Despite the fact that there’s a fair bit of RNG involved in this game, Genshin also has some predictable statistics behind the wishing system. I recently came across this very helpful analysis on Reddit with a table of probabilities compiled by a very helpful user named Dologue, and wanted to share my strategy for planning wishes to ensure maximum luck, minimal disappointment.
For this analysis I will be focused on the limited character banner only as I do not have personal experience with the weapon banner.
The TLDR version: Save at least 119 wishes, up to 161 wishes, for the best odds in your favor! Read on to find out why.
For Starters:
Did you know that while your chances of winning the 50/50 are indeed 50:50, your chance of getting the featured 5 star is also 50% at 80 wishes? However, the distribution of probability is nonlinear, so your odds are actually best in a certain wish range. Let’s talk about that ideal range now!
Disclaimer:
Repeat after me: your mantra for wishing should be “Assume Average Luck.”
Yes, some people manage to get 5 stars at low pity. Yes, these people post on Hoyolab and make it feel like everyone gets super lucky. Yes, I have personally experienced this as well (9 pity Shenhe), but for your sanity, try to wipe this out of your mind. Expecting better odds will most likely lead to disappointment and frustration. Please believe in the math, and if you really are super lucky, it might be a good time to go buy a lottery ticket 
Ok, back to the math!
The Probability Table:
The below table is from the original Reddit post:
Credit to Reddit user u/Dologue
You can see that your odds of getting the featured 5 star go from 20% to 60% between 69 and 92 wishes. That’s only a difference of 23 wishes but a threefold increase in probability!
Also interestingly, the odds quickly ramp up from 90% probability to 99% between 155 and 161 wishes, or only 6 wishes difference. While statistically it is possible to lose 50/50 at 80 pity and take the full 180 wishes to get your featured 5 star, the odds are very unlikely, so for all intents and purposes, it’s safe to say the number of wishes for guarantee is 161.
How to Plan Your Strategy:
First, decide what range of probability you would like to target.
I do not recommend pulling if you want the featured 5 star with any less than 80 wishes on hand as your chances for getting the 5 star are lower than your chances for… not getting the 5 star.
If you just have wishes to burn and you want to try your luck with low expectations, go for 34 wishes. This gives you a 10% chance at the featured and roughly an 18% chance of a standard 5 star.
However, please be very careful going above 34 and up to 72 wishes if you are only pulling for fun. Your odds of “ruining” your pity by pulling the wrong character or losing your 50/50 significantly increase at this point!
I recommend going for at least 70% probability, so 119 wishes and up. The odds increase very quickly when you hit 153 wishes to 80% probability, so it gives you a realistic range to be able to grind if F2P, and a lower number needed to recharge. As stated above, the realistic maximum is 161 wishes and not 180.
How to Estimate Wishes
Each patch typically lasts for 41 days, so you have 20-21 days per banner. You can also throw in the 5 wishes that can be redeemed from the Starglitter shop, and BP players can also factor in the 4 extra fates.
If you don’t have a detailed primogem projection calculator like I do, just take a look at your Traveler’s Diary for the last three months and take the average. Divide it by 30 to get your daily average, and multiply by the number of days from now until the end of the banner . That will be the likely amount of primogems you will get at your current playing pace. Be sure to exclude special bonus mail gems and annual events like Lantern Rite so you don’t overestimate!
Example:
- Start saving on 4/1
- 32 days until Baizhu banner
- Baizhu banner 5/2 to 5/23 = 21 days
- Total time to save = 53 days
- Jan primos 8000, Feb primos 6000, March primos 10000, average is 8000 per month, or 267 primos per day
- 267 primos per day x 53 days = 14151 primos or 88 wishes, plus 5 wishes from Starglitter shop = 93 wishes
- Probability of getting Baizhu is 61% so the odds are slightly in your favor!
- However, at the start of his banner you will most likely only have 8544 gems or 53 wishes + 5 Starglitter shop wishes available, so your odds when pulling immediately are only 17% at 58 wishes. In this case, it’s better to wait towards the end of the banner to ensure your odds are better than 50%, or you will likely feel disappointed and discouraged with the result, making it harder to keep working towards earning the rest of the wishes needed.
And that’s it! With a basic understanding of math and probabilities, you can save yourself headache and disappointment. May the odds be in your favor!
