The coupon-collector problem
If a pack has K distinct Blooks with 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-number term grows slowly but meaningfully. For a pack with 20 equally-rated Blooks, the expected pack count is roughly 20 × 3.6 = 72, not 20. That extra factor is dupes; every duplicate you open delays completion until you eventually roll one of the Blooks you don't yet have.
Within-rarity math
Blooket packs aren't equal-rate: rarities have different drop rates, and within a rarity the Blooks are equally likely. So the completion problem splits into separate coupon-collector problems, one per rarity. The rare tiers dominate the budget.
For a market pack, Common and Uncommon sets complete fast, often by pack 40. Rares take longer. Epics are where the budget stretches. Legendaries typically take most of the budget to collect because each individual Legendary has a tiny drop rate, and you need one of each.
Why the last few are brutal
The final Blook in any rarity tier is the most expensive single acquisition in the set. If Common has 20 Blooks at equal rate within the tier, the expected packs for just the last Common is 20 packs (inside the Common fraction of the drop). For the last Legendary in a 3-Legendary pack, it's 3 / (Legendary rate), which at 0.3% rate is 1,000 extra packs at the end of the grind.
The practical consequence: set completion follows a hockey-stick cost curve. You get 80% of the way there in roughly 30% of the budget, and the last 20% costs the remaining 70%. Decide early whether you're going for 100% or "close enough."
Resell changes the picture
The good news is that a set-completion run produces enormous numbers of duplicates. At the volume required to collect every Legendary, you'll be sitting on hundreds of Common/Uncommon/Rare duplicates that can be sold back for tokens. That recovery materially shortens the real-money cost of the run, often by 40–50%.
See the resell strategy guide for per-rarity recovery values, and the ROI calculator to see net cost in real time.