Gacha Pity Calculator
Pity changes the maths completely.
Work out Gacha Pity. Pity changes the maths completely. States the assumption instead of hiding it.
Expected pulls
62.3
124.59 expected · 180 worst case at 90 pulls
A hard pity converts an unbounded geometric distribution into a bounded one, which changes the expected cost substantially — often by a third or more. A naive 1/p calculation on a 0.6% rate gives 167 pulls; with pity at 90 the true expectation is far lower. Soft pity pulls it down further by raising the rate as the counter climbs. Many games do not publish the soft pity curve, so the values here are approximations of commonly-observed behaviour rather than official figures. The worst case is the number to budget against, not the expectation. Half of all players will exceed the median, and the distribution is wide — planning to the average means being short more often than not.
How the Gacha Pity Calculator works
Expected pulls and cost with hard and soft pity modelled. A hard pity converts an unbounded distribution into a bounded one, which cuts the expected cost substantially against a naive 1/p calculation.
Also known as: how many pulls to guarantee · soft pity odds · expected cost of a banner · gacha budget calculator
Frequently asked questions
How many pulls will I need?
Far fewer than 1 divided by the base rate, if there is pity. A 0.6% rate naively suggests 167 pulls; with hard pity at 90 and soft pity from 74, the true expectation is well under it.
What is soft pity?
A rising rate as the counter climbs toward the guarantee. Many games do not publish the curve, so figures here are approximations of commonly-observed behaviour rather than official numbers.
Should I budget for the average or the worst case?
The worst case, which is hard pity. Half of all players exceed the median and the distribution is wide, so budgeting to the average means being short more often than not.
Does the pity counter carry over between banners?
In most systems, yes for the counter and sometimes not for the guarantee. It varies enough between games that it is worth checking rather than assuming.
Is a 50/50 mechanic included here?
No. Where a first pity result can be a non-featured item, the effective cost for a specific character is roughly double what this shows.
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