Gacha Pity Calculator

About this calculator

The probability of getting at least one success across n independent pulls at a fixed drop rate p is 1 − (1−p)ⁿ — one minus the probability that every single pull fails. This complement trick is the standard way to answer "how many tries until I probably get it" questions for any independent, fixed-probability event, and it's the baseline math behind gacha-game loot odds before any pity system kicks in.

Many gacha games layer a pity counter on top of this base rate — a guaranteed drop after a fixed number of consecutive failures — specifically because the raw geometric odds this calculator computes can leave a small but real chance of very long unlucky streaks. Players use this calculation to gauge realistic expectations before a pull session, while game designers use the same math when tuning base drop rates and pity thresholds to hit a target average cost per item.