The most successful gacha games usually include a pity system of some kind, and Genshin Impact is no different in this regard. Some gacha games that have a pity system go the extra mile and include a soft pity system to minimalize a player's frustration when summoning.
Genshin Impact has both a pity system and a soft pity system, making up for its near 1% five-star unit summon rates. Some players assume that the pity system doesn't exist because they never get the five-star unit they want.
However, it's important to note that the pity system requires several summons (90 to be precise) for a player to be guaranteed a five-star unit. If they miscount and only do 80, that's not the game's fault. Fortunately, they can still get their desired unit through the soft pity system.
The pity and soft pity system of Eula banner in Genshin Impact
Eula is a five-star unit like Zhongli and Hu Tao. She will likely have the same summon rates as these two units, including the pity and soft pity system.
However, the pity system doesn't guarantee that the player will get the five-star unit that they want.
The pity system in Genshin Impact
The pity system for characters in Genshin Impact works as follows: a player is guaranteed to get a five-star character on their 90th summon. The player can be guaranteed access to any five-star character currently in the game depending on whether they already have Eula.
If a player is rolling for Eula and they're on their 89th summon, they could get a random five-star like Qiqi. If they haven't gotten Eula yet, they would have a 50% chance of getting her on the 90th summon. If they do not have her by then, they will have to summon another 90 to be guaranteed to get her (so it will be on the 180th summon).
The above image is for the regular banner, "Wanderlust Invocation." The main difference is that there is no 50% chance to get one of the promoted units. However, the same requirement for 90 attempts still exists here, so Eula will likely require the same 90 summons to potentially be obtained in Genshin Impact.
Essentially, the pity system guarantees that the player has a 50% chance of getting Eula in their first 90 summons if they don't have her yet. If they don't get her then, they will obtain her on the 180th summon. Once a player gets Eula, they're guaranteed a five-star unit on their 90th summon, regardless of who it is.
The soft pity system
If a player feels like they're too unlucky to make use of the regular pity system, then perhaps the soft pity system will alleviate their fears. The soft pity system isn't listed anywhere in-game, but it does exist, according to Genshin Impact data analysts.
Typically, the soft pity system will take place starting at the 74th summon, from which the chances of getting a five-star unit improves, with it maxing out at 100% on the 90th summon. For example, the player's chances of getting Eula is better when they summon at 87 as opposed to 77 (in the scenario that they haven't pulled any five-star unit by then).
So, everything before the 74th summon will operate on the normal 0.6% summon rate of acquiring a five-star unit. If a player gets a five-star unit before the 74th one, then the pity and soft pity system will reset. Remember, once a player gets any five-star unit, these rates will be reset to their default values.
Based on all of the above information, one can summon Eula for the first time by the 180th summon. Getting additional Eula copies will be entirely luck-based, although the pity and soft pity systems will get the player more five-star units to choose from.
Of course, lucky players will acquire Eula beforehand. It should also be noted that pity rates transfer across banners, so players who summon a lot in the Zhongli banner right now should be more likely to get Eula with fewer summons. For example, if a player didn't pull anything on 89 Zhongli summons, their first summon in the Eula banner can either give them Eula or another five-star unit.
From there, a player would only have to summon 90 more times to guarantee summoning Eula.