HesapHanem

Gacha Pity Calculator

Find your odds of at least one drop

How it is calculated

The tool assumes every pull has the same independent drop chance. With p = rate ÷ 100 and N pulls, the chance of at least one success is P = (1 − (1 − p)N) × 100 as a percentage, and the expected number of pulls for the first success is 1 ÷ p. The rate is entered in percent (0.6 for 0.6%) and must be above 0 and at most 100. Attempts must be at least 1. It does not model a rising rate or a guaranteed pity pull: if the game raises the odds as you approach the pity counter, the real chance is higher than shown.

Worked example

An item drops at 0.6% per pull and you plan 90 pulls. Here p = 0.006, so the chance of missing on one pull is 0.994. Raise 0.994 to the 90th power, about 0.5818, and subtract from 1: the chance of at least one drop is 41.82%. The expected number of pulls is 1 ÷ 0.006 = 166.67. Even at 166 pulls the chance is only 63.18%, so going past the average is common.

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Common mistakes

  • Believing that the expected number of pulls (166.67) guarantees a drop. At that point the chance is still only about 63%.
  • Entering the rate as a fraction (0.006) instead of a percent (0.6). The tool would read it as 0.006%.
  • Ignoring soft pity or a guaranteed pull. The tool uses a flat rate, so it underestimates the chance in games that raise odds late.
  • Treating earlier failed pulls as improving the next one. Each pull is independent, unless the game states a pity counter.
  • Using the sum of rates for a pool of several featured items. Calculate the chance for the exact item you want.

Sources

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.

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Comments (1)

  • Editorial team

    To budget a session, work backwards: try different pull counts until the chance reaches the confidence you want. At a 0.6% rate, 383 pulls gets you past 90% for at least one drop, far above the 167-pull average. The figure covers only the first copy; wanting several copies of the same item takes more pulls. What drop rate and pull budget are you planning around?

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