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Mathematical pen-and-paper game
Hackenbush is a two-player game invented by mathematician John Horton Conway. It may be played on any configuration of line segments connected to one another
Hackenbush
1937 Marx Brothers film by Sam Wood
Hugo Z. Hackenbush. Tony overhears her praise of Hackenbush, who is, unknown to anyone, a horse doctor. Tony gets an idea to invite Hackenbush to run the
A_Day_at_the_Races_(film)
Type of game defined in mathematics
that is, games that are equivalent to a number plus an infinitesimal. Hackenbush can only represent cold and tepid games (by its decomposition into a purple
Hot_game
Number used in combinatorial game theory
Nim-sum of the number of spaces between the tokens on each row be 0. Hackenbush is a game invented by mathematician John Conway. It may be played on any
Nimber
Infinite series summable to 1/3
the infinite blue-red Hackenbush string that represents the surreal number 1/3: LRRLRLR... = 1/3. A slightly simpler Hackenbush string eliminates the
1/2_−_1/4_+_1/8_−_1/16_+_⋯
Book by Berlekamp, Conway and Guy
not included Hackenbush Blue-Red Hackenbush Blue-Red-Green Hackenbush (Introduced as Hackenbush Hotchpotch in the book) Childish Hackenbush Ski-Jumps Toads-and-Frogs
Winning Ways for Your Mathematical Plays
Winning_Ways_for_Your_Mathematical_Plays
Alternative decimal expansion of 1
segments in Hackenbush and binary expansions of real numbers, motivated by the idea of data compression. For example, the value of the Hackenbush string LRRLRLRL
0.999...
Branch of game theory about two-player sequential games with perfect information
were used as motivating examples for the introductory theory: Blue–Red Hackenbush - At the finite level, this partisan combinatorial game allows constructions
Combinatorial_game_theory
Concept in combinatorial game theory
{\displaystyle +_{0}} and − 0 {\displaystyle -_{0}} , tiny-0 and miny-0. In Hackenbush, a 1-petaled delphinium, that is, a blue edge on top of a green edge,
Up_(game_theory)
British comics artist and writer (born 1952)
producing Brainstorm Comix, the first three of which formed The Chester P. Hackenbush Trilogy, a character reworked by Alan Moore as Chester Williams for Swamp
Bryan_Talbot
English mathematician (1937–2020)
work. For instance, he discussed Conway's game of Sprouts (July 1967), Hackenbush (January 1972), and his angel and devil problem (February 1974). In the
John_Horton_Conway
South African writer, musician, and activist (born 1936)
Hackenbush trilogy in one volume in 1982. He published a third edition in 1999, titled Bryan Talbot's Brainstorm: The Complete Chester P. Hackenbush and
Lee Harris (South African writer)
Lee_Harris_(South_African_writer)
Mathematical models of strategic interactions
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Game_theory
Game of strategy
the end of the game. Android Nim Chomp Dr. NIM Fibonacci nim Fuzzy game Hackenbush Notakto Octal games Raymond Redheffer Scarney Star (game theory) Subtract
Nim
American comedian (1890–1977)
his latter years, Groucho increasingly referred to himself by the name Hackenbush, referring to the character of that name he played in A Day at the Races
Groucho_Marx
Game defined by mathematical parameters
football Rhythmomachy Tak Tic-tac-toe Tic-tac-toe variants Graph pebbling Hackenbush Chopsticks (hand game) Mancala Nim Sim Sprouts Four fours Contract Bridge
Mathematical_game
Logical paradox in decision-making theory
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Paradox_of_tolerance
British rapper (born 1976)
his brother Farma G are both sons of musician Peet Coombes. Chester P Hackenbush's style has been noted as 'psychedelic', and has been described as the
Chester_P
1976 mathematics book by John Conway
(non-traditional, mathematically inspired) two-player games, such as nim, hackenbush, and the map-coloring games col and snort. The development includes their
On_Numbers_and_Games
Hungarian and American mathematician and physicist (1903–1957)
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
John_von_Neumann
2003 American comedy horror film by Rob Zombie
Rufus T. Firefly was taken from Duck Soup (1933), and lastly Hugo Z. Hackenbush derived from A Day at the Races (1937). Despite only allusions to this
House_of_1000_Corpses
Standard example in game theory
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Prisoner's_dilemma
game Bulls and cows Clique game Col Dots and boxes (19th century) Ghost Hackenbush (1982) Icosian game (1857) Join five Jotto (1955) Kropki Labyrinth Notakto
List of abstract strategy games
List_of_abstract_strategy_games
American comedy team (1905–1949)
Driftwood Fiorello Tomasso —N/a A Day at the Races Sam Wood 1937 Dr. Hugo Z. Hackenbush Tony Stuffy —N/a Room Service William A. Seiter 1938 Gordon Miller Harry
Marx_Brothers
Proof all ranked voting rules have spoilers
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Arrow's_impossibility_theorem
Finding an optimal algorithm for playing chess
