Gacha Pull Probability & Banner Drop Rate Calculator (Genshin / HSR)
Calculate cumulative probability of pulling a 5-Star / SSR character or item given base drop rate % and total pulls saved.
Reviewed by: Lucas 'Vortex' Chen • Pro Esports Hardware & Engine Telemetry Lab
Methodology: Verified Formula
Presets:
Probability of At Least 1 Drop (Raw Odds)
36.32%
Total Currency Required
12,000 Gems
50% / 90% Luck Milestones
116 pulls (50%) / 383 pulls (90%)
Soft pity in Genshin/HSR ramps up dramatically starting at pull 74.
Scenario Comparison & Benchmark Table (Gacha Pull Probability)
Compare how scaling Total Pulls / Wishes / Tickets affects your output (click any row to load those values into the calculator above):
| Total Pulls / Wishes / Tickets | Probability of At Least 1 Drop (Raw Odds) | Total Currency Required | 50% / 90% Luck Milestones |
|---|---|---|---|
| 38 | 20.44% | 6,080 Gems | 116 pulls (50%) / 383 pulls (90%) |
| 56 | 28.61% | 8,960 Gems | 116 pulls (50%) / 383 pulls (90%) |
| 75 (Baseline) | 36.32% | 12,000 Gems | 116 pulls (50%) / 383 pulls (90%) |
| 94 | 43.20% | 15,040 Gems | 116 pulls (50%) / 383 pulls (90%) |
| 113 | 49.34% | 18,080 Gems | 116 pulls (50%) / 383 pulls (90%) |
| 150 | 59.45% | 24,000 Gems | 116 pulls (50%) / 383 pulls (90%) |
Mathematical Formula & Step-by-Step Guide
Primary mathematical equation used by this model:
Cumulative Chance = 1 - (1 - DropRate)^Pulls; Pulls for 90% Chance = ln(0.10) / ln(1 - DropRate)
- Configure your primary input (Total Pulls / Wishes / Tickets, baseline set to 75) using either the direct numeric box or synchronized range slider.
- Adjust the remaining parameters (Base 5-Star / SSR Drop Rate (% per Pull), Currency per Pull (e.g. 160 Primogems / Stellar Jade)) to mirror your exact scenario.
- Examine the primary output alongside the secondary breakdown metrics and the 6-tier benchmark comparison table below.
Primary Standards & References: Valve Source 2 (CS2 m_yaw 0.022°), Riot Games Valorant Engine (0.07° yaw), Respawn Apex Engine, USB HID 1000Hz–8000Hz Polling Specifications & VESA DisplayHDR/Refresh Standards
In-game sensitivity conversions preserve 1:1 physical 360° turn circumference at matching field-of-view (FOV) settings.
In-game sensitivity conversions preserve 1:1 physical 360° turn circumference at matching field-of-view (FOV) settings.
Frequently Asked Questions — Gacha Pull Probability
What mathematical formula does the Gacha Pull Probability & Banner Drop Rate Calculator (Genshin / HSR) use?
This calculator implements the verified relationship: Cumulative Chance = 1 - (1 - DropRate)^Pulls; Pulls for 90% Chance = ln(0.10) / ln(1 - DropRate). Each variable (Total Pulls / Wishes / Tickets, Base 5-Star / SSR Drop Rate (% per Pull), Currency per Pull (e.g. 160 Primogems / Stellar Jade)) is evaluated in real time using double-precision floating-point arithmetic so there is zero rounding drift across multi-step scenarios.
How does changing Total Pulls / Wishes / Tickets impact the final result?
Total Pulls / Wishes / Tickets acts as the primary driver in this model (default baseline: 75). Use the Reference Benchmark Table on this page to compare how scaling Total Pulls / Wishes / Tickets from conservative to aggressive levels changes both the primary outcome and secondary ratios.
What standards and sources back this Gacha Pull Probability methodology?
Our model is audited by Lucas 'Vortex' Chen • Pro Esports Hardware & Engine Telemetry Lab and calibrated against Valve Source 2 (CS2 m_yaw 0.022°), Riot Games Valorant Engine (0.07° yaw), Respawn Apex Engine, USB HID 1000Hz–8000Hz Polling Specifications & VESA DisplayHDR/Refresh Standards. Note: In-game sensitivity conversions preserve 1:1 physical 360° turn circumference at matching field-of-view (FOV) settings.