Mystery box and pack EV calculator

A box advertises the value of what is inside it. What matters is what a purchase returns on average, what that is worth once it has been sold back, and how often a purchase comes back worth less than it cost. Those are three different numbers.

The purchase
What one box, pack or case costs.
How many independent draws one purchase makes. Usually 1.
What it costs to turn an item into money
The share of an item's value the seller returns instead of shipping it. Leave blank if you would keep the item.
Charged per purchase, so it is spread across the items it contains.
The odds table

One row per outcome, copied from the seller’s published odds. A row needs its probability and a value someone outside the seller has recorded — an eBay sold price, an index quote — before it can contribute to a realisable figure. Leave a value blank rather than estimating it: a blank produces an honest refusal, an estimate produces a wrong number.

Result

Enter the price and at least one outcome. Everything runs in your browser and nothing is sent anywhere.

How this calculation works

A mystery box, a sealed collectible pack, and a digital case opening are the same object seen three ways: a fixed price, a distribution over outcomes, and a value attached to each outcome. This calculator turns a published odds table into what the purchase returns on average, and then into what that average is worth after the item has been turned back into money.

The gap between those two figures is usually large and is rarely mentioned. A seller that values an item at its catalogue price and buys it back at 70% of that value has taken 30% of the headline before delivery is considered — and the headline was already a price nobody pays. That is why the seller’s own valuation and an independently observed price are separate columns here and are never mixed.

The third figure is the one an average hides. A box can return more than its price on average while nine purchases in ten come back worth a fraction of it, because one rare outcome carries the whole mean. The chance a draw loses money, the average size of that loss, and the value of the median draw are reported beside the average for exactly that reason.

Where the published odds do not add up to certainty, or an outcome carries a probability but no price anyone outside the seller has recorded, no expected value is produced at all. That is not a limitation being worked around; averaging over part of a distribution gives a confident figure for a distribution nobody is buying.

What you need to enter

Inputs required by the randomised purchase economics calculation, with the unit each is measured in.
InputUnitWhat it means
PriceUSDWhat one box, pack or case costs.
Items per purchasecountHow many independent draws one purchase makes. Per-draw figures are compared against the price divided by this.
Sell-back ratepercentOptional. The share of an item’s value the seller returns instead of shipping it. Leave blank if you would keep the item; a blank is not treated as 100%.
Delivery costUSDOptional. Charged per purchase, so it is spread across the items that purchase contains.
Chance, per outcomepercentThe seller’s published probability for that outcome on one draw. A blank means undisclosed, which stops the calculation rather than counting as zero.
Seller’s value, per outcomeUSDOptional. What the seller says the item is worth. Reported so it can be compared with the observed price, never averaged in its place.
Observed price, per outcomeUSDA price recorded somewhere the seller does not control — a completed sale, an index quote. This is what the realisable figures rest on.

The formula

  • M = Σ pᵢ (disclosed probability mass; the model refuses unless M = 1)

  • EV_declared = d × Σ (pᵢ × vᵢ)

  • EV_market = d × Σ (pᵢ × mᵢ)

  • realisableᵢ = max(0, mᵢ × b − s ÷ d)

  • EV_liquid = d × Σ (pᵢ × realisableᵢ)

  • Implied margin = (P − EV_liquid) ÷ P

  • Cash-out friction = 1 − (EV_liquid ÷ EV_market)

  • P(down) = Σ pᵢ over outcomes where realisableᵢ < P ÷ d

  • E[shortfall] = Σ pᵢ × ((P ÷ d) − realisableᵢ) ÷ P(down), over those same outcomes

