In combinatorial game theory, Maker-Breaker games are a subclass of positional games. It is a two-person game with complete information played on a hypergraph (V,H) where V is an arbitrary set (called the board of the game) and H is a family of subsets of V, called the winning sets. The two players alternately occupy previously unoccupied elements of V. The definition of Maker-Breaker game has a subtlety when and . In this case we say that Breaker has a winning strategy if, for all j > 0, Breaker can prevent Maker from completely occupying a winning set by turn j.