Binary game
In mathematics, the binary game is a topological game introduced by Stanislaw Ulam in 1935 in an addendum to problem 43 of the Scottish book as a variation of the Banach–Mazur game.
In the binary game, one is given a fixed subset X of the set N of all sequences of 0s and 1s. The players take it in turn to choose a digit 0 or 1, and the first player wins if the sequence they form lies in the set X. Another way to represent this game is to pick a subset of the interval on the real line, then the players alternatively choose binary digits. Player I wins the game if and only if the binary number, that is,. See, page 237.
The binary game is sometimes called Ulam's game, but "Ulam's game" usually refers to the Rényi–Ulam game.
