Positional games

Biased positional game

A biased positional game is a variant of a positional game. Like most positional games, it is described by a set of positions/points/elements and a family of subsets, which are usually called the winning-sets. It is played by two players who take turns picking elements until all elements are taken. While in the standard game each player picks one element per turn, in the biased game each player takes a different number of elements. More formally, for every two positive integers p and q, a (p:q)-positional game is a game in which the first player picks p elements per turn and the second player picks q elements per turn. The main question of interest regarding biased positional games is what is their threshold bias - what is the bias in which the winning-power switches from one player to the other player. (Wikipedia).

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