Gacha Expected Value Calculator

What is gacha expected value?

Gacha expected value is the long-run average number of pulls needed for a target item. Based on geometric distribution theory, without pity the expected pulls are roughly 1 divided by the drop rate — for example, a 0.6% character has an expected value of about 167 pulls. Pity, soft pity and guarantee mechanics can reduce that average significantly, but they do not remove randomness.

Pity Mechanics Explained

Pity mechanics come in two forms: "hard pity" and "soft pity." Hard pity guarantees a high-rarity result once you reach a fixed number of pulls. Soft pity means that starting from a certain pull count, the probability rises with every pull. In Genshin Impact, for example, soft pity begins at pull 74 and hard pity guarantees a 5-star at pull 90.

Soft Pity Mechanics

Soft pity means that from a certain pull count onward, the odds for each pull climb sharply. Using Genshin Impact as an example: pulls 1-73 sit at the base rate of 0.6%, then starting at pull 74 the rate increases by roughly 6% per pull until it reaches 100% at pull 90. Community statistics show that about 80% of 5-star results land between pulls 74 and 80.

50/50 System Explained

The 50/50 system means that the first time you pull a 5-star, there is a 50% chance it's the current featured (rate-up) character and a 50% chance it's a standard/off-banner 5-star (commonly called "losing the 50/50"). If you don't get the featured character, your next 5-star is 100% guaranteed to be the featured one — commonly called the "big pity" or hard guarantee.

Formula Notes

• Simple mode: expected pulls = 1 ÷ drop rate.
• Advanced mode: expected pulls = (1 - (1-p)^G) ÷ p, where G = hard pity count.
• Professional mode: accounting for soft pity + 50/50, expected pulls ≈ 62.5 × 1.5 = 93.75 pulls.

Frequently Asked Questions

Why does my luck feel worse than the calculator?

Each pull is an independent random event — past results do not affect future ones. Even after many pulls without a hit, the odds on your next pull remain the same. This is a common misunderstanding known as the "gambler's fallacy." Short-term results can be far above or below the average; the calculator describes probability over many attempts, not a promise for your next pull.

Does soft pity matter?

Yes. According to community statistics, about 80% of Genshin Impact 5-stars appear between pulls 74 and 80, so soft pity has a significant effect — it lowers the expected pull count from roughly 167 pulls down to about 62.5 pulls.

Is the hard pity (guarantee) really 100%?

Yes. When your previous 5-star was not the featured character (you "lost" the 50/50), your next 5-star is 100% guaranteed to be the current featured character — this is the hard guarantee, also called "big pity."

How different are the odds across games?

The difference is significant. FGO has no pity system at all. Arknights has soft pity but no hard pity. Genshin Impact and Honkai: Star Rail both have a full system combining soft pity, hard pity, and the 50/50 mechanic.

Related Calculators

For other chance and planning tools, try the random wheel selector or the percentage calculator.

Disclaimer

This calculator is for reference only and does not constitute spending advice. Gacha pulls are random events — please spend responsibly and play in moderation. All probability figures should be verified against each game's official announcements.