dice
Enable an AI agent to recognise physical dice, assess whether their outcomes can be produced and read reliably, and decide how they may be used.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
Researched by: Codex + Grok
Purpose and description
Enable an AI agent to recognise physical dice, assess whether their outcomes can be produced and read reliably, and decide how they may be used.
A die is a small rigid polyhedron made to be thrown as a discrete randomizer: each face (or, on a tetrahedron, a designated vertex) carries a unique mark, and after the body comes to rest that mark is the outcome; fairness as a uniform generator requires isohedral geometry, matched face finishes, and even mass distribution.
It can be Identify and select dice with the outcome vocabulary required for a task.; Roll or tumble a die using a recorded method and compatible surface.; Read a settled position and translate it into an outcome under an explicit convention.; Combine distinguishable dice into a composite result when a supplied convention defines their roles.; Inspect markings and physical condition, then clean or remove a die from use as appropriate.; Collect repeated-roll observations to assess a specified probability or suitability claim..
Distinguishing features
The object is intended to generate a discrete outcome by being rolled, tossed or tumbled and then read from its resting position.
Its physical positions or markings support an identifiable outcome-reading convention; a decorative polyhedron without that function is not automatically a die.
Outcome selection depends on the body's landing position rather than a pointer rotating against a separate scale, distinguishing it from a spinner.
Numbers or pips alone are insufficient: a numbered counter placed deliberately to show a value serves a different role unless it also functions as a rolled outcome selector.
Blank, damaged or altered dice can retain their identity as dice even when their present ability to yield a readable or suitable outcome is unresolved.
Scope
+ Individual dice and membership in sets whose dice must be distinguished or read together
+ Physical form and the resting positions that may represent outcomes
+ Face markings, symbols and mappings from observed positions to reported outcomes
+ Dimensions, material, balance-related features and condition relevant to rolling
+ Roll observations, readability and evidence about outcome frequencies
+ Compatibility with a specified rolling method, surface and outcome-reading convention
- Game rules, turn sequences, scoring systems and player strategy
- Bets, stakes, payouts and gambling transactions
- Dice trays, cups, towers and playing surfaces as independently managed objects
- Software dice simulations and other nonphysical random-number generators
- Manufacturing equipment and production workflows
- Industrial cutting dies, stamping dies and semiconductor dies
Characteristics
- Die or set identity
- Individual die identifier; set identifier; member role Keeps observations attached to the correct die and preserves distinctions when several dice contribute to one result.
- Body form
- Observed geometric form; face count where applicable; irregular or unresolved Supports recognition and identifies which resting positions require interpretation.
- Outcome mapping
- Physical face or resting position to label, symbol or interpreted value; reading convention Separates what is physically displayed from what the result means, including repeated labels.
- Dimensions and mass
- Dimensions in mm; mass in g; measurement method and uncertainty Helps select compatible rolling equipment and compare physical differences between dice.
- Material and construction
- Observed or documented material; solid, hollow, composite or unknown; inserts or cavities if established Provides context for handling, wear and investigation of unusual rolling behaviour.
- Marking readability
- Readable, conditionally readable, ambiguous or unreadable under recorded viewing conditions Determines whether an agent can report an outcome without guessing.
- Physical condition
- Observed chips, cracks, deformation, edge wear, marking loss or contamination; location and severity Supports decisions to inspect, clean, restrict or retire a die.
- Observed outcome frequencies
- Counts by physical outcome and interpreted result; trial count; rolling protocol Allows suitability claims to be evaluated against evidence without assuming equal probabilities.
- Current roll status
- Not rolled, moving, settled, cocked, obstructed, outside the permitted area or unreadable Separates a visible marking from a result that may be accepted under the applicable convention.
- Use suitability
- Die or set to intended use, requirements, assessment and supporting evidence A die may be suitable for one task while lacking the required markings, readability or probability behaviour for another.
Also called
Where this came from
wikidata · CC0 1.0
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 6 bundles · 11 layers · 18 findings · 28 questions.
Die identity and form Establishes what physical die is present and how its form supports outcome selection.
A polyhedral shape or numbered surface alone does not establish dice identity or explain how the object functions.
Recognition and role
Distinguishes dice from similar objects and records individual or set roles.
Physical outcome selector
Record the evidence that the object is intended to select outcomes through rolling or tumbling, including whether it currently serves another role.
- What establishes that this object is a die rather than a decorative solid, numbered counter or other marked object? definition
- Is this an independently read die or a member of a set whose members have distinct roles? boundary
Outcome-bearing geometry
Records the body's relevant surfaces and resting positions without assuming that face count equals outcome count.
