Complete Collection Probability

Complete Collection Calculator for Capsule Toys

This tool calculates the average number of pulls needed to collect every item from a capsule toy machine (gashapon), blind box, or random prize draw where all items appear with equal probability. It's based on the classic Coupon Collector's Problem from probability theory.

This is different from social game gacha. Mobile game gacha systems have varying drop rates by rarity, but this tool is specifically for cases where every item has the same chance (1/n) of appearing. Think convenience store prize draws, capsule machines, candy toy collections, or random trading card packs. For social game drop rate calculations, use our [Gacha Probability Calculator](/en/calc/gacha-probability/).

Why Is the Last Item So Hard to Get?

For n equally likely items, the expected number of pulls is E = n × H(n), where H(n) is the harmonic series (1 + 1/2 + 1/3 + ... + 1/n). For 10 items that's about 29.3 pulls, for 20 items about 71.9, and for 50 items about 224.9.

You might expect 10 items to take 10 pulls, but it actually takes roughly 3 times that. The difficulty spikes dramatically for the last few items — when you have 9 out of 10, there's only a 10% chance each pull gives you the missing one, so you need an average of 10 more pulls just for that last item.

Key Features

- Instant expected pulls & cost — just enter the number of types and cost per pull - "What are my odds in N pulls?" — exact completion probability using inclusion-exclusion - "How many pulls for 90% confidence?" — reverse calculator with preset targets - Completion probability curve — visual graph of how odds improve with more pulls - Stage-by-stage table — see exactly which items are hardest to get, with cost column