Conway’s Game of Sprouts
E29420
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.
All labels observed (3)
| Label | Occurrences |
|---|---|
| Conway’s Game of Sprouts canonical | 1 |
| Sprouts (game) | 1 |
| misère Sprouts | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T231138 — 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 Game of Sprouts Context triple: [John H. Conway, notableWork, Conway’s Game of Sprouts]
-
A.
A Loop
A Loop is a modern streetcar route in Portland, Oregon, that provides circulator service through the central city and adjacent neighborhoods as part of the Portland Streetcar system.
-
B.
The Gamester
The Gamester is a Caroline-era tragicomedy play by English dramatist James Shirley, centered on themes of gambling, honor, and social intrigue.
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C.
Two Can Play That Game
Two Can Play That Game is a 2001 romantic comedy film about modern dating mind games, starring Vivica A. Fox and Morris Chestnut.
-
D.
De ratiociniis in ludo aleae
De ratiociniis in ludo aleae is a pioneering 17th-century treatise on probability theory, particularly as applied to games of chance.
-
E.
On Computable Numbers with an Application to the Entscheidungsproblem
"On Computable Numbers, with an Application to the Entscheidungsproblem" is Alan Turing’s landmark 1936 paper that introduced the Turing machine model and founded the formal study of computability and the limits of algorithmic decision procedures.
- 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 Game of Sprouts Target entity description: 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.
-
A.
A Loop
A Loop is a modern streetcar route in Portland, Oregon, that provides circulator service through the central city and adjacent neighborhoods as part of the Portland Streetcar system.
-
B.
The Gamester
The Gamester is a Caroline-era tragicomedy play by English dramatist James Shirley, centered on themes of gambling, honor, and social intrigue.
-
C.
Two Can Play That Game
Two Can Play That Game is a 2001 romantic comedy film about modern dating mind games, starring Vivica A. Fox and Morris Chestnut.
-
D.
De ratiociniis in ludo aleae
De ratiociniis in ludo aleae is a pioneering 17th-century treatise on probability theory, particularly as applied to games of chance.
-
E.
On Computable Numbers with an Application to the Entscheidungsproblem
"On Computable Numbers, with an Application to the Entscheidungsproblem" is Alan Turing’s landmark 1936 paper that introduced the Turing machine model and founded the formal study of computability and the limits of algorithmic decision procedures.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
combinatorial game
ⓘ
mathematical game ⓘ pencil-and-paper game ⓘ topological game ⓘ |
| basicMove |
draw a curve connecting two distinct dots
ⓘ
draw a curve from a dot to itself ⓘ |
| complexity | exact general winning strategy is not known for arbitrary starting size ⓘ |
| educationalUse |
illustrating ideas in topology and graph theory
ⓘ
teaching basic combinatorial game theory concepts ⓘ |
| feature |
game length is finite for any finite starting number of dots
ⓘ
game tree grows rapidly with the number of starting dots ⓘ positions can be represented as planar graphs with degree at most three at each vertex ⓘ supports deep combinatorial analysis despite simple rules ⓘ |
| gameCategory | two-player impartial game ⓘ |
| inventor |
John H. Conway
ⓘ
surface form:
John Horton Conway
Michael S. Paterson ⓘ |
| lineType | curves drawn in the plane ⓘ |
| mathematicalArea |
combinatorial game theory
ⓘ
combinatorics ⓘ graph theory ⓘ topology ⓘ |
| maximumMovesFormula | 3n - 1 for a game starting with n dots ⓘ |
| minimumMovesLowerBound | 2n for a game starting with n dots ⓘ |
| misèreRule | in misère play the player who makes the last move loses ⓘ |
| playConvention | normal play ⓘ |
| playEnvironment |
classroom demonstrations
ⓘ
informal recreational mathematics settings ⓘ |
| positionRepresentation | planar embedding of a graph with degree constraints ⓘ |
| publicationContext | studied in the context of Conway’s work on combinatorial games ⓘ |
| relatedConcept |
Euler’s polyhedron formula
ⓘ
surface form:
Euler characteristic
combinatorial game value ⓘ planar graph ⓘ |
| relatedGame | Sprouts ⓘ |
| researchTopic |
analysis of nim-values for small starting positions
ⓘ
computer search of game trees ⓘ pattern conjectures for winning positions ⓘ |
| rule |
a player who cannot move loses under normal play
ⓘ
each dot has a maximum degree of three incident lines or line-ends ⓘ each move must create a new dot on the drawn line ⓘ lines must not cross existing lines ⓘ players alternate turns making legal moves ⓘ |
| startingDotsNotation | n-sprouts for a game starting with n dots ⓘ |
| startingPosition | finite set of dots on a sheet of paper ⓘ |
| terminationCondition | no legal moves remain ⓘ |
| typicalMedium | paper ⓘ |
| typicalTools | pencil ⓘ |
| variantOf |
Conway’s Game of Sprouts
self-linksurface differs
ⓘ
surface form:
misère Sprouts
|
| winningCondition | last player to move wins under normal play ⓘ |
| yearInvented | 1967 ⓘ |
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 Game of Sprouts Description of subject: 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.
Referenced by (3)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
misère Sprouts
subject surface form:
John H. Conway
this entity surface form:
Sprouts (game)