Real probability · no vibes
The Odds Calculator
Take the ratio printed on the box, pick how many boxes you're willing to buy, and see the honest numbers: chance of a secret, expected boxes for a full set, and how many duplicates you should brace for.
Published box ratios — printed per series and wave on official packaging. Always verify on the current packaging before you buy.
P(≥1 secret in 12)
8.0%
1 − (1 − 1/144)^12
Expected secrets
0.08
12 × 1/144 — the long-run average
How the math works
Secret pulls. Each box is an independent draw. If the published secret ratio is p (say 1/144), the chance of seeing no secret in N boxes is (1 − p)N, so the chance of at least one is 1 − (1 − p)N. The expected number of secrets is simply N·p. Intuition check: at 1/144, a full case of 12 gives about 8% — most cases contain no secret at all, which is exactly what the ratio says.
Full sets. Collecting all k regulars from blind singles is the classic coupon-collector problem: the expected box count is about k·H(k), where H is the harmonic number. Six figures ≈ 15 boxes; twelve figures ≈ 37. The first few figures come fast, the last one is brutal — that asymmetry is the whole economics of blind boxes.
Duplicates. After N singles of a k-figure set you can expect k(1 − (1 − 1/k)N) distinct figures; everything beyond that is dupes. This is why seasoned collectors buy a sealed case for the set (most 12-figure formats pack one of each regular per case) and chase only the secret blind.
A responsible-collecting note
Blind boxes are gambling-adjacent by design — that's the published ratio doing its job. Decide a budget before you pull, treat the odds above as the price of entry, and when you want one specific figure, buy it as a single on the secondary market instead of pulling for it. The math says that's almost always cheaper.
FAQ
- How do you calculate the chance of pulling a secret?
- If the published ratio is 1/144, each box is an independent 1-in-144 chance. The probability of at least one secret in N boxes is 1 − (1 − 1/144)^N. Twelve boxes at 1/144 gives roughly an 8% chance — buying a full case does not guarantee a secret.
- How many boxes does a full set really take?
- For a series of k equally likely figures bought as blind singles, the expected number of boxes to collect all k is about k times the k-th harmonic number (the coupon-collector problem). A 12-figure set averages about 37 boxes — roughly three times the set size. Sealed cases often pack one of each regular, which is why set-chasers buy cases.
- Where do the ratios come from?
- Makers print pull ratios on official packaging, per series and per wave. We catalog the commonly published ratio class for each series, but ratios change between waves — the number printed on the box in your hand is the only one that applies. This calculator works with whatever ratio you give it.
- Does buying more boxes improve my odds per box?
- No. Each blind box is independent; the per-box probability never changes. More boxes raise the chance of at least one secret overall, but with diminishing returns — and the expected cost rises linearly. Set a budget first; that is the responsible way to play published odds.
Want it pre-computed for every series we track?
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