SCARCITY HAS A CLIFF, AND IT SITS AT 300 COPIES

Boxed Up is a card collecting game with an open marketplace. Players buy and sell cards with each other, and nobody sets a price but them. We also know exactly how many copies of every card exist, because we minted them.

That combination is rare enough to be worth reporting: a real market where the supply of every good is known exactly, and observable against what people actually paid. Over 90 days that came to 668,744 trades across 9,006 cards.

The curve

Every traded card, grouped by how many copies are in circulation across all players:

From 34 copies to 899 — 26 times the supply — the average price falls by a factor of 509. And then it stops. Past 1,200 copies the price does not keep falling; it ticks back up — which turns out to be a composition effect rather than a broken demand curve. See below.

Two different markets

Split the same cards at 300 copies and they behave like two unrelated economies.

Below 300 copies, supply explains most of the price and does so steeply: a slope of −2.46 means halving supply multiplies price by about 5.5. Above 300, the correlation is +0.12 — which is to say, nothing at all.

The floor underneath everything

One rule of the game matters here, and it is the reason the curve flattens rather than falling forever. Players can always sell a card back to the game for a fixed amount set by its rarity: 50 coins for a basic, 250 for a rare, 5,000 for an epic, 50,000 for an ultimate. Nobody rationally accepts less than that from another player, so every card has a guaranteed floor that has nothing to do with how many exist.

That also explains the tick upward past 1,200 copies. The most abundant band holds 2.6 times the proportion of high-rarity cards as the band below it (12.9% against 4.9%), and those carry buy-back floors 2.25 times higher — while their prices are only 1.57 times higher. The rise is what those cards are worth by rule, not collectors bidding up something plentiful.

So the cliff has two sides with different rules. Below it, scarcity prices cards and players set the number. Above it, supply is irrelevant and price sits on a rarity-linked floor the game defines. The threshold is where a market stops being a market.

Isn't this just the numbered cards?

Some cards carry a hard cap — a fixed run, with each copy numbered. They are also, by design, the scarcest cards in the game, so the obvious objection is that we have measured a badge rather than a supply effect.

Matching capped and uncapped cards at near-identical circulation:

It does not hold up. The advantage flips direction twice, and the two rows favouring capped cards have much the smallest samples. Once supply is matched, being numbered does not reliably command more — the premium visible in coarser groupings was the scarcity underneath it.

Worth stating plainly: no capped card in this dataset exceeds 300 copies, so this comparison exists only below the cliff. In a game where every numbered card is also a scarce one, the two questions cannot be fully separated.

Why a cliff, and not a slope

The likely reason is that scarcity only prices when it is felt. At forty copies in circulation, a collector who wants one has to find a specific person who has one and persuade them to part with it. That is a negotiation, and the price reflects it.

At a thousand copies there is always another seller. Nobody has to outbid anyone, so nothing pushes the price up, and it settles at whatever the floor happens to be. The extra supply beyond that point changes nothing, because the constraint was already gone.

The cliff is where a card stops being something you hunt and starts being something you can just buy. Everything above it is the same market wearing different numbers.

Method

Every completed player-to-player sale on the Boxed Up marketplace in the 90 days to 3 September 2026: 668,744 sales, 9,562 distinct sellers, 9,006 distinct cards.

Prices are the coins actually received by the seller, not the asking price. Asking prices include auction listings and cap placeholders that would badly distort an average — using them puts a common card at 242 million coins, which is a placeholder, not a sale.

Circulation is every copy of a card held by any player, counted directly rather than inferred from its rarity label. Correlations and slopes are computed on logs, across the 8,690 cards with at least five sales.

The rules that shape this economy, since they bound what the numbers can mean: cards enter circulation through packs and timed drops, some with a hard cap on copies and some without. They leave it through a fixed-price sell-back to the game, and through being spent on other in-game systems. That sell-back is the floor described above. Rarity tiers govern both how often a card appears and what it sells back for, so rarity and supply are correlated by design rather than independent.

Two things we deliberately did not use. Which cards are owned most, because that is a function of how many we printed rather than of what anyone wanted. And the real-world resale price of the sneaker on the card: retail price conflates luxury pricing with collector demand — plenty of designer shoes cost more than a hyped Jordan without anyone chasing them — so it is too noisy a proxy to carry an argument.

See the marketplace

Boxed Up is free on iPhone and Android. The same marketplace runs in Tuned Up for music and Filmed Up for film.

Questions people ask

Isn't this circular — rare things are expensive because they're rare?

If it were, the effect would be smooth: more copies, lower price, all the way up. It isn't. It is very strong below about 300 copies and vanishes above it — past 1,200 copies the price stops falling and slightly rises. A tautology would not switch off at a specific number.

Is this real money?

No. Coins are Boxed Up's in-game currency, earned by playing and by selling cards to other players. No part of this analysis involves real-money transactions.

Why not measure which cards people own most?

Because that measures supply, not demand — the most-owned cards are simply the ones we printed most of. Sales are the only signal where a collector chose to give something up to get something else.

Why does price rise again above 1,200 copies?

Composition, not demand. Players can always sell a card back to the game for a fixed amount set by its rarity, which gives every card a floor unrelated to supply. The most abundant band holds 2.6x the proportion of high-rarity cards as the band below it, and those carry buy-back floors 2.25x higher — while their prices are only 1.57x higher. The rise is the floor moving, not collectors bidding up something plentiful.

Is the effect just the numbered cards?

No. Matching capped and uncapped cards at near-identical circulation, the advantage flips direction twice and the rows favouring capped cards have the smallest samples. Once supply is matched, being numbered does not reliably command more.

Does the rarity label explain it instead?

The bands are built on counted copies, not on rarity tiers, so the labels play no part in the grouping. Run the same test inside a single rarity tier and the pattern repeats: it is strong in the scarce tiers and near zero in the abundant ones, which is the same cliff seen from another angle.

How big is the dataset?

668,744 completed player-to-player sales over 90 days, 9,562 distinct sellers, 9,006 distinct cards. The curve uses the 8,690 cards with five or more sales.