How Many Primogems Do You Need to Pull One Character in Genshin Impact?

Have you ever wondered how many wishes it takes to get that character you want in Genshin Impact?

To pull one limited 5-star character in Genshin Impact, you need at most 180 wishes. However, it's extremely rare to actually need the full 180 wishes to get a 5-star character.

So, how many Primogems should you save to feel confident about getting your desired character?

Methodology

Feel free to skip this section if you're not interested in the technical details.

• Used simulation to calculate probabilities
• Computer performs X number of gacha pulls
• Count the number of successful attempts (getting 1+ characters)
• Divide successful attempts by total attempts to get probability
• Example: If 500 out of 1000 people succeed with 100 pulls, the probability is 50%

I also calculated expected values - specifically, how many wishes are needed on average to get X characters.

This involves having the computer pull until X characters are obtained, then calculating the average number of wishes required. It's the same method used to calculate average test scores.

Results

First, let's calculate the expected value for getting 1 character: 94 wishes

This might seem surprisingly low. Since the pity system guarantees a 5-star at 90 wishes, this means on average, you'll get your desired character in 94 wishes.

Next, let's check the probability of getting at least one 5-star character in 94 wishes.

The result is 60%.

Is this higher or lower than you expected? I personally thought it was quite low.

Ultimately, even if you pull the expected number of wishes, there's only a 60% chance of getting your desired character. This feels insufficient. I would want at least 90%, or even 95%+ probability.

120 wishes reaches 70% probability.

152 wishes reaches 80% probability.

The jump from 70% to 80% takes quite a while. At 90+62 wishes, we're still not in the soft pity zone where rates increase.

157 wishes reaches 90% probability. 160 wishes gets us to 96%.

The late-game surge is impressive!

What we learn is that if you want about 90% probability of getting one character, you need 157 wishes - quite a sobering result.

Additional Analysis

Since the single character results were somewhat disappointing, let's also calculate for C6 (7 copies total).

The expected value for getting 7 characters is 660 wishes. Surprisingly reasonable!

The probability of getting 7 characters in 660 wishes is 50%. This is lower than the single character case.

721 wishes (115,360 Primogems) for 70%,

760 wishes (121,600 Primogems) for 80%,

810 wishes (129,600 Primogems) breaks through 90%.

For a completely F2P player without Welkin Moon, this would require over a year of saving without pulling.