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Soft Pity on Banners​

By: vibe checker#5502
Added: 2021-06-03 (v. 1.5)
Last tested: 2021-06-03 (v. 1.5)
Discussion

Finding: Soft pity is 74 on the featured character/standard banner, and 63 on the weapon banner.

Evidence: Wish Tally 1, Wish Tally 2 and Wish Tally 3

The second link shows that the probability of rolling a 5-Star massively increased on the 74th roll, as opposed to the 75th, and the third link shows that the probability for rolling a featured weapon on the weapon banner massively increased on the 63rd roll, not the 65th.

Significance: fixing misconceptions that soft pity is 75/65, allowing players to save their primogems more effectively

Estimated 5-Star Pulls for Weapons/Characters​

By: KBphan#0001
Added: 2021-04-19 (v. 1.4)
Last tested: 2021-04-19 (v. 1.4)

Finding: It takes approximately 12.5 5-Star pulls to R5 a specific weapon

Average 5-Stars pulled for specific rate up 5-Star weapon:

  • R1 weapon (no pity) - 2.5
  • R1 weapon (with pity) - 2.25
  • R5 weapon (not starting with pity) - 12.5
  • R5 weapon (starting with pity) - 12.25

Average 5-Stars pulled for rate up 5-Star character

  • c0 character (no pity) - 1.5
  • c6 character (not starting with pity) - 10.5
  • c6 character (starting with pity) - 10

Evidence:
I made a program to brute force 10,000,000 trials of attempting to R5 a specific rate up 5-Star using the pity rules for the weapon banner. On average it will take a player 12.5 5-Star pulls to R5 their desired weapon if they only want one of the rate up 5-Star weapons. This leads to an average rate of 40% for a specific 5-Star weapon on the rate up banner.

Significance: This information can be useful for whales to figure out around how many pulls they will need to get a specific R5 on average.

Resin Efficiency of Acquaint Fates from Character Levelling​

By: Moonrobin#2608
Added: 2020-12-19 (v. 1.1)
Last tested: 2020-12-19 (v. 1.1)

Finding:
Level all characters to 20/40 for the Fate.
From that point, getting them to 50/60 takes around 2 days of F2P resin budget.
This is worth overall, as there are no other ways to convert Resin to rolls. I would treat the 70/80 Fate as a bonus rather than the goal. It costs 5 days worth of resin, which is probably not worth the expected rewards from a single roll.

Evidence:
With the introduction of acquaint fates from character leveling in 1.2, it is now possible to convert resin to rolls.
A question that many will have is how much does that Acquaint fate actually cost, in terms of resin investment. To answer this, I aggregated character leveling and ascension costs to hit the Fate thresholds.
Note that this is for WL7 drop rates, and only includes permanent sources of materials (i.e. Event rates are not considered).

Significance:
20/40 is a no brainer for the Fate, do it now to get it out of the way.
20/40 to 50/60 is actually an investment of ~427.2 resin for the fate.
50/60 to 70/80 is 5 days worth of F2P resin budget. Consider if you have no other uses for resin.

Weapon banner Gacha Rates with Epitomized Path​

By: Tim#5259, Mcpie#8672
Added: 2021-11-11 (v. 2.2)
Last tested: 2021-11-11 (v. 2.2)
Discussion

Finding:
Weapon banner gacha rates with Epitomized Path.

Evidence:
Analytic solution, no pity: 1.984375 5* weapon rolls: Discord image
Analytic solution, pity: 1.8125 5* weapon rolls: Discord image
Monte-carlo verification: Pastebin

Significance:
Expected 5* weapon rolls to desired 5* using epi path without pity at start: 1.984375
Expected 5* weapon rolls to desired 5* using epi path with pity at start: 1.8125
R5, epi path, no pity to start; expected num of weapons: 9.921875
R5, epi path, pity to start; expected num of weapons: 9.75

R1, no epi path, no pity: 2.5
R1, no epi path, pity: 2.25
R5, no epi path, no pity: 12.5
R5, no epi path, pity: 12.25

Number of Wishes on Weapon Banner to Fully Level a 5 Star Weapon​

By: hanpw#5824
Added: 2021-12-16 (v. 2.3)
Last tested: 2021-12-16 (v. 2.3)
Discussion

Finding:
How many wishes on the weapon banner does it take to fully level a 5-Star weapon to Level 90?

Evidence:
Weapon Fodder EXP
Weapon Banner Wish Counts and Rates
Calculations

  • Using data from Genshin Wishes to get the 3 star, 4-Star, and 5-Star weapon rates, we can calculate that the average weapon EXP per wish is 10,597.30.
  • 5-Star weapons need 9,064,450 total EXP to get to level 90, so the average number of wishes needed is 855.35.

Significance:
Average number of wishes needed on weapon banner to level a 5-Star weapon to 90 is 855 wishes.

Gacha Calculator​

By: Tibo#4809
Added: 2022-02-19 (v. 2.5)
Last tested: 2022-02-19 (v. 2.5)
Discussion

Finding 1: Statistical model for Genshin Impact's droprates.

Evidence:
Source: Cgg and Genshin Wishes (posted with permission)

The soft-pity system starts at pull 74 (5* char), pull 63 (5* weapon) and at pull 9 (4*). At soft-pity, the drop rate increases with (the base rate * 10) every pull

For more details/graphs/data, see their HoYoLAB post

Significance:
Better understanding of how the soft-pity system works.

Finding 2: Gacha rate calculator

Evidence: Based on this statistical model, I've made a rate calculator for a specific rate-up 5 char/weapon and 4 char.

Some percentile/pulls needed:
| Item | 50th Percentile | 95th Percentile | 99th Percentile |
| :--- | :--- | :--- | :--- |
| C0 of a rate-up 5* character | 80 | 158 | 161 |
| C6 of a rate-up 5* character | 654 | 843 | 917 | | R1 of a rate-up 5* weapon | 99 | 199 | 204 |
| R5 of a rate-up 5* weapon | 527 | 731 | 811 |
| C0 of a rate-up 4* character | 26 | 93 | 141 |
| C6 of a rate-up 4* character | 231 | 384 | 464 |

Small note with these calculations: to keep the amount of calculations/paths to explore down in the 4* char calcs, there's assumed to be no 5*'s to eat up/delay guaranteed 4* char. This will make the required 4* count slightly lower than needed. I've assumed that the difference is negligible.

Significance:
Better budgeting/planning if users want to be X% sure to get char Y at CZ. Especially more useful for budgeting of higher constellations as averaging of low/high pity pulls. A calculator has the advantage that people can enter their current situation (pity/guaranteed).