Interpret gacha odds and expected pulls

Single-pull odds differ from the chance of obtaining a reward over several pulls. Select the pool, level and target, and distinguish a specific Cookie from an entire rarity. A rarity probability is not the probability of one particular Cookie.

This mathematical example assumes independent pulls at a constant 0.1% with no pity. It is not a current banner rate or an actual pull record.

Chance of at least one success within n pulls = 1 − (1 − p)ⁿ. Use a decimal for p: 0.1% = 0.001.

Average waiting time: 1000

Pulls needed for at least 90% chance: 2302

An average of 1,000 pulls does not guarantee success within 1,000. Previous failures do not raise the odds of the next independent pull.

Read pity and expected cost carefully

If the same target is guaranteed by pull m and earlier pulls have constant chance p, expected pulls are [1 − (1 − p)ᵐ] ÷ p. For p=0.001 and m=100 remaining: 95.21

The current tool estimates a guarantee interval from cumulative rewards with the target item ID. Other rewards, selectors, changing odds or irregular milestones may not satisfy this assumption. Check the in-game target reward rules first.

Expected currency is expected pulls × cost per pull, rounded up. It is an average, not a minimum budget or a purchase recommendation. Random pull previews and pity calculations are separate; previews are not records of actual cumulative reward claims.