Methodology & sources
Every number on this site comes from one engine, tested in the open. This page documents its model, its verification cases and where each rate comes from. Snapshot: October 2026
The documented rates
| Parameter | Character event | Weapon event | Standard | Source |
|---|---|---|---|---|
| Base 5★ rate | 0.6% | 0.7% | 0.6% | Official - in-game Wish Details |
| Consolidated 5★ rate | 1.6% | 1.85% | 1.6% | Official - in-game Wish Details |
| Soft pity starts | wish 74 | wish ≈63 (estimates 62–65) | wish 74 | Community-measured |
| Ramp per wish | +6 pts | +7 pts | +6 pts | Community-measured |
| Hard pity | 90 | 80 | 90 | Official |
| Featured per 5★ | 50%, guarantee on loss; ~55% consolidated with Radiance (v5.0+) | 75% featured pair; 50% between them; 1 fate point (v5.0+) | - | Official - v5.0 notes |
HoYoverse publishes base and consolidated probabilities but not the exact soft-pity curve; the start points and slopes above are the long-standing community consensus from large exported-wish datasets, and they reproduce the official consolidated rates almost exactly (see verification below).
The probability engine
For plain 5★ odds we multiply survival probabilities wish by wish: P(at least one 5★ within N) = 1 − ∏(1 − pi), where pi is the rate for the i-th wish in your current cycle.
For the target (featured character, selected weapon), guarantees make naive products wrong, so we run an exact forward dynamic program over the joint state: pity counter combined with either the 50/50 phase (won-last / lost-last / guaranteed) or the weapon banner's fate points. “Wishes needed” inverts this curve by scanning for the first N that reaches your confidence level - closed-form where possible, exhaustive where not. Nothing on this site estimates by simulation; the simulator is for intuition, and its 20,000-run batch mode doubles as a live cross-check against the exact values (the test suite enforces the same agreement).
Capturing Radiance model
Official (v5.0): when a 50/50 is lost, Radiance may convert the loss into a win, raising the consolidated featured probability from 50% to ≈55%. Community measurements put the rescue at ≈10% of losing 50/50s. We model a 50/50 you enter right after a loss (i.e., you lost, took the guaranteed pull, and are on a 50/50 again) as “armed” with win probability 0.5 + 0.5 × 0.10 = 55%; other 50/50s stay 50%. Some community analyses argue Radiance preferentially fires after longer loss streaks (3rd–4th consecutive loss); our flat model is the mainstream reading and matches the official consolidated figure. You can disable Radiance in the calculator for conservative planning.
Savings-planner convention
One patch = 42 days (editable). “Recurring income” presets are built from documented sources: 60 primogems/day dailies, 600 × 2 Abyss resets, ~600/month Imaginarium Theater, events, maintenance mail and livestream codes - 160 primogems = 1 wish. Welkin adds 90/day + 300 Genesis; Gnostic Hymn adds 680 primogems + 8 Intertwined Fates; the Stardust shop adds 5 fates/month. One-time exploration rewards vary per patch and are excluded from the recurring presets (the “F2P - everything” preset includes a typical allowance).
Verification (build-time, same engine)
| Case | Expected (published) | Computed |
|---|---|---|
| P(5★ within 62 wishes), character banner | ≈ 31% (community: “62.5 is the mean, not the median”) | 31.1% |
| Median wishes to a 5★ (character) | 75–78 (community datasets) | 76 |
| Mean wishes to a 5★ vs consolidated rate | 62.5 vs 1.60% (official in-game figure) | 62.3 vs 1.61% |
| Weapon banner mean vs consolidated rate | 54.1 vs 1.85% (official in-game figure) | 53.3 vs 1.88% |
| Wishes for 90% confidence of a 5★ | ≈ 80 (community rule of thumb) | 80 |
| P(5★ within 90 wishes) = hard pity | 100% | 100.0% |
| Featured character, fresh 50/50: 50% / 90% / mean / worst | - (derived) | 80 / 155 / 93.4 / 180 |
| 20,000-run Monte Carlo vs exact DP (fresh, 80 wishes) | within 1.5 points | passes (see test suite) |
Sources
- In-game Wish Details panel (base/consolidated probabilities, 50/50 & guarantee wording, Epitomized Path rules) - checked October 2026.
- HoYoverse Version 5.0 update notes - Capturing Radiance (~55% consolidated featured probability) and the Epitomized Path change to one fate point maximum.
- Community statistical analyses of exported wish history (large crowdsourced datasets, e.g. wish trackers and the classic pity-curve studies) - soft-pity start 74 / ≈63, ramp ≈ +6–7 points per wish, median 5★ in the mid-70s.
- Community “primogem census” threads - per-patch income ranges used to sanity-check the savings presets.
Limitations & disclaimer
Soft-pity curve values are community-measured and could shift with future versions; the calculator is a planning aid, not a promise. PityHub is an unofficial fan tool, not affiliated with or endorsed by HoYoverse / COGNOSPHERE. All original content and code; no game assets used.