What a drop rate is
A drop rate is a probability. When a pack lists its Legendary rate as 0.5%, it means that on any single opening of that pack, the slot that could be a Legendary resolves to "yes, Legendary" with probability 0.005: five thousandths. The flipside of that same slot is a 0.995 probability of "no, not Legendary." Every time you open a pack, the dice are re-rolled. Clean slate.
The rate is not a counter. The game is not quietly tracking "you've opened 199 non-Legendaries, so pack number 200 is guaranteed." Slot machines don't do that, gacha games don't do that, and Blooket packs don't do that either. A drop rate is an input to a probability calculation, not an output of a schedule.
Why packs are independent
Two events are independent when the outcome of one does not affect the probability of another. Pack openings are independent because each one pulls from the same distribution every time, with no memory of prior pulls.
This has a counter-intuitive consequence. If you open 500 Safari packs and pull zero Chromas, your chance of pulling a Chroma on pack 501 is exactly the same as it was on pack 1. The probability doesn't rubber-band in your favour because you've "earned" it. That's the difference between probability and fate.
The single-pack math
For a single pack, the math is trivial. If the rarity has drop rate p, the chance of getting one in one opening is p. The chance of not getting one in one opening is 1 − p.
P(one in one pack) = pFor a 0.02% Chroma, that's 0.0002: two ten-thousandths. The complement, 0.9998, is the probability you opened a pack and didn't see it.
What happens over many packs
Independent probabilities multiply. The chance that N consecutive packs all come back without the target is (1 − p)^N. Which means the chance that at least one of them hits is the flip side of that.
P(at least one in N packs) = 1 − (1 − p)NThis is the single most useful equation on the site. Every "what's my chance after 100 packs" answer comes from plugging numbers into this formula. The chance calculator runs it forward, and the threshold calculator runs it backward.
Combining rarities
When a pack lists both a Legendary rate and a Chroma rate, those are typically separate rolls on separate slots, not a single combined lottery. The practical consequence: your chance of pulling either from a single pack is close to the sum of the two, not the product.
Mathematically, for two independent rare events with probabilities p₁ and p₂:
P(either) = 1 − (1 − p₁)(1 − p₂)Since both probabilities are small, the cross-term is negligible, and P(either) ≈ p₁ + p₂. A pack with a 0.5% Legendary and a 0.05% Chroma gives you about a 0.55% chance of a top-tier pull per opening. Over 100 packs, that's roughly 1 − (1 − 0.0055)^100 ≈ 42.3% chance of at least one Legendary-or-better.
Why variance feels unfair
Probability tells you the long-run average. It does not tell you what any single run will feel like. Two players opening the same 500 packs from the same pack will have wildly different results, and that's not a bug, it's the point. When drop rates are small, the distribution is skewed: most people finish around the median, but a meaningful tail opens a huge number of packs without a pull. That's the reason the 50/90 rule is useful at all.
If you want the feeling of the variance without spending real tokens, open some virtual runs in the pack simulator to see the streaks and dry spells that the expected-value number alone doesn't capture.