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octal game

vr.tr.octal-game · thing-q3177938

Let an agent explain octal games and their code notation, analyse a given octal game with Sprague-Grundy theory, relay known periodicity results with attribution, and separate octal games from other take-and-break games.

Thing Registry Cross-cutting context XCT.REL
Bundle → Layer → Finding → QuestionsClassifiersWhat it isWhy it existsDistinguishing featuresWhat robots and AI may and may not doMoral aspectsOwnersLinks to other meta-modelsIdentity and identifiersDirect propertiesRecognitionCapabilities and actionsHazards and failure modesStandards and interfacesContext of useSources

Bundle → Layer → Finding → Questions Filled

4 bundles · 8 layers · 8 findings · 16 questions

Rules Codes and rules.

Code

Octal code.

Code

Code.

  1. How does an octal code encode which moves are allowed? definition
  2. Is the game an octal game or another take-and-break game? boundary

Examples

Classic games.

Examples

Examples.

  1. Which classic games are octal games, and what are their codes? provenance
  2. Which entry fits Nim? action
Analyse Grundy values.

Grundy

Sprague-Grundy analysis.

Grundy

Grundy.

  1. How are Grundy values computed for an octal game, and how do they decide the winner? action
  2. Which entry fits the Sprague-Grundy theorem? action

Periodicity

Periodicity.

Periodicity

Periodicity.

  1. Which octal games have proven periodic Grundy sequences, and which remain open? provenance
  2. What is proven versus conjectured? boundary
Compute Computation.

Algorithms

Algorithms.

Algorithms

Algorithms.

  1. How are Grundy sequences computed efficiently, and what do the periodicity theorems allow? action
  2. What are the computational limits? measurement

Misere

Misere play.

Misere

Misere.

  1. How does misere play change the analysis? provenance
  2. Which references are standard? provenance
Context History and teaching.

History

Origins.

History

History.

  1. How did Guy and Smith introduce the octal notation, and how did Winning Ways develop it? provenance
  2. Which entry fits combinatorial game theory? action

Teach

Teaching.

Teach

Teaching.

  1. How are octal games used to teach game theory? action
  2. Which misconceptions arise? provenance

Classifiers Filled

Family
Thing Registry
Category
Cross-cutting context
Entry kind
thing
Plane
XCT
Domain
XCT.REL

What it is Filled

A class of impartial combinatorial games played with heaps of counters in which a move removes some counters from a heap and may split the remainder into at most two heaps, with the allowed moves encoded by a sequence of octal digits; Nim, Kayles and Dawson Kayles are octal games, and their outcomes are analysed with Sprague-Grundy values.

Why it exists Filled

Let an agent explain octal games and their code notation, analyse a given octal game with Sprague-Grundy theory, relay known periodicity results with attribution, and separate octal games from other take-and-break games.

Distinguishing features Filled

  • Impartial heap game
  • Moves encoded in octal
  • Analysed by Sprague-Grundy values
  • Many have periodic Grundy sequences

What robots and AI may and may not do Filled

Must not

  • Claim the periodicity of an octal game is proven when only computed to some heap size.
  • Misread an octal code and analyse the wrong game.
  • Attribute results to researchers who did not obtain them.

Only with a human decision

  • Correcting published tables of values.

May

  • Explain octal games, their codes and how their Grundy values are computed.
  • Play, analyse or teach octal games.

Moral aspects Filled

  • Many results rest on long computations whose limits should be stated.
  • Accurate attribution matters in research.

Who is affected

  • Students
  • Researchers

Owners Filled

Steward

Nobody owns the concept; it belongs to mathematics.

Links to other meta-models Filled

parent

  • Q11371326 - registry parent class

related

  • impartial game - the game class
  • Kayles - a classic example
  • Sprague-Grundy theorem - the theory
  • subtraction game - a simpler class without splitting

What else AI and robots need to interact with it Filled

Identity and identifiers required Filled

  • Vercy registry: vr.tr.octal-game
  • Wikidata: Q3177938 (https://www.wikidata.org/wiki/Q3177938)

Direct properties not applicable Not applicable

  • Kayles code: 0.77 octal code
  • Dawson Kayles code: 0.07 octal code

Plane XCT: no invented physical properties.

Recognition optional Filled

  • Rules encoded by octal digits per number of counters removed
  • Impartial, normal play
  • Partizan games and games with other splitting rules are outside the class
  • Not visible; heaps of counters and a code such as 0.77.

Capabilities and actions required Filled

  • decode an octal code into rules
  • compute Grundy values for heap sizes
  • relay known periodicity results
  • identify classic games by their codes

Hazards and failure modes required Filled

  • Misreading the octal code
  • Assuming periodicity that is not proven
  • Confusing normal and misere play

Standards and interfaces required Filled

  • No regulation; conventions follow Winning Ways and the research literature

Context of use required Filled

  • Not for anything; a family of games studied in combinatorial game theory.
  • Nim as an octal game
  • Kayles and Dawson Kayles
  • games with finite codes
  • games with infinite codes
  • hexadecimal and other generalisations

Sources Filled

  1. Wikidata item Q3177938: octal game - identity and sense of the item
  2. Wikipedia: Octal game - general description of the item

Open questions

  • Should Kayles and Nim be separate entries?
  • How should Grundy value tables be linked?
  • Which games with unproven periodicity, such as Grundy game, should be recorded?

Machine files

Card as JSON Specification Card backlog vercy.card/1

Provenance

thing registry research (pass 2) · unreviewed

Built from: models/things/publications/thing-q3177938/spec.json