Gacha Pull Probability Calculator
Chance of pulling a featured unit (or several copies) in N gacha pulls at a flat rate, with an optional spark or exchange: pulls for 50%, 90%, 99% or your own target, expected pulls and copies, the guarantee point, premium currency and cash still needed, and the full copy-count distribution.
How it works
P(≥1 in n pulls) = 1 − (1 − p)ⁿ · P(≥k) = 1 − Σ_{j<k} C(n, j) pʲ (1 − p)ⁿ⁻ʲ · with a spark every S pulls, sparks = ⌊(n + points) ÷ S⌋ and luck needs k − sparks · expected pulls per copy = 1 ÷ p (k ÷ p for k copies) · pulls for a target c = the smallest n with P ≥ c
On a banner without pity, each pull is an independent roll at the published rate, so the chance of getting nothing in n pulls is (1 − p)ⁿ and the chance of at least one copy is one minus that. For duplicates the number of copies follows a binomial distribution, and the calculator adds up the exact probabilities instead of using a shortcut. Many games soften pure luck with a spark or exchange: every so many pulls on the banner you can pick the unit outright. The calculator counts those guaranteed copies first, so luck only has to provide the rest, and it shows the pull count that guarantees your goal. You also get the pulls needed for a 50%, 90%, 99% or custom chance, the average pulls per copy, the full spread of how many copies you might end up with, and, under More options, how far your premium currency and cash go. Because misses compound, a 0.6% unit needs about 116 pulls for a coin-flip chance and about 383 for 90%, far more than the 167-pull average suggests.
Worked example
At a 0.6% rate, 100 pulls give 1 − 0.994¹⁰⁰ = 1 − 0.5478 = 45.22% chance of at least one copy. The average copy takes 1 ÷ 0.006 ≈ 166.7 pulls, a 50% chance takes 116 pulls, 90% takes 383 and 99% takes 766. On a banner with a 200-pull spark, 100 pulls are still 45.22%, but the goal is guaranteed at 200 pulls and the average falls to about 116.6 pulls. Wanting 2 copies with 300 pulls and that spark gives 83.56%, because one copy comes from the spark and luck only needs to supply the second.
Sources: Bernoulli trial (Wikipedia) · Binomial distribution (NIST/SEMATECH e-Handbook)
Frequently asked questions
Why is my chance under 50% with a lot of pulls?
Low base rates compound slowly. With a 0.6% rate you need 116 pulls just to reach a coin-flip chance, and even at the average 167 pulls the cumulative probability is only about 63%, not certainty. The table and chart show how the chance grows pull by pull.
What does expected pulls per copy mean?
It is the long-run average, 1 ÷ rate. Over many players it holds, but any single player can hit early or go far past it. About 37% of players still have nothing after the average number of pulls, and about 13.5% after twice that, which is why gacha feels streaky.
How does a spark or exchange change the odds?
A spark lets you pick the unit after a set number of pulls on the banner, such as 200 or 300. Enter that number and any points you already have, and the calculator counts the guaranteed copies first, so luck only needs to supply the rest. Your chance can only go up, and the goal becomes guaranteed at the spark point.
Does this include soft pity, hard pity or a 50/50?
No. This page is for flat-rate banners, optionally with a spark. Pity systems raise the rate after a run of misses and reset when you win, and 50/50 banners can give the wrong unit first. Use the soft pity calculator for those.
How do I count my premium currency?
Open More options, enter the currency you have and the price of one pull, and turn on the bonus if a 10-pull gives 11. The calculator converts the currency to whole pulls, adds them to your pulls, and shows how much more you need for a 90% chance. Add a cash price per pull to see what your goal costs in real money.
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This calculator is for educational purposes. Double-check important results before acting on them.