Biased positional game

Summary

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 ($X$) and a family of subsets ($\mathcal{F}$), 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.