What the rule is
For any Blook you're chasing, there are two pack counts worth knowing. The 50% threshold is 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, and you can compute it, but for most Blooks it roughly doubles the 90% number.
The math, plain English
Every pack is an independent trial. The chance you miss a rare Blook on any single pack is (1 − p), where p is the drop rate as a decimal (0.0005 for 0.05%). The chance you miss it every pack in a row over N openings is (1 − p)^N. Subtract from 1 to get the chance you hit it at least once.
P(at least one) = 1 − (1 − p)NSolve 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.
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.
| 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 |
Using it to budget
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.
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.