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.
Cumulative probability across many packs
The natural instinct when you see “1% drop rate” is to multiply: one percent times a hundred packs equals one hundred percent, job done. That calculation is what statisticians call the expected value(the long-run average), and it's genuinely useful. But it is not your chance of pulling the Blook at least once.It's a different question with a different answer.
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, and it's the engine behind the entire blooket calculator. The chance calculator runs it forward, and the threshold calculator runs it backward. For a deeper dive into the term itself, see the cumulative probability glossary entry.
The shape of the curve
Plot the cumulative chance against pack count and you get a curve that's steep at first, bends sharply around the 50% mark, and then asymptotes toward but never touches 100%. For a 1% drop rate, the first 20 packs take you from 0% to 18%. The next 20 take you from 18% to 33%. The next 20 from 33% to 45%. Each additional pack adds less chance than the one before.
This is called a geometric distribution, and it shows up anywhere you repeat an independent trial with a fixed success probability. Slot machines, radioactive decay, basketball free-throw streaks: same shape.
| Packs opened (p = 1%) | Cumulative chance |
|---|---|
| 10 | 9.6% |
| 50 | 39.5% |
| 69 | 50.0% |
| 100 | 63.4% |
| 200 | 86.6% |
| 230 | 90.0% |
| 459 | 99.0% |
| 1,000 | 99.996% |
Why you never hit 100%
The cumulative chance formula has an asymptote at 100%. No matter how many packs you open, the probability approaches but never quite reaches certainty, because there's always some nonzero chance the next pack (and the one after) comes back empty. This is not a bug, it's fundamental to how independent probabilities compose. The only way to get “guaranteed” would be a game mechanic that tracks misses and forces a pull after some threshold (a pity timer). Blooket does not have one.
In practice, the distinction between 99.9% and 100% doesn't matter. 99% is where most people budget because the remaining 1% of unlucky runs is small enough to absorb emotionally. Above that you're spending a lot of tokens to eliminate a tiny tail risk.
The 50 / 90 rule
For any Blook you're chasing, there are two pack counts worth knowing. The 50% thresholdis the number of packs at which you're as likely to have pulled it as not: a coin flip. The 90% threshold is the number of packs at which missing the pull would be a real stroke of bad luck. Almost every useful budgeting decision sits between those two numbers.
Below the 50% mark, you're playing optimistically. Between 50% and 90%, you're paying insurance. Above 90%, you're paying a lot of insurance for a diminishing return. The 99% threshold exists too, but for most Blooks it roughly doubles the 90% number.
Solve the cumulative formula for N at a given confidence:
N = ln(1 − target) / ln(1 − p)Target 0.5 gives the 50% threshold. Target 0.1 gives the 90% threshold. Target 0.01 gives the 99% threshold. The guaranteed Legendary guide works the 90% and 99% thresholds backward into a token budget you can actually save toward.
Reference table: common drop rates
Round numbers for the drop rates you actually encounter. Pair with any pack's token cost for the token budget. The threshold calculator runs the same numbers for any rate you plug in.
| Drop rate | 50% in… | 90% in… | 99% in… |
|---|---|---|---|
| 1.0% | 69 packs | 230 packs | 459 packs |
| 0.5% | 139 | 460 | 919 |
| 0.3% | 231 | 767 | 1,533 |
| 0.1% | 693 | 2,302 | 4,603 |
| 0.05% | 1,386 | 4,605 | 9,209 |
| 0.03% | 2,310 | 7,675 | 15,350 |
| 0.02% | 3,466 | 11,512 | 23,025 |
| 0.01% | 6,931 | 23,025 | 46,050 |
Pick the confidence level you can stomach. The 50% number is useful because it's small, but you will miss half your runs. The 90% number is what people actually mean when they say “I'll eventually pull this.” The 99% number is what you need when a birthday-gift set is on the line and “unlucky” is not an answer.
Multiply the pack count by the pack's token cost (20, 25, or whatever the pack is) to get the token budget. If you're planning to resell duplicates from the same run, you recover roughly 50–60% of the cost; see the resell strategy guide for what each rarity actually returns, and the blook value guide for the rarity-by-rarity ceiling on what a chase is worth if you do land it.
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 simulatorto see the streaks and dry spells that the expected-value number alone doesn't capture.
Common mistakes
The two confusions that trip most players up:
- “A 0.05% drop rate means 1 in 2,000 packs guaranteed.” No. 1/0.0005 = 2,000 is the expected value: the long-run average number of packs per pull over thousands of trials. On any single run of 2,000 packs, you have a 63% chance of having seen it at least once, which also means a 37% chance of opening 2,000 packs and seeing nothing. That's the entire point of the 50/90 rule.
- “I opened 500 packs and got nothing, so I'm due.” You're not. Every pack is independent. Past misses don't raise future probabilities. The curve shifts for the packs you have left to open, not the ones already behind you.
- Multiply-and-done.“1% × 100 packs = 100% chance” isn't how independent probabilities work. Use the exponential formula above, or the calculator.
- Budgeting to the expected value.The expected value lands around 63% confidence. If you want 90%, you need about 2.3× the expected value in packs. If you can't afford to be on the slow half, budget to the 90% threshold instead.