Gacha Pity Calculator
Calculate the probability of getting a 5-star in gacha games within N pulls including pity. Enter values for instant results with step-by-step formulas.
Reviewed by Daniel Agrici, Founder & Lead Developer
Formula
P(success) = 1 - Product(1 - rate_i) for i = 1 to N
The cumulative probability is calculated by finding the probability of NOT getting the item on every single pull, multiplying them together, and subtracting from 1. After soft pity begins, the per-pull rate increases linearly, dramatically boosting cumulative probability.
Worked Examples
Example 1: Genshin Impact Standard Pity
Problem:A player has done 80 pulls on the character banner with 0.6% base rate, soft pity at 74, hard pity at 90, and 6% increase per pull after soft pity. What is the probability of having a 5-star?
Solution:Pulls 1-73: rate = 0.6% each\nPull 74: rate = 0.6% + 1 x 6% = 6.6%\nPull 75: rate = 0.6% + 2 x 6% = 12.6%\n...\nPull 80: rate = 0.6% + 7 x 6% = 42.6%\nP(no 5-star in 73 pulls) = (0.994)^73 = 0.643\nP(no 5-star in pulls 74-80) = 0.643 x 0.934 x 0.874 x ... x 0.574 = 0.052\nCumulative probability = 1 - 0.052 = 94.8%
Result:94.8% chance of 5-star within 80 pulls. Expected pulls: ~62.
Example 2: Budget Planning for Guaranteed
Problem:A free-to-play player wants to know the cost of guaranteeing a specific featured character assuming worst-case 180 pulls (two full pity cycles for 50/50 loss).
Solution:Worst case: 180 pulls at ~$1.60/pull = $288\nExpected case: ~105 pulls = $168\nBest case (win 50/50, early): ~40 pulls = $64\nWith Welkin Moon ($5/month for 90 primos/day):\n30 days x 90 = 2,700 primos = ~17 pulls/month\nSaving for 3 months = ~51 free pulls\nRemaining needed (expected): 54 pulls = ~$86
Result:Expected cost: $168. With monthly pass savings: ~$86. Worst case: $288.
Frequently Asked Questions
Does the pity counter reset between different banners?
Pity counter mechanics vary by game and banner type. In Genshin Impact, pity carries over between banners of the same type. For example, if you are at 50 pity on the character event banner and the banner changes to a new featured character, your pity remains at 50 on the new character event banner. However, pity does NOT carry over between different banner types. The character event banner, weapon banner, and standard banner each maintain separate pity counters. Additionally, the guaranteed featured character mechanic (losing the 50/50) also carries over between same-type banners. Understanding which banners share pity and which are independent is crucial for strategic pull planning and budgeting.
References
Reviewed by Daniel Agrici, Founder & Lead Developer · Editorial policy