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.
[1] Given a subset
of real numbers, two players alternatively write down arbitrary (not necessarily in
) positive real numbers
Player one wins if and only if
[2] 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.
[3] Thus in this situation the second player has a winning strategy.