Results will appear here.
Simulation mode:
Banner type:
Starting pity values:
Featured roll status (event character and event weapon banners only):
Realistic non-featured 4-star pull behavior (event character and event weapon banners only):
Desired result (desired result mode only, not applicable to standard banner):
Epitomized Path options (event weapon banner only):
The behavior of Genshin Impact's wish system is not entirely clear when it comes to resolving a scenario where a 4-star guarantee and 5-star guarantee
would trigger on the same wish. Finding exact information on this scenario has also proven considerably difficult due to its rarity and specific nature.
To resolve this scenario, the simulator will replace the previous wish (which could have only been a 3-star - otherwise, one of the guarantees wouldn't
be triggering) with the 4-star guarantee trigger. Should this occur on the first wish in the simulator (meaning no prior wish exists), the 4-star guarantee
will instead be delayed until the next wish.
Note that this system will not trigger if a 5-star (that isn't guaranteed) is rolled on the 4-star guarantee. In-game probabilities explicitly state that this is a possibility; on
the simulator, this will result in the 5-star being kept and the 4-star pity counter resetting.
In-game probabilities claim that, barring modifications from featured character and weapon pull chances, there is a 50/50 split determining whether or not a 4-star item
will be a character or a weapon. While these statements are accurate regarding featured items, these statements are false regarding non-featured items.
By observing global pull data on paimon.moe, biases can be seen in the event character and event weapon banner in non-featured
4-star items. For event character banners, the featured characters represent roughly 66.67% of the 4-star rolls, courtesy of the 50% pull chance and guarantee system. However,
around 5% of the 4-star rolls are non-featured characters, while 28.33% of the 4-stars are non-featured weapons. For event weapon banners, the featured weapons represent
roughly 80% of the 4-star rolls; then, 18.5% of the 4-stars are non-featured characters, and a mere 1.5% of the 4-stars are non-featured weapons.
An option is available to toggle how the simulator approaches these non-featured 4-star roll odds. If the option is disabled, the simulator will use the even 50/50 split
for characters and weapons as described in in-game probabilities. If the option is enabled, the simulator will use probabilities that attempt to emulate the results reflected
in the actual wish data seen on paimon.moe.
By simulating a large number of wishes according to the probabilities given in-game in Genshin Impact, the base pull rates and guarantees are not sufficient
to match the given pull rate after pity. For instance, the game states that 5-star characters on an event character banner have a 1.6% average pull rate with pity applied.
Simulating a large number of pulls using only the 0.6% base pull chance and guaranteed 5-star on the 90th wish without a 5-star yields results that fall short of this 1.6%
claimed (simulated results tended to yield around a 1.435% chance). Similar conflicts arose simulating 4-star rolls on event character banners (the claimed average with pity
is 13%; simulated results with the 5.1% base pull rate and guaranteed 4-star on the 10th wish without a 4-star tended to yield around a 12.45% 4-star rate). It is clear that
a factor is missing and unstated in-game.
The Genshin Impact community has compiled statistics on actual wishes performed by players, and noted that this missing factor is likely a form of "soft pity" that occurs well before
the guarantee on the 90th pull, which is referred to as "hard pity". Soft pity on an event character banner, based on these compiled statistics, was observed to begin around 73
wishes without pulling a 5-star. Soft pity notably increases the odds that a 5-star is pulled, thus raising the pull rate - this would provide the explanation for the 1.6% average
pull rate with pity given in game.
This simulator does not account for soft pity. As a result, the wishes simulated here will likely yield slightly fewer 4-star and 5-star pulls than would be actually
encountered in-game. I may attempt to add an option to simulate soft pity in the future, provided that data is available for the banner type in question and I can properly
translate the statistical results into probabilities that influence the simulation.
If you want to see some data and discussion regarding soft pity, please refer to these Reddit posts:
| Result | Base probability | Average probability after pity |
|---|---|---|
| 5-star character/weapon | 0.6% | 1.6% |
| 4-star character/weapon | 5.1% | 13% |
| 3-star weapon | 94.3% | 85.4% |
| Result | Base probability | Average probability after pity |
|---|---|---|
| 5-star character | 0.6% | 1.6% |
| 4-star character/weapon | 5.1% | 13% |
| 3-star weapon | 94.3% | 85.4% |
| Result | Base probability | Average probability after pity |
|---|---|---|
| 5-star weapon | 0.7% | 1.85% |
| 4-star character/weapon | 6% | 14.5% |
| 3-star weapon | 93.3% | 83.65% |