Hackenbush

E163079

combinatorial game impartial game mathematical game partizan game

Hackenbush is a combinatorial game played on colored line-graphs, famous in recreational mathematics for illustrating concepts in game theory and surreal numbers.

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All labels observed (6)

Label	Occurrences
Hackenbush canonical	3
Blue-Red Hackenbush	1
Blue-Red-Green Hackenbush	1
Green Hackenbush	1
finite Hackenbush	1
infinite Hackenbush	1

Statements (51)

Predicate	Object
instanceOf	combinatorial game ⓘ impartial game ⓘ mathematical game ⓘ partizan game ⓘ
analyzedIn	On Numbers and Games ⓘ Winning Ways for your Mathematical Plays ⓘ
application	recreational puzzle design ⓘ teaching combinatorial game theory ⓘ visualizing surreal numbers ⓘ
category	two-player perfect-information game ⓘ
chanceElement	no randomness ⓘ
field	combinatorial game theory ⓘ recreational mathematics ⓘ surreal number theory ⓘ
hasColor	blue ⓘ green ⓘ red ⓘ
hasComponent	branches ⓘ ground line ⓘ vertical edges ⓘ
hasRule	players alternately remove edges of their own color ⓘ the player unable to move loses under normal play ⓘ when an edge is removed all disconnected components not touching the ground are removed ⓘ
hasVariant	Hackenbush self-linksurface differs ⓘ surface form: Blue-Red Hackenbush Hackenbush self-linksurface differs ⓘ surface form: Blue-Red-Green Hackenbush Hackenbush self-linksurface differs ⓘ surface form: Green Hackenbush Hackenbush self-linksurface differs ⓘ surface form: finite Hackenbush Hackenbush self-linksurface differs ⓘ surface form: infinite Hackenbush
illustrates	cold games ⓘ fuzzy games ⓘ game values ⓘ hot games ⓘ infinitesimal game values ⓘ numbers in combinatorial game theory ⓘ surreal numbers ⓘ switches in combinatorial game theory ⓘ
informationType	no hidden information ⓘ
introducedBy	John H. Conway ⓘ surface form: John Horton Conway
moveType	edge deletion ⓘ
notableProperty	finite blue-red strings represent dyadic rational numbers ⓘ game values can form infinitesimal and infinite numbers ⓘ positions correspond to surreal numbers in certain cases ⓘ
playerRole	Left ⓘ Right ⓘ
solvedClass	finite blue-red strings ⓘ
typicalConvention	Left plays blue edges ⓘ Right plays red edges ⓘ
uses	colored graphs ⓘ edge-colored graphs ⓘ planar graphs ⓘ
winCondition	last move wins under normal play ⓘ

Referenced by (8)

Full triples — surface form annotated when it differs from this entity's canonical label.

Winning Ways for your Mathematical Plays → coversConcept → Hackenbush ⓘ

On Numbers and Games → topic → Hackenbush ⓘ

Part Two: Games → hasWorkExample → Hackenbush ⓘ