🎰 Gacha Pity Calculator

Assuming each pull is independent with the same probability p, the number of pulls until the first hit follows a geometric distribution. The chance of obtaining it by pull N is 1−(1−p)^N. For a 0.6% rate with a 90-pull pity, the chance of a natural hit strictly before the guaranteed 90th pull is 1−(0.994)^89 ≈ 41.5% — meaning more than half the time you'll actually need the pity to kick in.

With a hard pity ceiling, expected pulls (a truncated geometric expectation) equal [1−(1−p)^pity] ÷ p. For the example above, expected pulls ≈ 69.7; at 3,000 per pull, expected cost is roughly 209,000. That's lower than the guaranteed worst-case cost (90 × 3,000 = 270,000), because some outcomes hit naturally before reaching pity.

A pity system guarantees you'll eventually get the item, but that guarantee isn't cheap. The "guaranteed cost" shown here is the worst-case spend if you never hit naturally, so budget against that figure — not the (lower) expected cost — when setting a spending limit. Since outcomes are random, avoid overspending on gacha-style products.