How to Use the Gacha Probability Reach Calculator
Mobile gacha banners advertise single-pull rates like 0.6%, 1%, or 3% for SSR, five-star, or rate-up characters, but those numbers rarely answer the real question: "How many pulls do I actually need?" This calculator takes a single-pull rate and computes the number of attempts required to reach cumulative success probabilities of 50%, 75%, 90%, and 99%.
The formula used is n = log(1 - target) / log(1 - single rate). At a 0.6% pull rate, you need about 116 pulls to reach 50% cumulative chance, 383 pulls for 90%, and 765 pulls for 99%. The 50% figure is not the average but the median — half of players reach the prize sooner, half take longer.
The expected pulls (mean) value 1/p accounts for unlucky tails, so it lands slightly higher than the 50% median. Games with pity systems or rate-up guarantees usually end your run at a fixed cap before the worst tails appear, so treat these numbers as the no-pity baseline.
Frequently Asked Questions
This tool assumes independent pulls. With pity or rate-up guarantees, your real worst case is capped, so actual completion usually takes fewer pulls.
1/p is the mean of a geometric distribution which has a long right tail. The median (50% reach) is always smaller than the mean in this kind of distribution.
A 10-pull bundle equals 10 independent pulls statistically. Cumulative probability does not change, so the same numbers apply.