Traits · rating · tiers · what the odds actually mean
Every card is a roll of six traits.
The same six traits draw the art and compute the rating, so you can point at any card and read why it scored what it scored. Every frequency on this page is the number the engine actually rolls against — this page is generated from it, not typed alongside it.
- Trait slots
- 6species · chroma · eyes · mark · cut · serial
- The formula
- 1 / √pone over the root of how likely your card was
- Floor
- 57an all-common roll
- Ceiling
- 9,128,7091 in 83 trillion — never actually reached
Species
6 values · the whole creatureThe visual family, and the only trait you can read from across a room. It picks which generator draws you. Sovereign is the chase: it is the one species that wears the gold foil, and it can never be bought — never on the pity ladder, never in the shop, pull-only.
Chroma
8 values · the creature’s colourPassed to the generator as a real colour, so the card you are looking at is the colour that scored.
Eyes
14 values · the faceFourteen values, passed through to the art. One of them turns up in three pulls in a thousand.
Mark
12 values · the corner sigilThe glyph on the frame. Weighted steeply on purpose — the rarest is 58× the commonest, so Mark is a real axis.
Cut
5 values · the card’s surfaceThe finish. Prism and Chrome are visible from across the room, which is what carries the instant read.
Serial
5 values · the printed numberWhich mint band your collector number is drawn from. #0001 exists and is half a percent of half a percent.
Your rating is one over the square root of how likely your card was.
p = the six trait frequencies, multiplied rating = round( 1 / √p )
That is the whole thing. Because rare combinations are rare multiplicatively, the distribution comes out heavy-tailed on its own — exactly the shape a leaderboard needs. No curve-fitting, no hand-tuned weights, no score nobody can audit. It is also why first place is permanently beatable: the top of the scale is real, computable, and about 1 in 83,333,333,333,333, which is not a number anybody reaches.
| Slot | Value rolled | Frequency | 1 in |
|---|---|---|---|
| Species | Drifter | 8.0% | 13 |
| Chroma | Pitch | 2.0% | 50 |
| Eyes | Glow | 2.0% | 50 |
| Mark | Ward | 4.0% | 25 |
| Cut | Chrome | 7.0% | 14 |
| Serial | #001–009 | 3.5% | 29 |
| p | all six, multiplied | 3.14e-9 | 318,877,551 |
17,857.00
Tier IV
This exact combination turns up about once in 318,877,551 rolls. One over the square root of that is 17,857.00, and 17,857.00 sits inside the 8,000–40,000 band, so the card prints Tier IV. Nobody assigned it that. It fell out of the arithmetic.
| Tier | Name | Rating band | What it means |
|---|---|---|---|
| I | Common | 0 – 200 | The floor. Every pack contains several, and they still count as cards. |
| II | Uncommon | 200 – 1,500 | Reached by one scarce roll, or several uncommon ones. |
| III | Rare | 1,500 – 8,000 | Reached by one scarce roll, or several uncommon ones. |
| IV | Epic | 8,000 – 40,000 | Reached by a scarce roll in two or more slots. |
| V | Legendary | 40,000 – 500,000 | Reached by a scarce roll in two or more slots. |
| Sovereign | 500,000 – no ceiling | Above the top band, and effectively unreachable: about 1 card in 1.29 billion. It exists to prove the rating has no ceiling, not as a tier anyone expects to hold. |
Species and tier are separate axes, on purpose. A card can read Blob · Tier IV — a common-looking creature that rolled monstrous everywhere else. That is exactly how real card games behave, and it means you have to read a card rather than pattern-match its silhouette.
The compensation is Cut: Prism and Chrome finishes are visible from across the room and correlate with high ratings, so there is still an instant read — it is just carried by the finish instead of the species.
| Where | Combination | p | 1 in | Rating | Tier |
|---|---|---|---|---|---|
| Floor | every slot rolls its most common value | 3.12e-4 | 3,201 | 57 | I |
| Worked example | the card below | 3.14e-9 | 318,877,551 | 17,857 | IV |
| Ceiling | all six rarest values at once | 1.20e-14 | 83,333,333,333,333 | 9,128,709 |
The ceiling exists and is never reached. Rolling all six rarest values at once has a probability of 1.2e-14 — about 1 in 83,333,333,333,333. That is the whole point: the top of the scale is real and computable, and there is no plausible amount of opening that arrives at it. First place is always beatable, permanently, without a single rule written to make it so.
Each of these six is a different roll, so each draws a different creature from a different generator — DiceBear for Blob and Bot, RoboHash for the other four, both free and seed-based. The seed is your domain plus the roll, so the same card is always the same picture and two different rolls are never the same creature.
Why continuous, and not a fixed set of card values. Because a ceiling ends the race: whoever pulls the best possible card holds first place permanently and the board is over. With an unbounded rating the k-th pull sets a record with probability exactly 1/k, so the lead changes about ln(k)+0.577 times over the board’s whole life whatever its scale — often enough to be live, rarely enough to matter. The arithmetic, worked out, and how it differs from a board where rank is a price: OutRip vs outbid.lol. The rest of the wave is counted at every board, measured.