Case 1
- Drop rate per pull
- 0.6%
- How many pulls?
- 90
0.418199
Open with these valuesGacha Probability Calculator
0.418199
Result: 0.418199Ninety pulls at a 0.6 % rate give you a 0.4182 chance of at least one rare — about 42 %, not the 54 % you get by multiplying rate by pulls. The right way is the complement: work out the chance of missing every single pull and subtract it from one. Pity systems are not included here.
Worked examples
Case 2
- Drop rate per pull
- 1%
- How many pulls?
- 100
0.633968
Open with these valuesCase 3
- Drop rate per pull
- 5%
- How many pulls?
- 20
0.641514
Open with these valuesHow it's calculated
P(at least one) = 1 − (1 − p)ⁿ
- StepEnter the banner's advertised drop rate for a single pull.
- StepEnter how many pulls you plan to make.
- ResultRead the probability between 0 and 1 — multiply by 100 for percent.
What this number means
Past pulls do not change the next one
Every pull is independent at the same fixed rate, so ninety-nine misses leave the hundredth exactly as likely as the first. Neither the banner nor this formula remembers what came before.
Ninety pulls at 0.6 % is 42 %, not 54 %
Multiplying the rate by the number of pulls counts the same rare more than once and can pass 100 %. The complement rule gives 0.418199 for those ninety pulls.
Even 90 % leaves one run in ten with nothing
High is not certain: a result of 0.90 means one run in ten ends empty-handed. Only a rate of 100 % makes the very first pull sure.
Pity and guarantees are not in this number
The formula assumes the same rate on every pull and ignores any threshold that raises it or hands out a rare. Where your banner has such a guarantee, your real odds are better than what you read here.
Commonly misread
I have missed 89 times, so the next pull is due.
Independent pulls have no memory. The ninetieth carries the same 0.6 % as the first.
0.6 % times 90 pulls is 54 %, so I am more likely than not to get it.
That double-counts and can exceed 100 %. The complement rule gives 0.418199, about 42 %.
The result says 0.4182, so I get about 0.42 copies.
The output is the probability of at least one, not a count of copies. Roughly 42 % of runs end with one or more.
My game guarantees a rare eventually, so this is my real chance.
This baseline ignores pity entirely. With a guarantee in play your true odds are higher than the figure shown.
Reference table
| Rate %, pulls | Situation | Chance of at least one |
|---|---|---|
| 0.6, 1 | A single pull at a typical banner rate | 0.006000 |
| 0.6, 90 | A full soft-pity run at that rate | 0.418199 |
| 1, 100 | A hundred pulls at one percent | 0.633968 |
| 5, 20 | Twenty pulls at a generous rate | 0.641514 |
| 50, 1 | One pull, a coin flip | 0.500000 |
| 100, 5 | A guaranteed rate — certain from the first pull | 1.000000 |
Questions
How do I calculate gacha pull probability?
Use the complement rule: the chance of at least one rare item is 1 − (1 − p)ⁿ, where p is the per-pull drop rate as a fraction and n is the number of pulls. For example, a 0.6 % rate over 90 pulls gives 1 − 0.994⁹⁰ ≈ 0.4182, or about 41.8 %.
What does the 'at least one' probability mean?
It is the chance of getting one or more copies of the rare item across all your pulls, as opposed to the chance on a single pull. It is always much higher than the per-pull rate, because every extra pull adds another opportunity to succeed.
Why can't I just multiply the drop rate by the number of pulls?
Multiplying overcounts and can even exceed 100 %, which is impossible for a probability. The correct approach is to find the chance of missing every pull, (1 − p)ⁿ, and subtract it from one. At low rates and few pulls the two are close, but they diverge quickly as pulls grow.
Does this calculator account for pity systems?
No. The formula assumes every pull is independent with a fixed rate and ignores pity and soft-pity mechanics that raise the rate or guarantee a rare item after a counter. Treat the result as the baseline odds before any guarantee kicks in.
Can the chance ever reach 100 %?
Not with a plain drop rate below 100 %. Because (1 − p)ⁿ stays above zero for any finite number of pulls, the chance of at least one rare item gets ever closer to certainty but never reaches it. Only an in-game pity guarantee can make a rare item certain.
Sources and last check
Information, not professional advice.