Conway’s games
E637294
Conway’s games are a class of combinatorial games introduced by mathematician John Horton Conway, forming the foundation of surreal numbers and studied for their rich algebraic and strategic properties.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Conway’s games canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7030649 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Conway’s games Context triple: [Conway’s soldiers, category, Conway’s games]
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A.
Conway’s Game of Sprouts
Conway’s Game of Sprouts is a pencil-and-paper topological game in which players alternately connect dots with lines under simple rules, leading to rich combinatorial and mathematical analysis.
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B.
Winning Ways for your Mathematical Plays
Winning Ways for your Mathematical Plays is a multi-volume book on combinatorial game theory that popularizes and systematically explores mathematical games and their underlying structures.
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C.
The Dots and Boxes Game: Sophisticated Child's Play
"The Dots and Boxes Game: Sophisticated Child's Play" is a mathematical analysis of the classic pencil-and-paper game Dots and Boxes, exploring its underlying combinatorial game theory and advanced strategies.
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D.
Mathematical Games
"Mathematical Games" is a long-running Scientific American column by Martin Gardner that popularized recreational mathematics and puzzles for a broad audience.
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E.
Conway’s soldiers
Conway’s soldiers is a mathematical puzzle and thought experiment in combinatorial game theory that explores how far checkers-like pieces can advance on an infinite grid under specific movement rules.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Conway’s games Target entity description: Conway’s games are a class of combinatorial games introduced by mathematician John Horton Conway, forming the foundation of surreal numbers and studied for their rich algebraic and strategic properties.
-
A.
Conway’s Game of Sprouts
Conway’s Game of Sprouts is a pencil-and-paper topological game in which players alternately connect dots with lines under simple rules, leading to rich combinatorial and mathematical analysis.
-
B.
Winning Ways for your Mathematical Plays
Winning Ways for your Mathematical Plays is a multi-volume book on combinatorial game theory that popularizes and systematically explores mathematical games and their underlying structures.
-
C.
The Dots and Boxes Game: Sophisticated Child's Play
"The Dots and Boxes Game: Sophisticated Child's Play" is a mathematical analysis of the classic pencil-and-paper game Dots and Boxes, exploring its underlying combinatorial game theory and advanced strategies.
-
D.
Mathematical Games
"Mathematical Games" is a long-running Scientific American column by Martin Gardner that popularized recreational mathematics and puzzles for a broad audience.
-
E.
Conway’s soldiers
Conway’s soldiers is a mathematical puzzle and thought experiment in combinatorial game theory that explores how far checkers-like pieces can advance on an infinite grid under specific movement rules.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
class of combinatorial games
ⓘ
mathematical structure ⓘ |
| component |
Left options set
ⓘ
Right options set ⓘ |
| documentedIn |
On Numbers and Games
NERFINISHED
ⓘ
Winning Ways for your Mathematical Plays NERFINISHED ⓘ |
| field |
combinatorial game theory
ⓘ
mathematics ⓘ |
| formalDefinition | games defined recursively by sets of left and right options ⓘ |
| foundationOf | surreal numbers ⓘ |
| hasConcept |
cold games
ⓘ
fuzzy games ⓘ hot games ⓘ infinitesimal games ⓘ loopy games (in extended theory) ⓘ numbers as games ⓘ short games (finite birthday) ⓘ |
| hasInfluenceOn |
mathematical foundations of game values
ⓘ
modern combinatorial game theory ⓘ research on surreal numbers ⓘ |
| hasProperty |
finite positions in basic theory
ⓘ
forms a field when restricted to numbers ⓘ no chance moves ⓘ ordered abelian group structure under addition ⓘ partizan games framework ⓘ perfect information ⓘ rich algebraic structure ⓘ supports addition ⓘ supports comparison ⓘ supports multiplication (via surreal numbers) ⓘ supports negation ⓘ well-founded game trees in basic theory ⓘ |
| hasRule |
Left chooses from left options
ⓘ
Right chooses from right options ⓘ a game is an ordered pair of sets of games (L,R) ⓘ player unable to move loses (normal play convention) ⓘ players move alternately ⓘ |
| introducedBy | John Horton Conway NERFINISHED ⓘ |
| relatedTo | surreal numbers ⓘ |
| studiedFor |
algebraic properties
ⓘ
applications in game analysis ⓘ strategic properties ⓘ |
| supportsOperation |
comparison via outcome classes
ⓘ
disjunctive sum of games ⓘ negation of games by swapping roles of players ⓘ |
| timeOfIntroduction | early 1970s ⓘ |
| usedIn |
analysis of impartial and partizan games
ⓘ
formalization of game values ⓘ theory of surreal numbers ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Conway’s games Description of subject: Conway’s games are a class of combinatorial games introduced by mathematician John Horton Conway, forming the foundation of surreal numbers and studied for their rich algebraic and strategic properties.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.