Gacha Pity Probability and Cost Calculator

What this estimate does and does not do

This calculator estimates gacha or loot-box pull probability using configurable base rate, soft pity, hard pity, and 50/50-style guarantee rules. It is useful for understanding odds before spending limited in-game currency.

It does not predict your actual result, change game odds, or recommend spending. Gacha systems can be expensive and psychologically sticky. Set a budget before pulling, and do not chase a probability number with money you cannot afford to lose. Also check the current in-game banner details, because pity and guarantee rules vary by game, banner, region, and patch.

Formula used

Without pity, the basic probability for at least one success is:

With pity and guarantees, pulls are not identical. This calculator uses dynamic programming over three pieces of state:

When a top-rarity result occurs, pity resets. If it is off-banner and the game has a guarantee-after-loss system, the next top-rarity result is treated as guaranteed target.

Worked example

Using common character-banner style settings:

• base top-rarity rate: 0.6%
• target chance after top-rarity: 50%
• soft pity starts at pull 74
• soft pity increase: 6% per pull
• hard pity: 90 pulls
• guarantee after losing 50/50: yes

If you start at 0 pity and plan 90 pulls, you are guaranteed at least one top-rarity result, but not necessarily the target if you are not already guaranteed. If you lose the 50/50 at hard pity, the target may require another pity cycle. That is why the worst case for one featured target can be 180 pulls in some systems.

How to use the result

• Use “chance for target goal” for the probability of reaching your desired number of copies.
• Use “expected target copies” as a long-run average, not a promise.
• Use “worst-case guarantee” only when your selected pity/guarantee rules actually guarantee the target.
• Use the 50%, 90%, and 95% pull milestones to understand probability, not to justify overspending.

Assumptions and limitations

• Soft pity is modelled as a linear increase per pull. Some games use hidden or different curves.
• The calculator assumes pity resets after any top-rarity result.
• The guarantee model assumes one off-banner top-rarity makes the next top-rarity guaranteed target.
• It does not model multiple simultaneous featured items, weapon paths, fate points, radiance/mercy mechanics, or banner-specific exceptions.
• If the game has no guarantee-after-loss system and the target chance is below 100%, there may be no true worst-case guarantee.