Pulls Needed to Complete a Gacha
Just enter the number of prize types to estimate the average pulls needed to complete a full gacha set. Add the cost per pull for an expected-cost estimate, or a target probability for the pulls required (assuming equal odds).
Input
Assuming every prize drops with equal probability, this tool estimates the average number of pulls needed to collect the full set. Real gacha (loot box) odds are often weighted, so treat the result as a rough guide.
Result
Expected pulls to complete all 10 types
29pulls
(exactly 29.3 pulls = 10 × H(10))
Expected cost
approx. 8,787
Expected pulls for the final type
10 pulls
Completion rate at the expected number of pulls
approx. 59.5 %
To reach a completion probability of 90% or higher , you should expect to pull about 44 pulls .
Average pulls to land each new type as you progress
| Types collected | Types remaining | Average pulls for the next type |
|---|---|---|
| 0 / 10 types | 10 types | 1.0 pulls |
| 1 / 10 types | 9 types | 1.1 pulls |
| 2 / 10 types | 8 types | 1.3 pulls |
| 3 / 10 types | 7 types | 1.4 pulls |
| 4 / 10 types | 6 types | 1.7 pulls |
| 5 / 10 types | 5 types | 2.0 pulls |
| 6 / 10 types | 4 types | 2.5 pulls |
| 7 / 10 types | 3 types | 3.3 pulls |
| 8 / 10 types | 2 types | 5.0 pulls |
| 9 / 10 types (final type) | 1 types | 10.0 pulls |
Completion probability by number of pulls
| Pulls | Completion probability | Cost |
|---|---|---|
| 10 pulls | 0.0 % | 3,000 |
| 15 pulls | 4.6 % | 4,500 |
| 22 pulls | 30.3 % | 6,600 |
| 29 pulls | 59.5 % | 8,700 |
| 37 pulls | 80.9 % | 11,100 |
| 44 pulls | 90.5 % | 13,200 |
| 59 pulls | 98.0 % | 17,700 |
How it works
- Enter the number of prize types and the tool computes the expected number of pulls to complete the full set. It assumes every prize drops with equal probability (1/n).
- The calculation uses the formula from the coupon collector's problem. With n types, the expected pulls = n × (1 + 1/2 + 1/3 + … + 1/n) = n × H(n), where H(n) is the harmonic number.
- Enter the cost per pull and the tool also shows the expected cost to complete, found by multiplying the expected pulls by the cost. The cost field is optional; leave it blank to see pull counts only.
- The fewer prizes you still need, the harder a new type becomes to land. When only one type remains, the average pulls to obtain it is n, making the end of completion the most time- and money-consuming stage.
- Enter a target completion probability (e.g. 90%) and the tool shows the approximate pulls needed to complete the set with at least that probability, derived from the completion probability via the inclusion-exclusion principle.
- Real gacha can have different drop rates per prize, and pity systems or featured items change the outcome. These figures assume equal odds and are only a rough guide.
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Pulls Needed to Complete a Gacha