A quick sim to calculate the average and median of getting 5*'s in Genshin Impact. Also calculcates the cost at certain pull counts.
Might turn this into an interactive sliding graph later.
Source: https://www.hoyolab.com/article/497840
Event Character Wish TL;DR:
- Pulls 1-73 have a 0.6% chance (base chance) to get a 5*.
- Starting with the 74th pull, your chance to get a 5* increases by 6 percent each time. This means the 74th pull will have 6.6% chance to get a 5*, the 75th pull will have a 12.6% chance, and so on.
- Because of this, it is near impossible to hit "true" pity at 90 pulls. The expected worst case to get ANY 5* character is 89 pulls.
- 50/50 guarantee: If the 5* character you get is not the event character, your next 5* is guaranteed to be the event 5* character. Expected worst case for 5* event character: 178 pulls. Theoretical worst case: 180 pulls.
Event Weapon Wish TL;DR:
- Pulls 1-62 have a 0.7% chance (base chance) to get a 5*.
- Starting with the 63rd pull, your chance to get a 5* increases by 7 percent each time. This means the 63th pull will have 7.7% chance to get a 5*, the 75th pull will have a 14.7% chance, and so on.
- Because of this, it is near impossible to hit "true" pity at 80 pulls. The expected worst case to get ANY 5* weapon is 77 pulls.
- Epitomized path: You have the option of selecting the rate-up 5* weapon you want. If the 5* you get on the banner is not that weapon, gain a pity point. At 2 pity points, your next 5* is guaranteed to be that weapon. Expected worst case for desired rate-up 5* weapon: 231 pulls. Theoretical worst case: 240 pulls.
This breakdown assumes the player has no pulls of their own, from any source (such as Genesis Crystals, Primogems, and Fates).
For cost in USD, the $100 Genesis Crystal pack (no top-up bonus) is used for calculation, as it is the cheapest for pulls (~$1.98 USD/pull).
Event Character Cost:
| # of Pulls | Cost in USD |
|---|---|
| 1 | $1.98 |
| 10 | $19.80 |
| 20 | $39.60 |
| 30 | $59.40 |
| 40 | $79.20 |
| 50 | $99.00 |
| 60 | $118.80 |
| 62 (average # of pulls for ANY 5*) | $122.76 |
| 70 | $138.60 |
| 76 (median # of pulls for ANY 5*) | $150.48 |
| 80 (median # of pulls for event 5*) | $158.40 |
| 89 (expected worst case for ANY 5*) | $176.22 |
| 90 (theoretical worst case for ANY 5*) | $178.20 |
| 93 (average # of pulls for event 5*) | $182.16 |
| 100 | $198.00 |
| 110 | $217.80 |
| 120 | $237.60 |
| 130 | $257.40 |
| 140 | $277.20 |
| 150 | $297.00 |
| 160 | $316.80 |
| 170 | $336.60 |
| 178 (expected worst case for event 5*) | $352.44 |
| 180 (theoretical worst case for event 5*) | $356.40 |
Event Weapon Cost:
| # of Pulls | Cost in USD |
|---|---|
| 1 | $1.98 |
| 10 | $19.80 |
| 20 | $39.60 |
| 30 | $59.40 |
| 40 | $79.20 |
| 50 | $99.00 |
| 53 (average # of pulls for ANY 5*) | $104.94 |
| 60 | $118.80 |
| 65 (median # of pulls for ANY 5*) | $128.70 |
| 70 | $138.60 |
| 77 (expected worst case for ANY 5*) | $152.46 |
| 80 (theoretical worst case for ANY 5*) | $158.40 |
| 90 | $178.20 |
| 100 | $198.00 |
| 110 (average/median # of pulls for event 5*) | $217.80 |
| 120 | $237.60 |
| 130 | $257.40 |
| 140 | $277.20 |
| 150 | $297.00 |
| 160 | $316.80 |
| 170 | $336.60 |
| 180 | $356.40 |
| 190 | $376.20 |
| 200 | $396.00 |
| 210 | $415.80 |
| 220 | $435.60 |
| 230 | $455.40 |
| 231 (expected worst case for event 5*) | $457.38 |
| 240 (theoretical worst case for event 5*) | $475.20 |