The coupon-collector problem
If a pack has K distinct Blooks at equal drop rates, the expected number of packs to collect all K is:
E[N] = K × (1 + 1/2 + 1/3 + … + 1/K)
The harmonic-sum term grows slowly but meaningfully. For a pack with 20 equal-rate Blooks, expected pack count is roughly 20 × 3.6 = 72, not 20. That extra factor is duplicates: every duplicate you open delays completion because you need to roll one of the specific Blooks you do not yet own.
For the per-rarity expected drops on any specific pack, run that pack's number through the pack odds calculator, the expected-value framing it returns is exactly what feeds into each coupon-collector sub-problem. Or run the same balance through the broader blooket calculator to compare set completion against a single-Blook chase on the same token budget.
Within-rarity math
Blooket packs are not equal-rate across all Blooks, rarities have very different drop rates, and within each rarity the Blooks are equally likely. The completion problem splits into separate coupon-collector problems, one per rarity, and then adds up.
The cheap tiers complete fast. Common and Uncommon rows are typically full by pack 40–60 because their per-Blook probability is high. Rares take longer. Epics are where the budget stretches, each Epic slot has only a 7% or lower drop rate, split between several Blooks. Legendaries dominate total budget because each one individually has a sub-1% drop rate, and you need one of every Legendary in the pack.
Why the last few are brutal
The final Blook in any rarity tier is the most expensive single acquisition in the set. If a rarity has 3 Blooks at equal rate, the expected number of packs to roll the last one is 3 / (rarity rate). For a pack with 2 Legendaries at 0.35% combined (0.175% each), the last Legendary costs on average 571 packs by itself, after you already own the first.
The practical result is a hockey-stick cost curve. You get 80% of the way to a complete set in roughly 30% of the total budget. The final 20% of the Blooks eats the remaining 70%. Decide early whether the goal is 100% or "deep enough."
Real numbers: Safari vs Medieval
Two representative market packs at 20 each:
| Pack | Hardest pull | Rate | 50% packs | Token cost (50%) |
|---|---|---|---|---|
| Safari | Rainbow Panda (Chroma) | 0.02% | ~3,465 | ~69,300 |
| Medieval | King (Legendary) | 1.00% | ~69 | ~1,380 |
Safari's Rainbow Panda is the long tail that makes a "complete Safari set" a multi-month project. Medieval's King at 1.0% is the most affordable set-completion grind in the market packs. If 100% collection is the goal, pick the pack with no sub-0.1% Blooks first.
Resell changes the picture
A set-completion run generates enormous numbers of duplicates. At the volume needed to collect every Legendary and Chroma, you will produce hundreds of Common, Uncommon, and Rare duplicates. Selling those back recovers 40–50% of the per-pack cost, which materially compresses the real token spend. See the resell strategy guide for per-rarity recovery values, and the ROI calculator for the net cost in real time with resell toggled on.
Practical rule: sell every duplicate beyond your first copy during the run. Only hold back if a specific Blook has Blook Score value you want to preserve, Legendaries are the main case where selling the spare costs you score points. Commons and Uncommons: sell immediately and reinvest.
100% or close enough?
Most players are not actually chasing a 100% complete set, they are chasing the rarest Blook in the pack. If your goal is the Legendary or the Chroma, you will have a near-complete set as a side-effect of the chase before you pull it. The question is whether you keep going after the pull for the last few Rares and Commons.
The right answer depends on Blook Score goals. Each Common adds 0 score and each Uncommon adds 5. If you are pushing toward a badge threshold, those additions matter. If you are purely chasing the rare Blook and have already unlocked it, stopping and reallocating to the next chase is usually the better ROI decision.