Genshin Impact Wishing Probability Calculator

Target Ranks

Pity System Next five-star (5*) character? Character pulls pity? Last five-star (5*) weapon? Weapon pulls pity? Epitomized path status?

Pulls Primogems Intertwined Fates Starglitter

Results are displayed here.

What is this, and how does this work?

This is a calculator for probabilities of successfully acquiring a target number of featured/limited five-star characters, and/or featured/limited five-star weapons from wishing in the game, Genshin Impact.

In a nutshell, this calculator works much like a simulator in terms of getting results, but without the random number generation, as it just iterates through the combinations/permutations of percentages (chances), multiplying and adding accordingly. Per this distinction, this should qualify as a calculator rather than a simulator. While "wishing for 5-stars" has a limit that is not too large, it is thus faster, and more accurate. Would you like a more verbose answer?

A more verbose, though not complete, description:

An essential idea used for this calculator is "x*y=z" where x is the probability to acquire something specifically on "pull count A", y is the probability to acquire something specifically on "pull count B", and z is the probability to acquire something on the total pull count ("pull count A" + "pull count B") through that permutation of the pull counts. Since there are multiple pairings of pull counts that add up to the pull count of z, it would have to process a summation of all the possible permutations to get the total probability for that pull count.

To explain further, we shall focus on calculating for featured five-star characters. To calculate, it will first get a distribution for which pull count the first copy would occur. To compute this distribution, imagine a list of pulls going from the first and to the last. From the start, there will be a starting population of 100%, the amount that has yet to encounter success. For each pull count, there is a percentage (the chance of getting the five-star on that pull count) of that population that will succeed, and be removed from the remaining population.

When the pity gets cleaned by acquiring the first five-star, and there is more to go for, the calculator will combine what it has calculated with pre-calculated data, which describes the cumulative chance for each pull count to have successfully obtained the target number of copies after a clean pity, which was calculated with the code uploaded to this github repository. Finally, it returns a result.

The process for featured five-star weapon probabilities, though a bit more complex, has just about the same (non-exhaustive) description.

If there are both more than zero copies to get on featured five-star characters, and specific featured five-star weapons, there'll be two distributions for the first copy of each, which will be combined, before going through the predefined set of data.

Notes

While there would basically be no difference between "single pulls" and "multis (ten pulls)", by technicality, the target selector for five-star characters is actually just "the number of limited (featured) five-star characters to get". This means that it actually does not specify which "limited five-star character" it is getting. It could be a combination of any limited five-star characters that sums up to that number, and as a "multi (ten pull)" risks resetting the "pity" mechanic by a few pulls on an unintended target, it is therefore deemed necessary enough to clarify that this calculator accounts for "single pulls", and not "multis". Related to this, the target selector for the weapon does not work like the character's, as the pity mechanic between the two is different. A significant part, specifically the epitomized path, of the weapon's pity mechanic can reset too variably.

For the current version, this calculator does not account for "return wishes", wherein "starglitter" can be acquired from pulling, and be exchanged for more pulls to be done for the target(s).

Per technical limitations, the calculator loses accuracy as a chance becomes less and less likely. Specifically, its result will be rounded to 12 decimal places (in decimal, non-percent form). This means to say that something with 1 in a trillion or less likely odds will probably just be rounded to zero.

The calculator has some set bounds for setting inputs to the necessary minimum or maximum.

Github Repository

This calculator's files are posted on Github. You may see the files (and code) in the github repository. If issues are found, it should be possible to post in the issues section.

Sources Of Information

This calculator was made based on information from an article by genshin-wishes.com on hoyolab, and a page on the fandom wiki.

Other info...

Last Updated: October 14, 2023.