From Rational to Binary

Chef and Divyam are playing a game. They start with a rational number $X$, such that $0 < X < 1$. In each turn, Chef chooses a positive real number $Y$. Then Divyam either adds or subtracts $Y$ to $X$. So $X$ is replaced with either $X+Y$ or $X-Y$. If this number becomes $0$ or $1$, then Chef wins. Otherwise, the game continues. You are given $X$, and you have to determine whether Chef can win i