Banach game
In mathematics, the Banach game is a topological game introduced by Stefan Banach in 1935 in the second addendum to problem 43 of the Scottish book as a variation of the Banach–Mazur game.
Given a subset of real numbers, two players alternatively write down arbitrary positive real numbers such that Player one wins if and only if exists and is in.
One observation about the game is that if is a countable set, then either of the players can cause the final sum to avoid the set. Thus in this situation the second player can win.
