What next?
Pity maths is probability, not luck. These extend it.
What your result means
Chance of a 5-star is the probability that at least one arrives within the pulls you have, starting from your current pity. Pulls to guaranteed counts down to hard pity, where the game gives you one outright. Soft pity is the point where the per-pull rate stops being flat and starts climbing steeply — it is not announced in game, and it is the reason your odds are far better than the advertised base rate suggests once you are deep into a counter. Expected pulls is the average from where you stand, and pulls for 90% is the planning number: how much you would need to be reasonably, rather than merely hopefully, confident.
Why this one is different
Five numbers, not one: the chance on your very next pull, where soft pity starts lifting the rate, how many pulls remain to the hard guarantee, the expected number from where you are standing, and how many it takes to be ninety per cent confident. The last is the one people mean when they ask how many pulls they need.
At 80 pulls the flat-rate answer is 38%. The real figure is over 90%.
The obvious way to build this tool is 1 − (1 − p)ⁿ, the standard "at least one success" formula. With a 0.6% base rate and 80 pulls it returns 38.2%, and it is not close to correct. The per-pull rate is not constant: it holds at the base rate until roughly pull 74, then ramps hard until a 5-star is certain at 90.
Model the ramp and the same 80 pulls come out above 91%. The model here reproduces four separately published figures — 35.6% of 5-stars arriving before pity, over 90% by pull 80, a mean around 62 pulls, and a consolidated rate of 1.604% against the developer’s stated 1.600%. That agreement is why the number above is worth trusting, and why a flat-rate answer is not.
How it works
The tool builds the probability of a 5-star landing on each individual pull, then adds up the ones inside your window. The per-pull rate is the base rate up to the soft-pity pull, after which it rises in equal steps until it reaches certainty exactly at hard pity. Turning per-pull rates into a distribution requires tracking the chance of having survived that far, so each pull’s probability is its own rate multiplied by the chance nothing has landed yet. Your pity counter is handled by conditioning: the distribution is built from pull one, then divided by the probability of having reached your current count empty-handed. Every figure on the page — the chance, the average, the 90% threshold — is read off that one distribution, so they cannot contradict each other.
How to use this calculator
- Pick your banner. Base rates and hard pity differ between character, weapon and light-cone banners, and the difference is large.
- Enter your current pity count — the number of pulls since your last 5-star, which the game shows on the banner history screen.
- Enter the pulls available to you now. Convert currency to pulls first if you need to.
- Read the 90% figure rather than the headline chance if you are deciding whether to spend. It is the difference between a plan and a hope.
- For a game not listed, choose Custom rates and enter its published base rate and hard pity. The soft-pity ramp is then an assumption, and the page marks it as one.
Formula
rate(n) = probability on pull n alone, survival(n−1) = chance nothing landed in the first n−1 pulls, step = (1 − base) ÷ (hard − soft + 1), chosen so the rate reaches certainty exactly at hard pity. Your chance across a window is the sum of P(pull n) over it, divided by the survival to your current pity.
Example calculation
A Genshin character banner at 0 pity with 80 pulls available — base rate 0.6%, soft pity 74, hard pity 90:
Pulls 1-73 each carry the flat 0.6%, giving 35.6% in total
Pull 74 onwards the rate climbs by about 6.2 points per pull
Summing pulls 1 to 80 gives 91.3%
Mean pulls to a 5-star = 62.3
Implied consolidated rate = 1 ÷ 62.3 = 1.604%
The published consolidated rate is 1.600% and the community dataset puts 91.8% of 5-stars by pull 80. Reproducing both from one model is the check that matters — and it is the reason the flat-rate figure of 38.2% should be discarded rather than quoted.
Frequently asked questions
What is soft pity and why is it not in the game’s published rates?＋
Soft pity is the point where the per-pull chance starts rising sharply instead of staying at the base rate. Developers publish the base rate and the hard-pity guarantee but not the ramp between them, so its shape has been inferred from very large community datasets — one built from around 25 million recorded pulls. The model here uses that inference, and reproduces the officially published consolidated rate almost exactly, which is good evidence it is close to right without being a guarantee that it is exact.
Does my pity carry over between banners?＋
Within a category, yes; across categories, no. In Genshin the character event banners share one counter that persists when a banner ends, while the weapon and standard banners each keep their own. Star Rail and ZZZ follow the same pattern. Losing a banner does not lose your progress towards the next 5-star.
Does this account for the 50/50 on the featured character?＋
No, and that is a separate coin flip on top of everything here. This page answers "will I get a 5-star", not "will it be the one I want". On most limited banners a 5-star has a 50% chance of being the featured one, with a guarantee that the next one is featured if you lose. To plan for a specific character, work out your chance of one 5-star here, then treat the featured outcome as roughly half of that unless you are already on a guarantee.
Is the pity counter really per-pull random, or is it decided in advance?＋
From the player’s side the distinction has no observable consequence. What can be measured is the frequency of 5-stars at each pity value across millions of pulls, and that is what the model reproduces. Whether the game rolls at pull time or fixed the outcome earlier, the odds you face from your current count are the same.
Why do I keep hitting hard pity when the average is 62?＋
Because 62 is a mean over a very skewed distribution, not a typical experience. Most 5-stars arrive in a cluster just after soft pity begins, around pull 75-80, and reaching 84 or beyond happens under 1% of the time. If it feels like you always go deep, that is partly because deep pulls are memorable and partly because the modal outcome genuinely is close to pity — the average of 62 is dragged down by the third of pulls that land early.
Can I use this for a game that is not listed?＋
Yes, with a caveat the tool makes explicit. Choose Custom rates and enter the published base rate and hard pity from that game’s details screen. The soft-pity onset is then placed at the same proportion as the modelled banners, which is an assumption rather than a measurement — if the game has no soft pity at all, the real odds will be lower than shown until close to the guarantee.
Related calculators
Assumptions & limitations
Every figure here comes from a simplified model. Keep these limits in mind when reading your result:
- The base rate and hard-pity guarantee are as published by the developer. The soft-pity onset and the shape of the ramp are not published: they are community estimates from large recorded datasets, and the model is validated by reproducing the published consolidated rate rather than by any official confirmation.
- The ramp is modelled as linear from the soft-pity pull to certainty at hard pity. The true curve may not be exactly linear; the fit to published aggregate statistics is close but is a fit, not a specification.
- Answers "at least one 5-star" only. It does not model the 50/50 on featured characters, rate-up weapons, Epitomized Path or Capturing Radiance, all of which sit on top of this and change what you actually receive.
- Assumes your pity counter is accurate and applies to the banner selected. Counters are per-category and are not shared between character, weapon and standard banners.
- Custom rates place soft pity at a fixed proportion of hard pity, because there is nothing to derive it from. For a game with no soft pity the real odds are lower than shown until the guarantee.
- Rates are those in force at the time of writing. Developers have changed banner mechanics before, and a game update can invalidate any of the constants here.