Gacha Probability Calculator
pity · soft pity · 50/50
Featured-target probability simulator
Choose a preset model and current pity to calculate mean pulls and the counts needed for target probabilities.
Select a model preset, enter pulls since the last rare drop and set the 50/50 options. The calculator shows mean pulls to the featured target and cumulative probability under those assumptions.
Choose a model.How to use the gacha probability calculator
Explore game-model presets, soft and hard pity, and an optional 50/50 rule. Calculate mean pulls to a featured target, estimated costs in USD and pulls needed for target probabilities.
A rare-drop probability, often labelled a 5-star rate, does not by itself describe a model with pity. Soft pity raises the rate after a chosen point, while hard pity guarantees a rare drop with probability 100% at a limit. This calculator applies the selected base rate, pity settings and optional 50/50 rule to estimate mean pulls to the featured target, costs in USD and counts needed for target probabilities. Presets represent simplified assumptions; they are not a certification of a game’s current banner rules.
Current pity is the number of pulls since the last rare (5-star) drop. The model starts from that state and calculates the conditional probability of obtaining the target in additional pulls. Near a hard-pity limit, the conditional distribution can require fewer further pulls. Calculations run in the current browser and inputs are not stored.
When this tool is needed
- Estimate mean pulls to a featured character or weapon under a chosen model
- Explore an estimated budget using your own cost per pull in USD
- Compare counts needed for a 50% or 90% chance from current pity
Before entering data
- Current pity counts pulls since the last rare (5-star) drop, starting at 0.
- In the simplified 50/50 model, enable the guaranteed state after a non-featured rare drop.
- Expected values describe a distribution; an individual result can differ substantially.
How to use
- Select a game/banner model preset to load its base rate, pity and 50/50 assumptions.
- Enter current pity: pulls since the last rare (5-star) drop.
- Set whether the 50/50 rule applies and whether the next rare drop is guaranteed featured.
- Review or edit the cost of 1 pull in USD, then check mean pulls and estimated cost.
- Compare counts for target probabilities of 50·75·90·99%.
How soft and hard pity work in the model
For example, a model may guarantee a 5-star drop at pull 90 and begin increasing the rate after pull 74. With a base rate of 0.6%, an independent-trial mean would be about 167 pulls. Applying a pity ramp can instead produce a single rare-drop mean around 60 pulls. These are illustrative model settings, not a statement that every game or current banner follows this curve. The featured-target mean also depends on the optional banner rule.
Calculation horizons and approximations
The cumulative distribution is evaluated up to 2,000 pulls in pity models and up to 5,000 without pity; selected settings can produce a shorter range. Each next-rare-drop mean is truncated at 9,999 pulls, so very low rates can give a smaller mean than an unlimited-trial model. The chance of at least N copies is a binomial approximation derived from the mean, and Monte Carlo samples also have a tail cutoff. Presets are examples of selected assumptions; check the current banner rules inside your game.
Model assumptions and careful use
The probability presets are generalized settings inherited from the earlier tool. Your game’s current in-game banner information takes priority. Native costs use your editable USD assumption; the starting value is a calculation example, not an official store price. Model inputs and calculation conventions were reviewed in the original tool on 2026-08-20. Current language and functional validation are tracked separately. Mean values do not predict an individual outcome, and the calculator does not recommend a purchase.
Probabilities and means are model estimates and can differ from a game’s latest published rules. The tool supports understanding the selected assumptions; it does not encourage spending.
FAQ
How does hard pity change the probability calculation?
In this model, hard pity sets the chance of a rare drop to 1 (100%) at the selected limit. Earlier pulls use their configured rates, and the calculator accumulates them to obtain a distribution and mean. A rare drop may still need to pass the optional featured-target rule, so reaching the rare-drop limit does not always guarantee the featured target.
Does the model include a soft-pity increase?
Yes. The inherited Genshin Impact, Honkai: Star Rail and other presets contain a soft-pity start and a linear increase. You can inspect or replace those assumptions in the custom pity tab. These simplified presets are useful for comparing models, but they do not certify the current official probability curve of a game.
What does the 50/50 option mean for expected pulls?
In this simplified banner model, a 5-star rare drop has a 50% chance to be featured. If it is not featured, the next rare drop is guaranteed featured. With 50/50 enabled and no guarantee already active, the mean equals the next-drop mean plus half the reset-pity mean. With the guaranteed state enabled, only the next-drop mean is needed.
What happens when I enter my current pity count?
Current pity counts pulls since the last rare (5-star) drop. The model starts at that position and calculates a conditional distribution for the remaining pulls. Approaching the hard-pity limit can reduce the additional pulls needed to reach a target probability under the selected model.
Does this calculator recommend spending?
No. It is a tool for understanding a probability model. An expected value is an average over a distribution, and individual outcomes can vary widely. The editable cost is an assumption for a calculation, not a recommendation to buy or a guarantee of obtaining an item.