Genshin wish probability calculator

Genshin pity calculator: how your count turns into odds

Pity is the number of wishes you have made since your last 5-star on that banner. It matters because the chance of a 5-star is not flat. On the character event banner the base chance is 0.6% for each wish. From about wish 74 it climbs by roughly six percentage points with every wish, so the 74th wish is near 6.6% and the 89th is near 96.6%. Wish 90 is certain.

Type your own pity count into the box and the tool starts from that point. At pity 60 with 20 wishes in hand, the chance of the featured character without a guarantee is 45.1%. The same 20 wishes from pity 0 give 6.0%.

5 star probability by number of wishes

This table works without any script. It uses the same model as the calculator, starting from zero pity. The second column is the chance of any 5-star at all. The other columns are the chance of the limited item.

Read the first column with care. At 90 wishes any 5-star is certain, yet the featured character without a guarantee is only 59.4%, because about half the time the first 5-star is the other kind. The numbers below show how many wishes it takes to reach a given confidence.

On average a 5-star of any kind takes 62.3 wishes in this model, which is a rate near 1.6% and agrees with the overall rate the game company publishes. The featured character takes 93.4 on average with the 50/50, and the chosen weapon 86.5.

Guaranteed 50/50: what the guarantee is worth

When a 5-star arrives on the character event banner it is the featured character in about half of cases. If it is not, the next 5-star is guaranteed to be the featured character. So the featured character is never more than two 5-stars away, which is 180 wishes in the worst case.

That is why the guarantee switch matters so much. From zero pity with a guarantee, you are certain to hold the featured character in 90 wishes, and the median is 76. Without it, the same 90 wishes give 59.4%. If you assume the community 55% win rate instead of 50%, 90 wishes give 63.5%. Since version 5.0 the game's wish details give a consolidated 55% for the featured character on a non-guaranteed 5-star, which includes Capturing Radiance, so you can compare both settings.

Worked example

With 12,800 Primogems and 10 Intertwined Fates you have 90 wishes. At pity 0 with no guarantee the calculator says 59.4% for the featured character. With the guarantee it is 100%, and on the 55% setting it is 63.5%.

Weapon banner: 75/25 and the Fate Point

The weapon event banner differs in three ways. The base rate is 0.7%, the soft pity starts earlier, near wish 63, and the hard limit is wish 80. And a 5-star is one of the two featured weapons only 75% of the time (about 37.5% each); the other 25% is a standard weapon. After a standard weapon the next 5-star is guaranteed to be a featured one.

You also choose one of the two featured weapons as your chosen weapon. When a 5-star is not that weapon, you earn a Fate Point, and since version 5.0 one point is enough: the next 5-star will be your chosen weapon. In this model a fresh start gives 51.1% for the chosen weapon by wish 80 and 80.4% for either featured weapon. With one Fate Point already earned, the chosen weapon is certain within 77 wishes and 100% by wish 80.

Fate Points reset when the weapon banner changes, so check your Epitomized Path screen before you copy a number in.

How the probability is worked out

The tool does not run random trials. It keeps a list of every state you could be in after each wish: how many wishes since the last 5-star, whether the next 5-star is guaranteed, and for weapons whether you hold a Fate Point. For one wish it moves each state forward. With the chance for that pity count it ends the search, restarts the pity counter, or goes on to the next count. Adding the paths that reach the target gives an exact answer for the model.

We checked the model against facts that must hold. With zero pity, one wish has a 0.6% chance of a 5-star. Ninety wishes from zero always contain a 5-star. The average wishes per 5-star is 62.3, a rate near 1.6%, which matches the overall figure the game company publishes. The weapon average is 53.3, near the 1.85% published figure.

What this does not know

The game company does not publish the shape of the soft pity climb, so the 74 and 63 starting points and the six and seven point steps are the common community model, not official numbers. Guides differ by a wish or so. The tool also assumes every wish is independent apart from pity, it ignores the 4-star pity, and it does not cover the standard banner, the chronicled wish or the beginner banner. If your own wish history looks very different, trust your history. To turn Primogems into wishes first, use our Primogems calculator. If you cannot decide who to pull for, try the Genshin Impact team randomizer.