Genshin Inferred Probabilities
Version: v3.15.1
Disclaimer
Genshin Impact publishes base rates, consolidated rates and hard pity limits per banner. This information alone is not enough to accurately model wishes. Our tooling is based on probabilities inferred from data obtained by community or our own team. These probabilities are our best guess at pity mechanics and are tuned to match the published consolidated rates. Our calculators should match the long-term behavior of actual in-game wishes. Sources are cited below. More detailed rationale can be found in our deep dive.
Sources
[4] GachaGuide study on four star pity
Banner data
[5] paimon-moe banner history (MIT)
[6] Genshin Impact Wiki, per-banner pages (CC BY-SA)
Standard and Character Banner
Five Star Probabilities per Pity, consolidated Rate: 1.60%
| Wish | Probability |
|---|---|
| 1 | 0.006 |
| 2 - 73 | 0.006 |
| 74 | 0.064 |
| 75 | 0.122 |
| 76 | 0.181 |
| 77 | 0.239 |
| 78 | 0.298 |
| 79 | 0.356 |
| 80 | 0.415 |
| 81 | 0.473 |
| 82 | 0.532 |
| 83 | 0.590 |
| 84 | 0.649 |
| 85 | 0.707 |
| 86 | 0.766 |
| 87 | 0.824 |
| 88 | 0.883 |
| 89 | 0.941 |
| 90 | 1.000 |
Uses linear ramping soft pity at 74th pull - per [3]. This results in a close match with the reported consolidated rate and fits the histogram in [1].
Four Star Probabilities per Pity, consolidated Rate: 13.0%
| Wish | Probability |
|---|---|
| 1 | 0.051 |
| 2 | 0.051 |
| 3 | 0.051 |
| 4 | 0.051 |
| 5 | 0.051 |
| 6 | 0.051 |
| 7 | 0.051 |
| 8 | 0.051 |
| 9 | 0.52 |
| 10 | 1.000 |
All pulls have 5.1% base rate until the 9th and 10th. The 10th has a 100% chance (hard pity) and the 9th pull probability was chosen to achieve a consolidated rate of 13.00%.
The five star 50/50
Since version 5.0 the 50/50 on character banners isn't quite a 50/50 any more. A five star won while you're not on a guarantee turns out to be the promotional character 55.000% of the time, and miHoYo publishes that figure along with the rule that you can never lose four in a row, but not the mechanic that produces either of them.
So we're modelling it as a 4.212% chance that a lost 50/50 gets converted into the promotional character, which becomes a guarantee once you've lost three in a row (it's the only constant trigger rate that gives us both published numbers at once). That works out to a promotional share of 68.966% of all five stars rather than 2/3, and 90.33 expected wishes per promotional character instead of 93.45, which is a decent chunk if you're budgeting.
One wrinkle and it's ours rather than the game's. The simulation is starting you at a loss streak of zero, so your first 50/50 will show up as 52.1% and not 55.000%. The 55.000% is what you converge to once streaks are in play. There's no input for your current streak yet.
Capturing Radiance is character banner only, so weapon and standard aren't affected at all.
Weapon Banner
Five Star Probabilities per Pity, consolidated rate: 1.85%
| Wish | Probability |
|---|---|
| 1 | 0.007 |
| 2 - 63 | 0.007 |
| 64 | 0.065 |
| 65 | 0.123 |
| 66 | 0.182 |
| 67 | 0.240 |
| 68 | 0.299 |
| 69 | 0.357 |
| 70 | 0.415 |
| 71 | 0.474 |
| 72 | 0.532 |
| 73 | 0.591 |
| 74 | 0.649 |
| 75 | 0.707 |
| 76 | 0.766 |
| 77 | 0.824 |
| 78 | 0.883 |
| 79 | 0.941 |
| 80 | 1.000 |
Uses linear ramping soft pity at 64th pull - per [3] but shifted. This results in a close match with the reported consolidated rate (1.85%) and fits the histogram in [1].
Four Star Probabilities per Pity, consolidated rate: 14.5%
| Wish | Probability |
|---|---|
| 1 | 0.06 |
| 2 | 0.06 |
| 3 | 0.06 |
| 4 | 0.06 |
| 5 | 0.06 |
| 6 | 0.06 |
| 7 | 0.06 |
| 8 | 0.41 |
| 9 | 1.000 |
| 10 | n/a |
Uses tuned probabilities from our own study [4] to match histogram shape. Base probability of 6% alone with hard pity at 9th pull does not give a 14.5% rate. From our data there is additional soft pity on the 8th pull. That value (0.41) is chosen to achieve the published consolidated rate of 14.5%.
Epitomized Path
Charting a course guarantees the weapon you picked, and since version 5.0 it only takes one Fate Point instead of two. Any five star weapon that isn't your choice earns you the point, so your weapon shows up on the first five star weapon 37.5% of the time and on the second one the other 62.5%. Never later than that. Two five star weapons, 160 wishes worst case, which used to be 240.
Our calculator actually models this, you tick the box on a five star weapon to set your choice.
Yeah it appears that community tables show 56.1% on the 9th wish for the character banner and 66.0% on the 8th for the weapon banner (from the Fandom wiki and GGanalysis, out of a 9.45 million wish study) but we chose 0.52 and 0.41 because they reproduce really close to miHoYo's published rates. I know there is a decent delta but I'd rather make sure we converge to published rates in our model. Their numbers give consolidated rates of 13.06% and 14.86%, ours give 13.01% and 14.50%, and the published figures are 13.0% and 14.5%.