P(at least one in N) = 1 − (1 − p)ⁿDefinition
Cumulative probability is the chance of an event happening at least once across N independent trials. In Blooket: the chance of pulling your target Blook in any of N packs you open.
It is not the same as multiplying the drop rate by the number of packs. A 1% drop rate × 100 packs is not a 100% chance — it's about 63.4%. Multiplication gives the expected count, not the probability of at least one hit.
The formula
Where p is the per-pack drop rate (as a decimal — 1% = 0.01) and N is the number of packs:
Compute the chance of missing every pack — that's (1 − p)^N. Then subtract from 1 to get the chance of at least one hit.
Worked examples (1% Legendary)
Plug p = 0.01 and a few values of N into the formula:
- 10 packs → 1 − 0.99¹⁰ = 9.6%.
- 50 packs → 39.5%.
- 69 packs → 50.0% (the 50% threshold for a 1% drop).
- 100 packs → 63.4% (the famous "1 − 1/e" constant).
- 230 packs → 90.0% (the 90% threshold).
- 459 packs → 99.0% (the 99% threshold).
Why you never hit 100%
The curve 1 − (1 − p)^N asymptotes toward 100% but never reaches it. Each additional pack subtracts a smaller and smaller slice of the remaining probability mass. There is no pity timer in Blooket — every pack opening is genuinely independent — so you can't guarantee a pull no matter how many packs you open.
In practice, the 99% threshold is where most token-budget calculations stop. The remaining 1% of unlucky runs is small enough to absorb, and chasing 99.9% costs roughly double the tokens for negligible additional confidence.