GachaMath
How this calculator works
Every wish is a weighted coin whose weight depends on your pity counter. We compute the full probability distribution with an exact dynamic-programming model over every (pity, guarantee) state — the same math a statistician would do by hand, just faster. The model: base 5★ rate 0.6%, soft pity ramping from wish 74, hard pity at 90, and a 50% featured chance with a guarantee after a loss.
Because it's an exact model, "chance with N wishes" accounts for everything at once: your current pity, an active guarantee, Capturing Radiance, and even wanting multiple copies — the multi-copy math chains full cycles correctly rather than multiplying single-copy odds.
Worked example
Standing at 30 pity, no guarantee, with 75 wishes: the calculator runs 75 pulls of the model from your state and reports the exact cumulative probability — typically a number people find lower than they hoped, which is precisely why planning with real math beats rules of thumb like "90 pulls = one 5★".
Frequently asked
What is soft pity in Genshin Impact?
From wish 74 of a cycle, the 5★ rate climbs steeply from the base 0.6% (community-measured at roughly +6 percentage points per pull) until the hard-pity guarantee at 90. That's why most 5★s land in the 74–79 range.
How many wishes for a guaranteed featured 5★?
Worst case is 180: hit hard pity at 90, lose the coin flip, then hit hard pity again with the guarantee. In practice the median player needs far fewer — check the confidence table above for your exact pity.
Does pity carry over between banners?
Yes — pity and the guarantee persist across character event banners (they do not transfer to other banner types). Your "current pity" is the number of wishes since your last 5★ on this banner type.
Is the 50/50 really 50%?
Since Capturing Radiance was added, losing streaks build a hidden counter that sometimes converts a lost coin flip into a win. Across millions of community-logged wishes the long-run featured share is ≈55%. This calculator models that aggregate; toggle it off to see the classic 50/50 math.