Gacha Pity and Pull Probability Calculator
Find the chance of pulling at least one top-rarity item in a number of pulls on a gacha banner, with the hard pity that guarantees it, an optional soft pity ramp and your current pity count: probability for N pulls, expected pulls per hit, and the pulls needed for 50%, 90% and 99% confidence.
Last updated: October 2026
Chance of at Least One Hit
25.99 %
Formula below · 2 sources (mathsisfun.com, genshin-impact.fandom.com) · Updated Oct 2026
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About this calculator
A gacha banner is a sequence of independent pulls, each with a small chance of the top rarity, plus a pity system that raises the odds as a dry streak grows and guarantees a hit at a fixed pull. The chance of at least one hit in N pulls is one minus the chance of missing every one: 1 − (1 − p1)(1 − p2)…(1 − pN), where pi is the rate on the i-th pull of your streak.
Without pity
If the rate is constant, P(at least one in N) = 1 − (1 − p)^N. At 0.6% that is 26% after 50 pulls, 45% after 100 and 70% after 200, and the expected number of pulls per hit is 1 ÷ p, about 167. A common mistake is to multiply: 50 pulls at 0.6% is not a 30% chance, and 167 pulls is not a certainty (it is 63%).
Soft and hard pity
Hard pity makes the rate 100% on a given pull: the streak can never exceed it, so the chance of a hit within N pulls is 100% once your current pity plus N reaches it. Soft pity ramps the rate up before that: in the default (the character banner in Genshin Impact and similar games) the base rate is 0.6%, soft pity starts on pull 74 and the rate rises by about 6 percentage points per pull, so pull 74 is 6.6%, pull 75 is 12.6% and so on, with hard pity at 90. With those numbers the expected pulls per 5-star is 62.3, the average rate including pity 1.6% (the figure the game publishes), and half of all 5-stars arrive by pull 76.
Using your pity count
The counter only matters because pity exists: at 70 pity, the next 10 pulls carry an 88% chance of a hit, against 6% for a fresh counter, because they run through the soft-pity ramp. Enter the pulls since your last hit and the calculator starts the probabilities from there. What the calculator does not model is the rate-up or 50/50 rule (a hit may be the standard pool rather than the featured item) or a separate guarantee counter; treat the result as the chance of a top-rarity hit of any kind, and halve the first hit's odds of being the featured one where a 50/50 applies.
How to use
Example: a banner with a 0.6% base rate, soft pity from pull 74 rising 6 points per pull, hard pity at 90, fresh counter, 50 pulls. All 50 pulls are below soft pity, so the chance is 1 − 0.994^50 = 1 − 0.740 = 26.0%. The expected pulls to a hit is 62.3, the pity-inclusive average rate 1.6%, and it takes 76 pulls for a 50% chance, 80 for 90% and 83 for 99%. Those are the defaults. Example 2: you are at 70 pity and have 10 pulls. Pulls 71-73 are at 0.6%, then 74 at 6.6%, 75 at 12.6%, 76 at 18.6%, 77 at 24.6%, 78 at 30.6%, 79 at 36.6% and 80 at 42.6%; multiplying the misses gives 12.4%, so the chance of a hit is 87.6%. Example 3: a weapon banner at 0.7% with soft pity from 63 at 7 points per pull and hard pity at 80 has an expected 53.3 pulls per hit, a 1.88% average rate.
Frequently asked questions
What is the chance of a 5-star in 50 pulls?
With a 0.6% rate and a fresh pity counter, 1 − 0.994^50 = 26%. In 75 pulls it is 36% (the first two soft-pity pulls help a little), in 80 pulls 90%, and at 90 pulls 100% because of hard pity. The pull count multiplies nothing: 50 pulls at 0.6% is not 30%.
How many pulls does a 5-star take on average?
With no pity, 1 ÷ rate: 167 pulls at 0.6%. With the default soft pity (from 74, +6 points per pull) and hard pity at 90, the expected number is 62.3, and half of all hits arrive by pull 76. The average rate including pity, 1 ÷ 62.3, is 1.6%, which is the figure banners of this type publish next to the 0.6% base rate.
What is soft pity?
A ramp in the rate before the hard guarantee. Starting at a given pull the rate rises every pull, so hits cluster just after the ramp begins and few streaks reach hard pity. Enter the pull where it starts and the increase per pull; set both to 0 for a banner that only has hard pity. The ramp figures for most games are community estimates from large pull samples, not published values.
Does pity carry over, and how do I use my current count?
In most games the counter carries between banners of the same type and resets only when you hit. Enter the pulls since your last top-rarity item in the current-pity box: the calculator then evaluates your next N pulls at the rates those pity positions carry. At 70 pity, 10 pulls give an 88% chance; at 0 pity the same 10 pulls give 5.8%.
What about the 50/50 and guaranteed featured item?
This calculator gives the chance of a top-rarity hit of any kind. On a banner where the first hit has a 50% chance of being the featured item and a miss guarantees it next time, the chance that a given hit is featured is 50% unless you are on the guarantee. To get the featured item for certain you may therefore need two hits: roughly double the pull figures, or at most two hard pities.
Why is 1 − (1 − p)^N the right formula?
Each pull is independent, so the chance of missing every one of N pulls is the product of the individual miss chances, (1 − p) multiplied N times, and at least one hit is the complement of that: 1 − (1 − p)^N. With pity the miss chances differ by pull, so the product uses each pull's own rate.
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