Card Pack Expected-Value Calculator
What a pack of trading cards is worth, net of resale fees, against what it costs to open it.
This prices one product's own published or entered pull rates and representative values. It does not know a specific product's real collation beyond what is entered or, for the two Magic presets, beyond what that set's own publisher article states. It does not track live secondary-market prices, and does not recommend buying or opening anything.
66%
of packs return less than the price paid
66 of every 100 packs return less than the price paid. The other 34 of 100 return at least the price paid.
Typical run:
$1.75
is the typical pack's value
Average run:
$7.10
86% of runs ended below the average
- 10th
- $1.00
- 25th
- $1.75
- median
- $1.75
- 75th
- $5.75
- 90th
- $10.50
Net of a 13.25% marketplace fee and $0.40 per sale, this pack is worth $5.76 (1.15x of the price paid), not $7.10. Most individual packs do not land on either average; see the spread above.
Computed exactly across every combination this 4-slot pack can draw, not simulated.
Against the price, by the pack, box and case
Price paid$5.00
Gross expected value$7.10
Net of fees$5.76
- EV per box
- $170.40
- EV per case
- $2,044.80
- Gross return ratio
- 1.42x
- Net return ratio
- 1.15x
- 99th percentile pack value
- $55.50
- Share returning under half the price
- 51.4%
- Share returning over 5x the price
- 7.8%
Chase a specific card? (optional)
Chance of at least one, by packs opened90% at 460 packsOne 24-pack box
- Odds per pack
- 1 in 200
- Chance of at least one in a 24-pack box
- 11.3%
- Average packs to pull it
- 200
- Packs for 90% confidence
- 460
- Cost to chase at that confidence
- $2,300.00
- Market value of the single
- $150.00
Chasing it costs $2,150.00 more than buying the single outright, at this confidence.
Real set presets (published pull rates, not a live quote)
Each loads a real Magic: The Gathering set’s own published, per-slot pull rates (not simplified into one averaged rate). You still enter every value: pull rates are fixed the day a set prints, but secondary-market prices move daily. See “Why does Magic have presets and nothing else?” below for why only one publisher in this category gets this treatment.
Worked examples (illustration, not a live quote)
Each loads a real product’s published pull rates, simplified into the rarity table above. Pull rates are stable once a product is printed; card values move daily, so treat the dollar figures as dated rather than current.
Which publishers actually tell you the odds?
Magic: The Gathering is the one family in this category whose publisher states real, per-slot pull rates for every set, in an official “Collecting <Set>” feature. The product with the largest search demand in the category, Pokémon TCG, publishes none at all: every pull-rate figure circulating for it is community-sampled, and no pack-EV page anywhere states which of the two a given number is.
| Publisher / family | Publishes per-rarity rates? | What that means for a figure you find |
|---|---|---|
| Magic: The Gathering | Yes | Treat a pull-rate figure as traceable to a named article, like the presets above. |
| Pokémon TCG | No | Every circulating figure is community-sampled with an unstated methodology. |
| Yu-Gi-Oh! | No | Same as Pokémon: nothing official to check a figure against. |
| One Piece Card Game | No | Same as Pokémon: nothing official to check a figure against. |
| Disney Lorcana | Pack composition only | Slot counts are published; probabilities within a slot are not. |
| Sports cards (Topps, Panini) | Unverified | Both candidate official sources returned an access error; not treated as absent and not worked around. |
Checked against each family’s own publisher site and, for the two unverified rows, the two candidate official odds pages directly (both declined access rather than confirming or denying a posting). This is one publisher’s editorial practice, not a category norm, and finding a second publisher that does this would be worth noting here rather than assumed.
This prices a pack from the odds and values you enter. It is not a recommendation to open packs: on almost every real product, the honest finding is that the expected return sits below the price, which is how a sealed product is priced.
Written and reviewed by Alexander Korsager · last reviewed October 4, 2026 · corrections
The idea
What this tool shows
A pack's price is fixed and printed on the wrapper. What it is worth is not, and every pack-EV page in the category quotes one number for it: a gross average built by multiplying each rarity's odds by a market value and adding it up. That number is real, and it is also not what a reader who actually opens the pack and sells what they pull keeps, because selling costs a marketplace fee and the result on any one pack is not the average, it is one draw from a spread that the average alone hides.
This calculator starts from the same published pull rates every competitor's page uses, and adds the two things a reader actually needs to weigh opening against buying singles directly: the figure net of a resale marketplace's own fee, shown beside the gross one rather than instead of it, and the actual distribution behind the average, not just its mean. It also prices the specific decision a chase-card hunter is making: how many packs it takes to reach a named card at a chosen confidence, and what that costs against simply buying the single.
