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Binary game : ウィキペディア英語版
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 X of the interval () on the real line, then the players alternatively choose binary digits x_0, x_1, x_2, .... Player I wins the game if and only if the binary number (x_0x_3_\frac\in{}X. See, page 237.
The binary game is sometimes called Ulam's game, but "Ulam's game" usually refers to the Rényi–Ulam game.
==References==


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