How the Pity & Pull Calculator works
The calculator is an exact Markov-chain walk over your pity, guarantee and copies, not a Monte-Carlo simulation. Here are the curves and rules it uses.
5★ rate per pull
p(n) = min(1, base + step × (n − softPity + 1)) for softPity ≤ n < hardPity
p(hardPity) = 1
| Banner | Base | Soft pity | Step | Hard pity | Featured | Mean pulls per 5★ |
|---|---|---|---|---|---|---|
| Genshin Impact — Character Event Wish | 0.6% | 74 | +6 pp | 90 | 50% | 62.3 |
| Genshin Impact — Weapon Event Wish | 0.7% | 63 | +7 pp | 80 | 75% | 53.3 |
| Honkai: Star Rail — Character Event Warp | 0.6% | 74 | +6 pp | 90 | 50% | 62.3 |
| Honkai: Star Rail — Light Cone Event Warp | 0.8% | 66 | +7 pp | 80 | 75% | 53.4 |
The mean pulls per 5★ from zero pity is the check against the official "consolidated" rates: 62.3 pulls corresponds to the published 1.6% consolidated 5★ rate on character banners.
What happens on a 5★
- Guaranteed (you lost the previous 50/50 or 75/25): the 5★ is featured; the flag clears.
- Not guaranteed: featured with probability 50% (characters) or 75% (weapons / light cones); a miss sets the guarantee.
- Capturing Radiance (Genshin characters): a counter of consecutive 50/50 losses; when it reaches 2, the next 5★ is featured regardless and the counter resets. This reproduces the published ~55% long-run featured rate.
- Epitomized Path (Genshin weapons): two featured weapons share the 75%; your chosen one is 37.5% per non-guaranteed 5★. One fate point (one miss) guarantees the chosen weapon on the next 5★.
The walk
for each pull: with p(pity+1) → 5★ branch (copies +1 if featured, update flags, pity = 0); else pity + 1
copies ≥ target is absorbing → P(target) = total mass in that state after N pulls
Running the same walk up to 2,000 pulls gives the certainty table: the first N at which P(target) crosses 50, 75, 90 and 99%. Currency is converted at 160 per pull plus whole fates or passes.
Not modelled
- 4★ drops, 4★ pity and the featured-4★ 50/50.
- Standard banners and chronicled / collab banners with different rules.
- The finer Capturing Radiance counter from data mines (small effects on single-pull odds; the two-loss guarantee and the ~55% average are preserved).
Sources and version (checked 12 November 2026)
- Base rates, hard pity, 50/50 and 75/25, Capturing Radiance and Epitomized Path (one fate point since 5.0): the in-game banner "Details" pages of Genshin Impact and Honkai: Star Rail.
- Soft pity start and step: community datasets of millions of recorded wishes and warps (Paimon.moe, Star Rail Station) — consistent with the consolidated rates printed in game.
- Constants are tagged
VERIFY-PATCHin the code and re-checked when a version changes banner rules.
Genshin Impact and Honkai: Star Rail are trademarks of HoYoverse (COGNOSPHERE). This site is an independent fan-made tool and is not affiliated with, endorsed by or sponsored by HoYoverse. Game names are used only to describe what the calculators are for. No game art, icons or logos are used. Formulas are compiled from public sources and may lag behind patches — each tool shows the game version it was checked against.