Gacha pity calculator
Budgeting a banner, not gambling on one: how many pulls until the guarantee is mathematically yours, and the honest probability of getting there sooner.
How pity systems actually work
Most gacha games run two layers. A tiny base rate applies to every pull, then a soft pity kicks in near the end where the rate climbs steeply each pull, and finally hard pity guarantees the drop outright. The defaults above match the common 90-pull structure with soft pity around 74 and a 0.6% base rate; change them to whatever your game uses.
The important consequence is that the average is not the guarantee. Because soft pity ramps aggressively, most players hit well before hard pity — but "most" is not "you". The only number you can actually plan around is the hard pity count, which is why the pulls-to-guarantee line is the one worth budgeting against. If you can't afford the guarantee, you are planning on luck.
This models the ramp as a steady increase through soft pity, which matches observed behaviour closely but isn't the exact undocumented curve any specific game uses. Treat the percentage as a good estimate and the guarantee count as exact.
Worth saying plainly: this is a budgeting tool, not encouragement. If you're calculating whether you can afford something, the answer the math gives is often "wait for the next banner" — and that's a legitimate answer.
Questions
What numbers should I use for my game?
The defaults match the widespread 90-pull standard: hard pity 90, soft pity ~74, 0.6% base rate. Games with 80-pull or 50-pull systems just need those fields changed — the math is the same shape.
Does losing a 50/50 count toward pity?
In most games your pity counter resets when you get any featured-rarity item, even the wrong one, while a separate guarantee flag ensures the next one is the banner unit. So plan for potentially two full pity cycles if you're chasing a specific character.
Why is my chance lower than I expected?
Because base rates are tiny — under 1% per pull — and almost all the real probability lives in soft pity. If your planned pulls don't reach the soft pity window, the odds stay low no matter how many you do.