Positional games

Maker-Breaker game

A Maker-Breaker game is a kind of positional game. Like most positional games, it is described by its set of positions/points/elements and its family of winning-sets (- a family of subsets of ). It is played by two players, called Maker and Breaker, who alternately take previously-untaken elements. In a Maker-Breaker game, Maker wins if he manages to hold all the elements of a winning-set, while Breaker wins if he manages to prevent this, i.e. to hold at least one element in each winning-set. Draws are not possible. In each Maker-Breaker game, either Maker or Breaker has a winning strategy. The main research question about these games is which of these two options holds. (Wikipedia).

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Conjunctive normal form | Strong positional game | Graph (discrete mathematics) | Clique game | Positional game | Biased positional game | Graph property | Shannon switching game | Pairing strategy | Hex (board game) | John Selfridge | Complete graph | Family of sets | Graph coloring | Arithmetic progression game | Chromatic number | Tic-tac-toe | Probabilistic method | Paul Erdős | Property B | Avoider-Enforcer game