Form and resting positions
Describe the observed geometry, dimensions and intended outcome-bearing positions, distinguishing these from exceptional landings.
- What body form, dimensions and physical surfaces can be observed or measured? measurement
- Which resting positions are intended to yield outcomes, and which require a separate acceptance decision? boundary
Markings and outcome meaning Connects physical markings and resting positions to reportable outcomes.
Dice can use different labels and reading conventions; an agent must not infer a value merely from the most visible mark.
Marking inventory
Records the actual outcome vocabulary and how markings are distributed.
Surface-to-label map
Record each relevant marking and its physical location, including blanks, repeated values and visually ambiguous symbols.
- What numbers, pips, symbols, colours or blank markings occur on each outcome-bearing surface? measurement
- Which markings repeat or require orientation cues to distinguish them? measurement
Result interpretation
Makes the reading convention explicit for individual dice and composite results.
Position-to-result convention
Record which physical feature is read and how its label becomes a result, with any set-level role assignment.
- Which face, vertex, edge or other feature determines the result when this die has settled? definition
- What instruction or agreed convention establishes label meanings and any ordering of dice in a composite result? provenance
Rolling and result acceptance Describes how a roll is produced, observed and accepted for the intended use.
A settled die can still be obstructed, unreadable or outside the permitted area, so orientation alone cannot establish an accepted result.
Roll production
Records the method and surroundings relevant to interpreting a roll.
Rolling method and context
Capture how the die is released and where it rolls, including equipment and interactions with other dice.
- What release method, rolling equipment, surface and containment are used? provenance
- What rolling procedure is required for this use, and can this die be rolled that way with the available equipment? action
Landing assessment
Separates observed landing state from the decision to accept or repeat a roll.
Readable and acceptable landing
Record whether the die has settled and can be read, then apply the supplied convention for exceptional landings.
- Has the die stopped moving, and is its result unambiguous from the available view? measurement
- Under the applicable convention, should a cocked, stacked, obstructed or out-of-area landing be accepted, inspected or rerolled? action
Physical integrity and alteration Records construction, damage and alterations relevant to dice behaviour and interpretation.
Changes to edges, surfaces, markings or internal construction may affect the suitability of a die and require evidence-based inspection.
Construction evidence
Distinguishes documented or observed construction from assumptions about internal balance.
Material and balance-relevant features
Record material, mass and established structural features while leaving unexamined internal properties unresolved.
- What material, mass, cavities, inserts or other construction features are documented or directly observed? provenance
- What evidence supports any claim about internal weighting, symmetry or deliberate alteration? provenance
Wear and serviceability
Assesses changes to the surfaces and markings that support rolling and reading.
Condition-based use decision
Locate damage, wear and contamination and connect observed defects to a handling or use decision.
- Where are chips, cracks, deformation, edge wear, lost markings or adhered material present? measurement
- Does the observed condition call for cleaning, further inspection, restricted use or removal from the intended use? action
Probability evidence and use fit Relates observed roll behaviour to explicit expectations and task requirements.
Suitability depends on the intended outcome distribution and use conditions; neither appearance nor a short sequence of rolls settles it.
Distribution assessment
Records the expected distribution and the evidence available to assess it.
Expected and observed outcomes
Keep expected probabilities, physical-position counts and interpreted-result counts distinct, with trial conditions and uncertainty.
- What probability distribution is expected for this use, and does it apply to physical positions or interpreted results? definition
- What outcome counts, trial count and rolling protocol support the assessment, and what uncertainty remains? measurement
Task-specific selection
Determines whether a die or set meets the requirements of a specified activity.
Requirements-to-dice match
Compare the required outcomes, reading conditions, set roles and probability expectations with the available dice and evidence.
- Which required values, symbols, member distinctions or reading conditions does this die or set satisfy? boundary
- Can these dice be selected for the task now, or is replacement, clarification or further testing needed? action
Evidence and external alignment What the world already says about this thing, gathered so the model can be checked against it.
A model that cannot be lined up against existing standards, identifiers and practice cannot be adopted by anyone who already uses them.
Reported evidence
Findings from the breadth pass, kept separate from the structural claims.
Kinds and varieties
Reported by the breadth pass; each item needs checking against its source before it becomes normative.
