What this site prints when the odds add to 0.97

Inputs

Odds table

Working

1. These figures are assumed, not a recorded product. The published chances are 7% and 90%, which add to 97%. Three percent of the distribution is missing.
2. An average over the named prizes would look confident — something between $40 and $150 — and it would be an exact answer to a question about a different product.
3. The missing 3% is where the largest outcome usually sits. If that 3% is a single item worth $5,000, its contribution to the true average is $150, which can dwarf the figure computed from the disclosed part.
4. Nothing in the disclosed rows signals this. The mass is missing because the seller did not publish it, so its size cannot be inferred from what was published.
5. So no expected value is produced. What is produced is the disclosed mass, 97%, and the missing mass, 3%. That is a smaller claim and a true one.

Result

The formula behind it

• 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

Assumptions

• 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

• 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.

Run these numbers yourself · All worked examples · Methodology