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Impartial game Jeu impartial Gioco imparziale
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2001 1982
prop-fr:auteur
---
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E. Berlekamp, J. H. Conway, R. Guy
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0 1
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anglais
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Winning Ways for your Mathematical Plays
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2
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Winning Ways for your Mathematical Plays
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Academic Press A K Peters Ltd
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In combinatorial game theory, an impartial game is a game in which the allowable moves depend only on the position and not on which of the two players is currently moving, and where the payoffs are symmetric. In other words, the only difference between player 1 and player 2 is that player 1 goes first.Impartial games can be analyzed using the Sprague–Grundy theorem.Impartial games include Nim, Sprouts, Kayles, Quarto, Cram, Chomp, and poset games. Dans la théorie des jeux combinatoires, un jeu impartial est un jeu dans lequel les coups autorisés, ainsi que les gains obtenus, dépendent uniquement de la position, et pas du joueur dont c'est le tour. Les jeux impartiaux incluent notamment le jeu de Nim, le jeu de Grundy, le jeu de Wythoff, les jeux octaux, le Sprouts, le jeu de Cram, ou Chomp. In teoria dei giochi combinatoria, un gioco si dice imparziale se la gamma delle mosse permesse dipende solo dalla configurazione attuale e non da quale dei due giocatori deve muovere, e dove i guadagni sono simmetrici.
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Dans la théorie des jeux combinatoires, un jeu impartial est un jeu dans lequel les coups autorisés, ainsi que les gains obtenus, dépendent uniquement de la position, et pas du joueur dont c'est le tour. Les jeux impartiaux incluent notamment le jeu de Nim, le jeu de Grundy, le jeu de Wythoff, les jeux octaux, le Sprouts, le jeu de Cram, ou Chomp. Le jeu de go ou les échecs ne sont pas impartiaux, car les coups disponibles à partir d'une position donnée sont différents pour le joueur blanc et le joueur noir.D'après le théorème de Sprague-Grundy tout jeu impartial est équivalent à un tas d'une certaine taille du jeu de Nim.Un jeu qui n'est pas impartial est appelé jeu partisan. In combinatorial game theory, an impartial game is a game in which the allowable moves depend only on the position and not on which of the two players is currently moving, and where the payoffs are symmetric. In other words, the only difference between player 1 and player 2 is that player 1 goes first.Impartial games can be analyzed using the Sprague–Grundy theorem.Impartial games include Nim, Sprouts, Kayles, Quarto, Cram, Chomp, and poset games. Go and chess are not impartial, as each player can only move pieces of their own color. Games like ZÈRTZ and Chameleon are also not impartial, since although they are played with shared pieces, the payoffs are not necessarily symmetric for any given position.A game that is not impartial is called a partisan game. In teoria dei giochi combinatoria, un gioco si dice imparziale se la gamma delle mosse permesse dipende solo dalla configurazione attuale e non da quale dei due giocatori deve muovere, e dove i guadagni sono simmetrici. In altri termini, in un gioco imparziale l'unica differenza tra i due giocatori è che all'inizio uno dei due muoverà per primo.I giochi imparziali possono essere analizzati usando il teorema di Sprague-Grundy.Alcuni esempi di giochi imparziali sono il nim, lo sprout, kayles, quarto, cram, and chomp. Il go e gli scacchi non sono imparziali, in quanto ogni giocatore ha le sue pedine, dalla cui disposizione dipendono le possibili mosse. Ci sono però casi anche di giochi, come Zertz e Chameleon, che sono non imparziali nonostante le pedine siano in comune tra i due giocatori: in questi giochi, infatti, i guadagni risultanti dalle mosse non sono sempre simmetrici.
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