- Precision casino cubes (transparent cellulose acetate, razor-square edges, flush density-matched pips, serialized and logo-stamped)
- Non-precision board-game cubes (opaque plastic, rounded corners, recessed pips; the ordinary drugstore d6)
- Platonic polyhedral RPG dice (tetrahedral d4, octahedral d8, dodecahedral d12, icosahedral d20)
- Pentagonal trapezohedron d10 and the percentile (d%) pair used with it
- Metal or stone-cast hobby dice (typically zinc-alloy or brass, much heavier than plastic)
- Pai gow and related Asian-table cubes (same cube logic, smaller edge length, sometimes ball corners)
- Wargame mass-roll cubes (typically 12 mm d6, bought and thrown in large handfuls)
- Historic organic dice (bone, ivory, antler, stone), including four-sided knucklebones as the pre-cube form
- Which of these kinds and varieties hold for the sense of dice this model covers, and on what evidence? provenance
Identifiers and schemes
Reported by the breadth pass; each item needs checking against its source before it becomes normative.
- Casino serial and house mark - Unique serial number plus the casino's name, trade name or logo impressed on each licensed cube - A specimen identifier required by several gaming regulators so a player cannot swap in a gaffed die; not a global catalogue code.
- Dice notation - dN or NdX (d6, 2d20, d%); German W-notation W6, W20 - Names the face count and how many bodies are thrown, not an individual physical die.
- Which of these identifiers and schemes hold for the sense of dice this model covers, and on what evidence? provenance
Standards and regulation
Reported by the breadth pass; each item needs checking against its source before it becomes normative.
- South Dakota Administrative Rule 20:18:19:10 - South Dakota Commission on Gaming
- New Jersey Administrative Code 13:69E-1.15 - New Jersey Division of Gaming Enforcement
- Nevada Gaming Control Board Regulation 14 (gaming equipment), as cited for ¾-inch precision cubes
- Saskatchewan Liquor and Gaming Authority, Dice Game Standards (June 2022)
- Which of these standards and regulation hold for the sense of dice this model covers, and on what evidence? provenance
Real-world use
Reported by the breadth pass; each item needs checking against its source before it becomes normative.
- Thrown in pairs against the pyramid bumper on a craps table from a matching serialized stick, usually of five cubes
- Rolled as one or two ordinary d6 in board and parlour games (Yahtzee, Monopoly and similar)
- Carried as a seven-die polyhedral set (d4, d6, d8, d10, d10 percentile, d12, d20) for tabletop role-playing
- Thrown in handfuls of 12 mm d6 in miniature wargames
- Used in sic bo and pai gow (and related Asian table games) as smaller or ball-corner cubes
- Inspected with micrometers, calipers, squares and magnets before a casino table opens, then cancelled or sold as souvenirs after wear
- Used to teach discrete uniform probability; historically also for divination from knucklebones
- Which of these real-world use hold for the sense of dice this model covers, and on what evidence? provenance
Typical measurements
Reported by the breadth pass; each item needs checking against its source before it becomes normative.
- Cube edge length - Board-game d6 ~16 mm; wargame d6 ~12 mm; casino 19.05-19.69 mm (0.750-0.775 in); pai gow ~16.18-16.33 mm (0.637-0.643 in) - mm
- Hobby polyhedron overall size (as sold) - d4 ~16-27 mm; d8 ~24-30 mm; d10 ~21-27 mm; d12 ~18-21 mm; d20 ~23-29 mm (brand-dependent) - mm
- Mass of a six-sided die - Injection-moulded plastic ~3-5; zinc-alloy hobby ~20-30 - g
- Pip-fill depth match (regulated casino cubes) - All spots the same depth within 0.0004 - in
- Face count in ordinary trade - 4, 6, 8, 10, 12 and 20; casino play is almost always 6 - faces
- Which of these typical measurements hold for the sense of dice this model covers, and on what evidence? provenance
Failure modes and hazards
Reported by the breadth pass; each item needs checking against its source before it becomes normative.
- Loaded, floating or density-mismatched dice that bias a face
- Shaved, nicked or burr-edged cubes that catch felt and stop non-randomly
- Player substitution of a gaffed die for a house die; serial and logo marks exist to stop this
- Dice sliding or other controlled shots that prevent a free tumble
- Rounded-corner drugstore cubes and voided injection mouldings that are not geometrically fair
- Historic cellulose-nitrate cubes: violent flammability and acidic sticky decay
- Cellulose-acetate cubes that shrink and go brittle in heat, humidity or UV
- Razor edges that cut skin; small cubes as a choking hazard
- Magnetic gaffs, detectable with a pit magnet
- Which of these failure modes and hazards hold for the sense of dice this model covers, and on what evidence? provenance
Regional variation
Reported by the breadth pass; each item needs checking against its source before it becomes normative.