What each symbol means

Variable definitions for randomised purchase economics.
SymbolNameUnitDefinition
PPurchase priceUSDWhat one purchase costs, before any cost of delivery or sell-back.
dDraws per purchasecountHow many independent draws one purchase makes. Per-draw figures are compared against P ÷ d.
pᵢDisclosed probabilityfraction of 1The seller’s published chance of outcome i on one draw. An undisclosed probability is not zero, and the model stops rather than treating it as one.
vᵢDeclared valueUSDThe value the seller states for outcome i. It is the seller’s own figure and is reported as such.
mᵢIndependently observed valueUSDA price for outcome i observed somewhere the seller does not control, with its venue, basis and date recorded.
bSell-back ratefraction of 1The share of an item’s value the seller returns when it is sold back rather than shipped. 1 when the item is kept.
sCost of deliveryUSDWhat it costs to take physical delivery of one purchase. Spread across its draws, because it is charged per purchase.

Worked example

A $100 box whose average beats its price

  1. A box costs $100 and publishes three outcomes: a 1% chance of an item that has sold for $2,000, a 9% chance of one at $150, and a 90% chance of one at $40.
  2. The average: 0.01 × 2,000 + 0.09 × 150 + 0.90 × 40 = 20 + 13.50 + 36 = $69.50. The box keeps 30.5% in expectation.
  3. Now the shape behind that average. Nine purchases in ten return the $40 item, so the median purchase is worth $40 against a $100 price.
  4. The chance a purchase comes back worth less than it cost is 90%, and the average size of that shortfall is $60.
  5. If the seller buys items back at 70% rather than shipping them, the $40 outcome is worth $28 and the average falls to $48.65 — a 51.35% margin, and 30% of the observable value lost purely in getting it out.

Takeaway. The average is the least informative of the three figures. A box can carry a respectable mean and still return a fraction of its price on almost every purchase, and the sell-back rate quietly takes a third of whatever is left.

Assumptions

These conditions have to hold for the result to mean what it says. Where one does not apply to your situation, the figure will be wrong in a direction the calculator cannot know about.

  • The published odds are the odds. The model checks that they sum to 1 and refuses otherwise, but it cannot check that a published table describes the draw that actually runs.
  • Draws within one purchase are independent and identically distributed, which is what makes a per-draw figure meaningful. Where a seller guarantees one item of a given tier per purchase, that is not true and the per-draw figures do not apply.
  • An independently observed value is a price someone else recorded for the same item, not an appraisal. Its venue, its basis and the day it was observed are published beside it.
  • The sell-back rate and the cost of delivery are the ones the seller states. Where either is unstated it is left out and the figure it would have affected is not reported.

Limitations

What this calculation cannot tell you:

  • No expected value is produced from an incomplete odds table. Missing probability mass does not make a figure slightly uncertain; if the missing mass holds the largest outcome it decides the answer, so no figure is published at all.
  • No expected value is produced from declared values alone where independent prices are missing. A catalogue price set by the seller is not a market, and averaging it would restate the seller’s claim as a finding.
  • The downside figures describe one draw against the per-draw price. The chance that a whole multi-draw purchase loses money is a different question and is not answered here.
  • An observed resale price is a record of past transactions at one venue. It is not a price anyone is obliged to pay, and a thin market can move a long way between observations.
  • Nothing here models the time, effort, or minimum thresholds involved in selling an item, beyond the stated sell-back rate and cost of delivery.
  • This is an average over the whole distribution. A single purchase is one draw from it, and for a box with a heavy top prize most purchases finish well below the average.

Method and version

This page uses box-economics v1.0.0. Every figure it produces comes from that method at that version, and the worked examples are pinned to the same version — when a method changes in a way that moves a published number, the example is re-derived at the new version.

Revision history for box-economics.
VersionDateChange
1.0.02026-09-08First published version.

Full details of how these models were chosen are on the methodology page.

A note on playing

This tool prices a randomised purchase. It is not a recommendation to make one. Every figure here is an average across many purchases, and no arithmetic changes what a single purchase does — a box whose mean is close to its price still returns far less than its price most of the time.

An expected value is an average over an enormous number of repetitions. It is not a prediction, a target, or a result you are owed. See responsible play.