keisoku

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.

types
%

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 collectedTypes remainingAverage pulls for the next type
0 / 10 types10 types1.0 pulls
1 / 10 types9 types1.1 pulls
2 / 10 types8 types1.3 pulls
3 / 10 types7 types1.4 pulls
4 / 10 types6 types1.7 pulls
5 / 10 types5 types2.0 pulls
6 / 10 types4 types2.5 pulls
7 / 10 types3 types3.3 pulls
8 / 10 types2 types5.0 pulls
9 / 10 types (final type)1 types10.0 pulls

Completion probability by number of pulls

PullsCompletion probabilityCost
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.