positional game
Let an agent explain positional games and their variants and examples, describe the main theoretical results and strategy methods, support analysing specific games, and support learning in combinatorics and game theory.
Bundle → Layer → Finding → Questions Filled
4 bundles · 8 layers · 8 findings · 16 questions
Understand What positional games are.
Concept
Concept and variants.
Concept
Concept.
- What is a positional game, and how do strong, Maker-Breaker and Avoider-Enforcer variants differ? definition
- Which variant or game is meant? boundary
Examples
Examples.
Examples
Examples.
- How are tic-tac-toe, Hex and the Shannon switching game positional games, and who wins them? provenance
- Which entry fits a specific game? action
Theory Theory and methods.
Theorems
Key results.
Theorems
Theorems.
- What do strategy stealing, the Erdos-Selfridge criterion and pairing strategies establish? provenance
- Which entry fits combinatorial game theory? action
Open
Open problems.
Open
Open.
- What open problems and recent results exist in positional game theory, with findings attributed? provenance
- Which findings are current? boundary
Analyse Analysing games.
Analyse
Analysing a game.
Analyse
Analysis.
- How can the winner or a strategy for this positional game be determined? action
- Which entry fits game solving? action
Compute
Computation.
Compute
Computation.
- How are positional games solved computationally, and what is their complexity? provenance
- Which entry fits computational complexity? action
Learn History and teaching.
History
History.
History
History.
- How did the theory of positional games develop from Hales-Jewett and Erdos-Selfridge onward? provenance
- Which references are standard? provenance
Teach
Teaching.
Teach
Teaching.
- How can positional games be taught in combinatorics? action
- Which misconceptions arise? provenance
Classifiers Filled
- Family
- Thing Registry
- Category
- Cross-cutting context
- Entry kind
- thing
- Plane
- XCT
- Domain
- XCT.REL
- Other names and narrower kinds
- Maker-Breaker game
What it is Filled
A finite two-player game in which players alternately claim previously unclaimed elements of a set, such as cells of a board or edges of a graph, with the winner determined by which player completes a winning configuration or prevents the other from doing so, including tic-tac-toe, Hex and the Shannon switching game, and the Maker-Breaker, Avoider-Enforcer and strong variants studied in combinatorics; positional games are analysed by strategy stealing, pairing strategies and potential methods.
Why it exists Filled
Let an agent explain positional games and their variants and examples, describe the main theoretical results and strategy methods, support analysing specific games, and support learning in combinatorics and game theory.
Distinguishing features Filled
- Claiming moves
- Winning sets
- Variants by objective
- Strategy theorems
What robots and AI may and may not do Filled
Must not
- Claim a game is solved or a strategy winning without proof.
- Assist a player during a competitive game where outside help is prohibited.
- Misattribute theorems or results to researchers.
Only with a human decision
- Publishing a claimed proof or new result.
May
- Explain positional games such as tic-tac-toe and Maker-Breaker games and their theory.
- Compute or describe strategies in a user's own analysis.
Moral aspects Filled
- Credit for mathematical results matters to researchers.
- Unfair assistance spoils games for honest players.
Who is affected
- Mathematicians
- Players
Owners Filled
Steward
Nobody: a mathematical concept held in common.
Links to other meta-models Filled
parent
- Q11371326 - registry parent class
related
- finite two-player zero-sum game - category
- Semi-Open Game - chess openings as another studied game structure
- binary relation - graphs underlying positional games
- determinant - algebraic tools in combinatorics
What else AI and robots need to interact with it Filled
Identity and identifiers required Filled
- Vercy registry: vr.tr.positional-game
- Wikidata: Q7233199 (https://www.wikidata.org/wiki/Q7233199)
Direct properties not applicable Not applicable
Not applicable
Plane XCT: no invented physical properties.
Recognition optional Filled
- Alternate claiming of elements to complete configurations
- Tic-tac-toe, Hex, Maker-Breaker games
- Chess is not a positional game in this sense; general combinatorial games are wider
- Not physical; abstract games on boards or graphs.
Capabilities and actions required Filled
- explain variants and examples
- describe theory and methods
- support analysis
- support learning
Hazards and failure modes required Filled
- Confusing variants
- Misapplying strategy stealing
- Overgeneralising results
Standards and interfaces required Filled
- Mathematical notation conventions
- No regulation of the concept
- Competition rules for specific games such as Hex
Context of use required Filled
- Games of claiming elements to form configurations.
- strong positional games such as tic-tac-toe
- Maker-Breaker games
- Avoider-Enforcer games
- games on graphs such as Hex and Shannon switching
- biased and random variants
Sources Filled
- Wikidata item Q7233199: positional game - identity and sense of the item
- Wikipedia: Positional game - general description of the item
Open questions
- Should Hex be a separate entry?
- How should research literature be linked?
- How should game implementations be linked?
Machine files
Provenance
thing registry research (pass 2) · unreviewed
Built from: models/things/publications/thing-q7233199/spec.json