OSRS Coupon Collector Calculator
Collecting every unique from a boss takes more kills than one drop alone. Enter the set size and rate, and see the expected grind with real 50% and 90% milestones.
Popular full sets, rates verified against the OSRS Wiki.
How many distinct uniques complete the set.
Each item's own drop rate (Zulrah uniques are 1/512 each).
For a time estimate.
How to use the coupon collector calculator
- Pick a preset set (Zulrah's four uniques, Bandos armour, and more) or enter your own.
- Each item must have the same drop rate; the per-item rate goes in "1 in...".
- Read the expected kills, then the 50% and 90% milestones that describe real grinds.
How it works
This is the classic coupon collector problem. Once you hold i of the k uniques, each kill hands you a new one with probability (k − i)/N, so the expected kills for the whole set is:
E[kills] = N x (1 + 1/2 + 1/3 + ... + 1/k) = N x H(k) Worked example: Zulrah's four uniques (each 1/512) need on average 512 x (1 + 0.5 + 0.33 + 0.25) = 1,067 kills, well above the 512 you might guess. The last duplicate-free drop is always the most expensive. Percentile milestones (50%, 90%, 99%) are computed exactly by convolving the geometric wait of each stage, no simulation involved.
What this model assumes
All items share one equal rate (true for Zulrah, GWD armour pieces at 1/381 each, and Cerberus crystals; not true for Corporeal Beast's sigils at 1/4095 vs 1/1365). Each kill rolls each item independently, which matches OSRS flat unique tables. Bosses whose loot comes from points systems or pity mechanics don't fit this model; for those, see the methodology page on what we deliberately don't model.
Frequently asked questions
Why is the expected grind more than k x (average kills per drop)?
Because early uniques are cheap: any of four uniques counts when you have none. Duplicates get more likely as the set fills, and the final item alone waits an average of N kills. The harmonic sum captures exactly that.
What are the 50% and 90% milestones?
The kill counts by which half (or 90%) of players would have completed the set. They bracket the average honestly: the distribution is right-skewed, so the 90% milestone sits far past the mean.
Can I add a pet to the set?
No, pets roll separately and usually at a different rate. Check a pet with the pet chance calculator and treat it as its own grind.
My boss has unequal rates. What do I do?
Split it: run each item through the drop chance calculator for your target confidence, or approximate with the rarest item's rate to stay safe. An exact unequal-rates mode is on the roadmap.
Does this include dupe protection?
There is none in OSRS: a 1/512 unique can drop twice in a row. That reality is exactly why completing sets overruns the naive estimate.
Related calculators
OSRS Drop Chance Calculator Enter a drop rate and kill count to see your chance of the drop so far - and in your next kills. Popular boss rates are built in.
OSRS Dry Calculator How unlucky are you, really? Compare your dry streak against every other player grinding the same drop.
OSRS Barrows Chest Calculator Chest odds by brothers killed: any item, a specific piece, expected loot.
Built and maintained by the OSRSCalc founder · Drop rates verified against the official OSRS Wiki on 2026-09-30 · Page last updated 2026-09-30
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