- Western cubes almost always pair opposite faces to sum to 7 (1 opposite 6, 2 opposite 5, 3 opposite 4); cubes are further split into left- and right-handed chirality by whether 1-2-3 meet clockwise or counterclockwise
- Chinese and much East Asian pip dice paint the 1 and often the 4 red, and may enlarge the ace pip
- Craps precision cubes are a North American casino standard; sic bo and pai gow drive smaller and sometimes ball-corner cubes in Asian-game pits
- English-language rules write d6/d20; German usage writes W6/W20 (Würfel)
- 12 mm vs 16 mm d6 is a wargame-versus-board-game size split in the hobby trade, independent of casino 19 mm cubes
- Which of these regional variation hold for the sense of dice this model covers, and on what evidence? provenance
Neighbouring kinds and how to tell them apart
Reported by the breadth pass; each item needs checking against its source before it becomes normative.
- Spindown d20 (collectible-card life counter) - Numbers run in sequence around the body for counting; an RPG d20 is numbered for a throw, typically with 20 opposite 1.
- Teetotum or barrel die - Spins about a fixed axis and falls on a side; a thrown polyhedral die tumbles freely until a face (or tetrahedron vertex) is up.
- Astragalus / knucklebone - A four-attitude irregular bone, not an isohedral manufactured polyhedron.
- Coin - A two-face flip, not a multi-face tumble to rest.
- Digital die roller - No physical body; fairness is a software RNG question, not geometry and mass.
- Roulette ball and wheel - A ball settling in a numbered pocket on a spinning wheel, not a polyhedron landing on one of its own faces.
- Which of these neighbouring kinds and how to tell them apart hold for the sense of dice this model covers, and on what evidence? provenance
Sources
- ARSD 20:18:19:10 Dice - physical characteristics - Regulated casino-cube size (0.750-0.775 in), cellulose transparency, square edges, equal-weight pip fill to 0.0004 in, opposite-face pairing 1-6 / 2-5 / 3-4, and serial-plus-licensee marking.
- N.J. Admin. Code § 13:69E-1.15 Dice; physical characteristics - Same cube construction rules as South Dakota, plus a smaller pai gow size band of 0.637-0.643 in.
- Dice Game Standards (June 2022) - Canadian provincial physical standards for casino dice: cube geometry, cellulose acetate, flush spots, serial and logo, and a ban on bull's-eye pips.
- It's majestic: Casino dice is unlike other dice - How ¾-inch translucent serialized cubes are used on a craps table, why sharp edges and transparency exist (tamper detection, random tumble), and substitution/sliding as live cheating modes.
- Dice Materials and Construction: What Sets Quality Dice Apart - Precision vs injection-moulded hobby construction; cellulose acetate casino cubes; typical plastic d6 mass 3-5 g vs zinc-alloy 20-30 g; Nevada Regulation 14 cited for ¾-inch cubes and ~0.0005 in edge variance.
- Precision Casino Dice (CIS 07.26 V1.1) - Manufacturer sizes (¾ in and 0.775 in; pai gow 0.640 in and ⅝ in), razor vs ball-corner edges, sanded vs high-polish finish, and use in craps, sic bo and pai gow.
- Spielwürfel - Which polyhedra are isohedral (fair in the geometric sense), and the Dungeons & Dragons seven-die set as the dominant non-cube trade assortment.
- How do they test casino dice? - Pit inspection tools (micrometer, balancing caliper, set square, magnet) and the New Jersey equipment-control practice of locking dice until table open.
- Dice Size Comparison of Different Dice - Measured hobby-set size bands (d6 about 16-18 mm; d20 about 23-29 mm) and the seven-die RPG pack as sold.
- What Dice Do You Need? 12mm vs 16mm, 40K, D&D & More - Practical split between 12 mm d6 for wargame handfuls and 16 mm cubes / seven-die polyhedral sets for role-playing games.
What the second pass must settle
- Does the registry intend dice to include coin-like, rounded or other nonpolyhedral outcome selectors, and where should that boundary fall?
- Should a dice set have its own modelled identity when member roles or matched properties matter, or remain a grouping of individual dice?
- Which authoritative sources establish reading conventions for unusual forms, repeated labels and composite results?
- What probability-assessment methods and evidence thresholds are appropriate for each intended use, especially when the expected distribution is unequal?
- Which construction and condition criteria justify restricting a die's use, and which require direct testing rather than visual inference?