Enter a product's pack price, how many cards come in a pack, and the pull rate and representative resale value for each rarity tier, and the result below this form prices the pack rather than repeating its own printed price back at you.
FAQ
Questions players ask
Why does the net figure matter more than the gross one?
Because the gross figure assumes every pulled card converts to cash at its full listed value, and no resale marketplace works that way. eBay's own published final value fee for its Trading Cards and Collectible Card Games category is 13.25% of the sale up to $7,500 (ebay.com, Selling fees, retrieved 2026-10-03), plus a flat $0.30 to $0.40 per order. A pack priced close to break even on the gross figure is usually underwater once that comes off, and the panel shows both side by side so the gap is visible rather than assumed.
Why model a pack as independent card slots instead of the product's exact collation?
Because collation varies by product and most published odds sheets do not disclose their full slot structure, only the overall per-pack or per-box rate for each named tier. Modeling a pack as several independent draws from one rarity table is the simplest structure that reproduces a product's own stated per-pack hit rate: set the cards-per-pack count to however many of a pack's slots can carry a meaningful pull, and the tier probabilities to the product's own published per-pack or per-box odds. A product that instead guarantees exactly one hit per box, rather than giving each pack an independent shot at one, is the one real structure this approximates rather than reproduces exactly: see the methodology section for how that case is handled.
Is pack opening gambling?
Opening a sealed pack for the value of what is inside, rather than to play or collect the cards themselves, is a gambling-shaped transaction: a fixed stake, an uncertain return, and a house-favorable average built into the product's own pricing. This page treats it as exactly that. It is not a recommendation to open packs, and the honest finding on almost every product's own published odds is that the expected return sits below the price, which is how a sealed product is priced to begin with.
Where do the two worked examples come from?
Both are built from a real product's published pull rates, simplified into the handful of rarity tiers this calculator's slot model uses, and are labeled with their source and retrieval date wherever they appear. They are illustrations of the method, not a live quote on either product: pull rates are stable once a product is printed, but secondary-market card values move daily, so treat the dollar figures as dated rather than current.
Why does Magic have presets and nothing else?
Because Magic: The Gathering (Wizards of the Coast) is the one publisher in the trading-card category that states real, per-slot pull rates for every set it prints, in an official “Collecting <Set>” feature (magic.wizards.com, retrieved 2026-10-04). Pokémon TCG, Yu-Gi-Oh!, One Piece Card Game and Disney Lorcana publish no equivalent probability breakdown; every pull-rate figure circulating for those games is community-sampled with an unstated methodology, not a number this tool can transcribe and cite the way it does for Magic. Topps's and Panini's own candidate odds pages both returned an access error when checked, so their status is recorded as unverified rather than absent, and not worked around. This is one publisher's editorial choice, not a rule of the category: a second publisher starting the same practice would earn its own preset.
Why does a Magic preset carry a per-slot structure instead of one rarity table?
Because a real Play Booster is not interchangeable slots drawing from one distribution: a wildcard slot, a guaranteed rare-or-mythic slot, a traditional-foil slot and a land slot each carry their own published odds, and collapsing them into a single averaged rarity table would keep the correct average pack value while silently distorting the spread around it (a right-skewed structure's tail is exactly what this tool exists to show). Each preset's own slot-by-slot table on the page states which published line each number came from, with the normalization applied where the publisher's own figures carry a “less than 1%” line that does not resolve to an exact percentage.
Methodology
How this is calculated
A pack is modeled as a fixed number of card slots. In the default, custom-entry mode every slot draws identically from one reader-entered rarity table (a probability and a representative resale value per tier).
The Magic: The Gathering presets instead supply a real per-slot structure, transcribed from the set's own publisher article: a wildcard slot, a guaranteed rare-or-mythic slot, a foil slot and a land slot each carry their own published odds rather than one averaged rate, because a product's actual slots are not interchangeable and flattening them into an average would preserve the mean while silently distorting the spread.
Expected value is the sum, over every slot, of that slot's own expectation (probability times value), which scales linearly to a box and a case regardless of which mode produced the structure.
The full distribution of a pack's total value, needed for every figure beyond the mean, is computed exactly by convolving each slot's own distribution into a running total one slot at a time, which is mathematically identical to enumerating every combination of slot outcomes and summing each one's probability and value, down to the rounding of floating-point arithmetic.
Below a stated size, that exact computation runs directly; past it, a seeded Monte Carlo simulation of 20,000 packs stands in, and the page states on every figure which method produced it.
