Why there's no real guarantee
Some gacha-style games include a "pity timer": a mechanic where after a certain number of failed pulls, the next one is guaranteed to hit. Blooket doesn't have one. Every pack is an independent dice roll, and no amount of bad luck influences future rolls.
That means the probability of pulling a Legendary approaches 100% as you open more packs, but never reaches it. The best practical target is 99%: enough confidence that a miss is genuinely unlucky rather than "likely enough to be annoying."
99% pack count by Legendary drop rate
Plugging each typical Legendary rate into the formula N = ln(0.01) / ln(1 − p):
| Legendary rate | Pack | Packs for 99% chance | Token cost |
|---|---|---|---|
| 1.00% | Medieval | 458 | 9,160 |
| 0.70% | Aquatic | 656 | 16,400 (25/pack) |
| 0.50% | Safari | 919 | 18,380 |
| 0.45% | Space | 1,022 | 20,440 |
| 0.30% | Wonderland | 1,533 | 30,660 |
| 0.03% | Bot (Mega Bot rate) | 15,350 | 307,000 |
For comparison, the 50% chance is always about one-seventh of the 99% count, and the 90% chance is about half. So if a 99% run is out of reach, a 90% run is typically half the budget, and a 50% run is reachable for most players within a month or two of grinding.
Reality check on budgets
For a standard 0.3% Legendary (Wonderland's King of Hearts), the 99% budget is roughly 30k tokens. At the daily 500-token cap, that's 60 days of grinding, two months, before you should expect to clear 99%. For a rare 0.03% Legendary (Mega Bot), the 99% budget is over 300k tokens, which is closer to 20 months of cap-grinding. Set the budget to the expectation, not the other way round.
If the 99% budget is too long, three options:
Cheaper alternatives
- Aim for 50% instead of 99%. Much cheaper, still useful. A coin-flip chance of the Legendary after every run is the default most players actually play with. See the 50/90 rule guide.
- Target the highest-rate Legendary in the cheapest pack. Medieval (1.0% King) at 20 tokens is the best market-pack rate by a wide margin, about half the budget of a 0.5% pack and a fifth of Wonderland's 0.3%.
- Toggle resell on in the calculator. Selling duplicates recovers about half the pack cost. That effectively doubles your pack budget for the same net spend; see the resell guide.
50%, 90%, and 99% pack counts side by side
To make the different confidence levels concrete, here's the Medieval pack (1.0% Legendary rate, 20 per pack) at all three thresholds:
| Confidence | Packs needed | Token cost | Days at 500-token cap |
|---|---|---|---|
| 50% | 69 | 1,380 | ~3 |
| 90% | 229 | 4,580 | ~9 |
| 99% | 458 | 9,160 | ~18 |
The 50% threshold is reachable in under a week of cap-grinding for most players. The jump from 90% to 99% doubles the pack count for only 9 percentage points of additional confidence. For most practical purposes, 90% is the sweet spot, statistically confident without being punishing.
For the full 16-Blook list of obtainable Legendaries with rate, source pack and trade range, see every Legendary in the game. For chase math on any specific target, the blooket calculator takes your token balance and returns the 50/90/99% pack counts in one shot.