  Schmidt games and the Cantor winning property give alternative notions of
largeness, similar to the more standard notions of measure and category. Being
intuitive, flexible, and applicable to recent research made them an active
object of study. We survey the definitions of the most common variants and
connections between them. A new game called the Cantor game is invented and
helps with presenting a unifying framework. We prove surprising new results
such as the coincidence of absolute winning and $1$ Cantor winning in doubling
metric spaces, and the fact that $1/2$ winning implies absolute winning for
subsets of $\mathbb{R}$, and we suggest a prototypical example of a Cantor
winning set to show the ubiquity of such sets in metric number theory and
ergodic theory.