The net-of-fee figure applies a reader-set marketplace fee rate and a flat per-sale cost to the gross expected value; the chase-card figures (odds as "1 in N", the chance of at least one in a box, and packs needed to reach a chosen confidence) come from treating the named card's own per-pack probability as an independent event across packs, which is the geometric distribution's own standard result.
Common misreadings2
- A positive net return ratio on the inputs entered is not a guarantee of profit on any one pack: the whole point of showing the distribution is that most individual packs land below the mean on a right-skewed structure, and a reader has to look at the spread, not only the headline ratio.
- The chase-card confidence figure states how many packs reach a stated likelihood of success, not a guarantee. At 90% confidence, one draw in ten still comes up short even after that many packs.
Assumptions6
- In custom-entry mode, every slot in a pack is drawn independently from the same rarity table. A real product's exact collation (which physical slot can hold which rarity) is rarely published in full; this reproduces a product's own stated per-pack hit rate for each tier rather than its internal mechanics. The two Magic presets do not carry this assumption: their slots are genuinely different from each other, per the set's own published structure.
- A product that guarantees exactly one hit per box, rather than giving each pack an independent shot at one, is approximated in custom-entry mode by spreading that same probability evenly across the box's packs (one in twenty for a twenty-pack box, for instance). That is a genuine approximation, not the guarantee itself: a true per-box guarantee means every box has exactly one hit, where this tool's independent-slots model allows a box to draw zero or several.
- Representative values are a single dollar figure per rarity tier, entered by the reader, in both modes. Two cards of the same tier rarely sell for the same price in practice; the figure stands in for the tier's typical resale value, not any one card's price. The Magic presets never supply a value themselves, only rarity structure and pull rates: pull rates are fixed the day a set prints, but secondary-market values move daily, so baking a value into a preset would make it stale by construction.
- The two Magic presets bucket frame and art variants (borderless treatments, artist-signature cards, foil finish) into their base rarity rather than pricing them as separate tiers, since those change a card's look, not its published probability of appearing. A handful of the publisher's own lines read "less than 1%"; each is entered as 0.9% and every slot is normalized against its own raw published sum (stated per slot on the page) rather than trusted as already exact.
- The marketplace fee is applied to the full gross value as a flat rate. Real fee schedules can tier by sale amount (eBay's own published rate steps down above $7,500 per item) and the flat per-sale cost here approximates a per-order charge that in practice is shared across however many cards one order contains.
- The chase-card figures treat pulling the named card in one pack as independent of every other pack opened, which is the ordinary assumption for a sealed, shuffled product and is not true of a product disclosed to use fixed, known slotting.
Limits4
- Nothing here prices the time cost of grading, listing, photographing, or shipping each card individually, beyond the flat per-sale figure entered. A reader who sells in bulk at a lower average price, rather than per card at the representative value, will realize less than the net figure shown.
- The exact-enumeration path and the Monte Carlo fallback agree in expectation but the Monte Carlo path carries sampling noise at a fixed trial count; the page states which method produced a given run's figures rather than implying both are equally precise.
- A representative value per rarity tier is not a per-card value, and the spread the distribution shows is the spread across that simplified structure, not across every individual card a real tier actually contains.
- The two Magic presets model 13 of a 14-card Play Booster; the double-sided token/art card carries no resale value and is left out. No other trading-card family in the category currently has a preset, because no other publisher checked states real per-rarity pull rates (see the page's own source-class table).
Evidence
packEV, enumeratePackValues, monteCarloPackValues and the chase-card functions in math.ts implement the identities stated in the summary above, over whichever structure (uniform or per-slot) computePackResult is given; math.test.ts checks packEV and enumeratePackValues against a hand-worked two-slot, two-rarity structure, checks that the exact and Monte Carlo paths agree within sampling tolerance on a structure small enough for both, checks the geometric packsForConfidence figure against the closed form it inverts, and checks atLeastOneInBox against 1-(1-p)^B directly. presets.test.ts checks that every preset slot's published shares sum to 1 within the stated normalization tolerance, that the two presets are genuinely heterogeneous (not every slot identical), and that a preset's real per-slot distribution differs from the distribution of its own flattened average, even though both agree on the mean.
The default marketplace fee rate (13.25%) and per-sale cost are eBay's own published Trading Cards and Collectible Card Games final value fee and per-order fee (ebay.com, Selling fees, retrieved 2026-10-03).
The two worked examples are built from a real product's own published pull rates (see each example's own citation), simplified into this tool's rarity-tier structure.
The two Magic presets are transcribed from Wizards of the Coast's own "Collecting <Set>" articles (magic.wizards.com, retrieved 2026-10-04; verbatim quotes and per-slot figures in presets.ts).
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