Expected Pulls Calculator

About this calculator

In gacha-style games, each pull is an independent trial with a fixed drop rate p, so the number of pulls until the first success follows a geometric distribution: the expected (average) number of pulls is 1/p, and the probability of getting at least one success within n pulls is 1 − (1 − p)^n. Rearranging that second formula for n gives the number of pulls needed to reach a chosen confidence level, such as 90% or 99%.

This calculator takes a drop rate and a target confidence level and returns the expected number of pulls and the pulls needed to hit that confidence. Gacha and loot-box game players use it to budget how much currency or how many pulls to save before a banner, and game economy analysts use the same geometric-distribution math when modeling expected player spend against a given drop rate during monetization design.