: 50 x $3 = $150
Result:44.5% chance of 2+ SSR | Expected: 1.5 SSR | Cost: $150
Frequently Asked Questions
How does gacha probability work?
Gacha probability follows the principles of independent random events. Each pull has a fixed probability (drop rate) of yielding the desired item, and each pull is independent of previous ones. The probability of NOT getting the item in a single pull is (1 - drop rate). For multiple pulls, the probability of getting at least one copy is calculated as 1 minus the probability of failing all pulls: P = 1 - (1 - r)^n, where r is the drop rate and n is the number of pulls. This means probability increases with more pulls but never reaches 100% without a pity system. A common misconception is that probabilities add up linearly, but they actually compound multiplicatively.
What is a pity system in gacha games?
A pity system is a mechanic that guarantees a rare item after a certain number of unsuccessful pulls. For example, if a game has a pity at 90 pulls, you are guaranteed the featured item by your 90th pull if you have not obtained it naturally. Pity systems come in several forms: hard pity provides a guaranteed drop at a fixed count, soft pity gradually increases the drop rate as you approach the pity threshold, and the 50/50 system gives a chance at the featured item versus any random item of the same rarity. Some games carry over pity count between banners while others reset it. Pity systems significantly affect the expected cost and make gacha outcomes more predictable for planning purposes.
How much should I budget for a specific gacha character?
Budget in pulls first and convert to money last, because the pull counts are computable while the exchange rate into real money is not. Ignoring pity, a 0.6 percent rate needs about 115 pulls before the cumulative chance passes 50 percent and about 383 pulls for 90 percent confidence, both from n = ln(1 - C) / ln(1 - r). A guarantee compresses those numbers sharply: with a 90-pull hard pity the median cannot exceed 90, and on a 50/50 featured system the absolute worst case is 180 pulls, because a lost 50/50 sends you through a second cycle that is then guaranteed. To turn pulls into money, use your own cost per pull rather than a published average: divide the price of the top-up bundle you would actually buy, in your own currency and store, by the premium currency it grants, then multiply by the currency cost of one pull. That rate shifts with region, platform, tax and one-time first-purchase bonuses, which is why Gacha Probability Calculator takes cost per pull as an input instead of assuming one. Set a firm budget in pulls before you start, and never chase losses.
What is the difference between rate-up and base rate?
The base rate is the overall probability of getting any item of a particular rarity tier in a gacha pull. The rate-up (or featured rate) is the probability specifically for the promoted or featured item. For example, a game might have a 1.6% base rate for any 5-star character, but the rate-up character might have a 0.5% specific drop rate within that 1.6%. When you do pull a 5-star, there is often a 50/50 chance it is the featured character versus a standard one. This distinction is crucial for calculating the true probability of getting a specific character. Some games implement an escalating guarantee where losing the 50/50 ensures the next 5-star is guaranteed to be the featured one.
How do I calculate the probability of getting multiple copies?
Getting multiple copies (for constellations, dupes, or limit breaks) requires binomial probability calculations. The probability of getting exactly k copies in n pulls with probability p per pull is: C(n,k) x p^k x (1-p)^(n-k), where C(n,k) is the binomial coefficient. For the probability of getting at least k copies, sum the probabilities from k to n. Multiple copies become exponentially more expensive. For example, with a 1% rate, getting at least one copy in 100 pulls has a 63% chance, but getting at least two copies in the same 100 pulls drops to only about 26%. This is why max-constellation or max-refinement targets can cost thousands of dollars in premium currency.
If a banner has no pity, does a long losing streak make the next pull more likely?
No. The pulls are independent Bernoulli trials, and the geometric distribution describing the wait to the first hit is memoryless. After 200 misses at a 0.6 percent rate, pull 201 still sits at 0.6 percent and the expected number of further pulls is still 1/r. Sunk pulls buy you nothing on a pity-free banner. Only a pity counter, which is state the game deliberately stores, lets past misses change future odds.
What do the expected hits and standard deviation figures actually tell you?
Expected hits is n times r, and the standard deviation is the square root of n times r times (1 - r) - the binomial mean and spread. With 100 pulls at a 1 percent rate you expect 1 hit with a standard deviation of about 0.99, so finishing with 0 or 2 copies is entirely ordinary. Read them together: when the spread is as large as the mean, a single session is dominated by noise and says nothing about whether the advertised rate is honest.
How many pulls does a given confidence level require?
Invert the cumulative formula: n = ln(1 - C) / ln(1 - r), rounded up, where C is the confidence you want. At a 1 percent drop rate, a 50 percent chance takes 69 pulls, 90 percent takes 230 and 99 percent takes 459. Notice the pattern: every additional nine of confidence costs the same fixed block of pulls, about ln(10) / ln(1 - r) or roughly 230 pulls at 1 percent. Certainty is bought in equal instalments, not at a flat price.
When should you use the binomial model instead of the geometric one?
Use the geometric or negative binomial view when the pull count is the unknown, as in how many pulls until the first copy or until the seventh. Use the binomial view when your budget fixes the pull count and the number of hits is the unknown, as in the chance of two or more copies from 90 saved pulls. On this page the at-least-k figure is binomial, summing C(n,k) r^k (1-r)^(n-k) upward, while expected pulls and the milestone counts are geometric.
Is a ten-pull batch better odds than ten single pulls?
For the top rarity tier, no. Ten singles and one ten-pull are the same ten independent trials, so the chance of at least one is 1 - (1-r)^10 either way. The difference is the batch guarantee: many gacha games promise at least one item of the middle rarity tier inside every multi-pull, which truncates the distribution for that tier only. Batches sometimes cost slightly less per pull as well, which changes your cost per copy rather than your odds.
References
Reviewed for accuracy by Daniel Agrici, Founder & Lead Developer · Editorial policy
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