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Solving_chess
Comic book limited series
Affair" was reprinted in Bryan Talbot's Brainstorm: The Complete Chester P. Hackenbush and Other Underground Classics, released by Alchemy Publications in 1999
The Adventures of Luther Arkwright
The_Adventures_of_Luther_Arkwright
Diplomatic policy of concessions
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Appeasement
Abstract strategy game
of Chomp games, where only the last final chocolate block loses. Nim Hackenbush Zeilberger, Doron (2001). "Three-Rowed CHOMP". Advances in Applied Mathematics
Chomp
Making of satisfactory, not optimal, decisions
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Bounded_rationality
Paper-and-pencil game for two players
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Tic-tac-toe
Overuse of a shared resource
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Tragedy_of_the_commons
Weakly optimal allocation of resources
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Pareto_efficiency
the film A Day at the Races (1937) starring the Marx Bros., Dr. Hugo Z. Hackenbush (Groucho Marx) asks his dinner companion Flo, (Esther Muir) if she would
Short_beer
Israeli-American psychologist and economist (1934–2024)
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Daniel_Kahneman
Search algorithm
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Alpha–beta_pruning
Pairing where no unchosen pair prefers each other over their choice
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Stable_matching_problem
Search heuristic for combinatorial games
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Aspiration_window
illustration of him bears a striking resemblance to Groucho Marx as Dr. Hugo Z. Hackenbush. In the Chuck Jones adaptation, Dr. Kakafonous A. Dischord is voiced by
List of The Phantom Tollbooth characters
List_of_The_Phantom_Tollbooth_characters
Game theory scenario
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Win–win_game
Game whose outcome can be correctly predicted
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Solved_game
Game theory concept
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Game_form
Human behavior pattern in which the participant takes on increasing risk
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Escalation_of_commitment
Economic Model
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Bertrand–Edgeworth_model
Hand game for two players or more
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Rock_paper_scissors
Economic model
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Cournot_competition
How to triumph at nim by playing safe, and John Horton Conway's game "Hackenbush" 1972 Feb Dr. Matrix poses some heteroliteral puzzles while peddling perpetual
List of Martin Gardner Mathematical Games columns
List_of_Martin_Gardner_Mathematical_Games_columns
Situation where total gains match total losses
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Zero-sum_game
Dynamical system
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Replicator_equation
Game where both players can't move
therefore win. Simple examples of zero games include Nim with no piles or a Hackenbush diagram with nothing drawn on it. The Sprague–Grundy theorem applies to
Zero_game
Concept in game theory
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Focal_point_(game_theory)
Problem about bus travel
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Wait/walk_dilemma
Solution concept of a non-cooperative game
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Nash_equilibrium
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Fictitious_play
Solution concept in game theory
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Rationalizable_strategy
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Asynchrony_(game_theory)
Problem in mathematical sociology
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Bankruptcy_problem
Concept in game theory
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Equilibrium_selection
Concept in conflict studies
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Conflict_escalation
Israeli psychologist (1937–1996)
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Amos_Tversky
Game that repeats a base game
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Repeated_game
Game illustrating paradox in rational choice theory
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Dollar_auction
Condition in economics and game theory
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Perfect_information
Model of humans as rational, self-interested agents
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Homo_economicus
Problem of sharing resources
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Fair_division
Type of combinatorial game
a win for Right; again this is a first-player win. In Blue-Red-Green Hackenbush, if there is only a green edge touching the ground, it is a fuzzy game
Fuzzy_game
Polish–American economist and mathematician (1917–2008)
