Architecture Matrix: Gacha Pity Tiers across Major Live-Service Titles
Modern character-collection games (such as Genshin Impact, Honkai: Star Rail, Zenless Zone Zero, and Wuthering Waves) structure monetization around probabilistic "Pity" systems. Hidden probability ramps ("Soft Pity") and guarantee inheritance rules dictate pull efficiency.
| Pity Tier / Metric | Base Probability (Hard Odds) | Soft Pity Acceleration Window | Hard Ceiling (Hard Pity) | Rollover / Inheritance Scope |
|---|---|---|---|---|
| Limited Character Banner | 0.6% base chance per single pull | Surges dramatically from pull 74 to 89 (~20%-32%/pull) | 90 pulls exact (guaranteed 5-star / SSR) | Rollover strictly within Limited Character pool |
| 50/50 Non-Featured Failover | 50% chance to win featured promotional unit | If non-featured standard unit drops, "Guarantee" triggers | Next SSR strictly 100% featured promotional unit | Guarantee carries forward indefinitely across future banners |
| Weapon / Light Cone Banner | 0.8% base chance per single pull | Surges from pull 64 to 79 | 80 pulls exact (or Fate Points system) | Fate Points reset between banners; pull counter rolls over |
| Standard / Permanent Banner | 0.6% base chance per single pull | Pulls 74 to 89 | 90 pulls exact | Isolated: Pity never shares with Limited Character banners |
| Novice / Discounted Banner | Flat discounted 20% currency cost | No soft pity acceleration | Capped at 50 pulls total | Expires upon exhaustion; does not roll into Standard pool |
The Mathematical Mechanics of the Soft Pity Ramp
The advertised "consolidated probability" (e.g. 1.6% including pity) is driven entirely by the soft pity inflection curve:
- Pulls 1 through 73 possess a flat 0.600% drop rate.
- At pull 74, an arithmetic multiplier adds approximately +6.0% probability per pull:
- Pull 74: ~6.6%
- Pull 75: ~12.6%
- Pull 76: ~18.6%
- Pull 77: ~24.6%
- Pull 78: ~30.6%
- Over 92% of all 5-star character drops occur mathematically between pull 75 and 82. Hitting true hard pity (pull 90) is an astronomical statistical outlier (< 0.00001% chance).
Pull Budgeting: Planning for the Worst-Case 50/50 Loss
To guarantee acquiring a desired limited character without cash shop panic:
- Calculate the True Guarantee Budget:
Maximum Pulls Required = (First 5-star Soft Pity ~80) + (Second Guaranteed Soft Pity ~80) = ~160 pulls Total Premium Currency Required = 160 pulls * 160 currency = 25,600 Primogems / Stellar Jades - Never Build Pity on Unwanted Banners: Pulling on a banner solely to "accumulate 4-star constellations" or "build pity" carries catastrophic opportunity cost if an early 5-star resets your guarantee counter to zero.
- Banner Isolation Rules:
- Pity accumulated on a Character Event Banner does not transfer to the Weapon Event Banner.
- Pity spent on the Standard Banner is permanently sequestered from limited promotional pools.
Auditing In-Game Wish History Logs
// PowerShell helper to extract game wish history URL from local web cache files
$CachePath = "$env:USERPROFILE\AppData\LocalLow\miHoYo\Genshin Impact\output_log.txt"
if (Test-Path $CachePath) {
$HistoryUrl = Get-Content $CachePath | Select-String "https://.*/event/gacha_info/api/getGachaLog.*" | Select-Object -First 1
if ($HistoryUrl) {
Write-Host "Extracted active Gacha History authentication URL." -ForegroundColor Green
}
}
- The in-game history log updates with an approximate 1-hour delay. Do not assume your pity counter is clean until the latest session renders in the history tab.