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Leonid_Hurwicz
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Conjectural_variation
Economic phenomenon
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Tyranny_of_small_decisions
Complete plan on how a game player will behave in every possible game situation
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Strategy_(game_theory)
Representation of a game in game theory
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Normal-form_game
work Honors Ref. Richard Bartle Spellbinder John Horton Conway Sprouts, Hackenbush, and Conway's Game of Life Howard Garns designer of the modern Sudoku
List_of_game_designers
Political model of international conflict resolution
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Two-level_game_theory
Concept in economics and game theory
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Global_game
Zero-sum game where competitions between strategies contain a cycle
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Intransitive_game
Variation of minimax game tree search
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Negamax
Simple game studied in game theory
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Matching_pennies
Model of conflict for two players in game theory
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Chicken_(game)
Variant of Nash equilibrium in game theory
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Trembling hand perfect equilibrium
Trembling_hand_perfect_equilibrium
American television variety series
André Tahon (puppeteer; mouse puppets sing I Feel Pretty) Groucho's Dr. Hackenbush sketch with Dee Hartford (sister of Groucho's wife Eden Hartford) and
The_Hollywood_Palace
Concept in game theory
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Stochastic_game
Game theory concept
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Subgame_perfect_equilibrium
Decision rule used for minimizing the possible loss for a worst-case scenario
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Minimax
Quality of a strategy in game theory
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Strategic_dominance
Hand game for two or more players
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Chopsticks_(hand_game)
American economist (born 1948)
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Paul_Milgrom
Field of economics and game theory
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Mechanism_design
Problem in process of sharing surplus
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Cooperative_bargaining
Solution concept in cooperative game theory
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Myerson_value
Solution concept in game theory
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Evolutionarily stable strategy
Evolutionarily_stable_strategy
heaps with sizes equal to the chains in the poset. A special case of Hackenbush, in which all edges are green (able to be cut by either player) and every
Poset_game
American economist
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
David_K._Levine
Strategy which only depends on the current state of a game
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Markov_strategy
Canadian minor league baseball league
14 Merlin Kopp St. Thomas RUNS 104 13 Bill Wright Guelph HITS 152 13 Hackenbush Hamilton 2B 28 11 E.T. Rogers Ottawa 3B 16 13 Bill Wright Guelph HR 10
Canadian_League_(Class_D)
Class of theorems about Nash equilibrium payoff profiles in repeated games
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Folk_theorem_(game_theory)
Formal rule for predicting how a game will be played
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Solution_concept
Concept in mechanism design
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Strategyproofness
Mathematical game
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Guess_2/3_of_the_average
Abstract strategy game
Bouton (1901–1902); Golomb (1966); Berlekamp, Conway & Guy (2001), "Green hackenbush, the game of nim, and nimbers", pp. 40–42. Golomb (1966); Eppstein (2018)
Subtraction_game
Argument in combinatorial game theory
Strategy-stealing argument Zugzwang Games Chess Chomp Clobber Cram Domineering Hackenbush Nim Notakto Subtract a square Sylver coinage Toads and Frogs Mathematical
Strategy-stealing_argument
HACKENBUSH
HACKENBUSH
HACKENBUSH
HACKENBUSH
Girl/Female
Indian, Kannada
One; United; Unique
Boy/Male
Hindu, Indian, Marathi, Tamil
Rich Man
Boy/Male
English
Lives in Wolfe's cottage.
Boy/Male
Hindu, Indian, Tamil, Telugu
Large; Mighty; Huge and Gigantic; One of Pandavas
Girl/Female
American, British, English, French, German, Hebrew
Darling; Beloved; Dear; Little and Womanly; A Man; The Plains
Female
Italian
Italian form of Greek Euphêmia, EUFEMIA means "Well I speak."
Girl/Female
Tamil
Affection, Love
Boy/Male
Hindu
Forest (Vipin)
Boy/Male
Hindu
Pure or holy
Girl/Female
Hindu, Indian
A Classical Melody
HACKENBUSH
HACKENBUSH
HACKENBUSH
HACKENBUSH
HACKENBUSH