Binary String Game

There is a binary string $S$. Alice and Bob are playing a game on it. Each turn, the following happens: 1. Alice selects a $01$ subsequence in $S$ and removes it from $S$. (a $01$ subsequence is a length $2$ subsequence whose first character is $0$ and second character is $1$) 2. Bob selects a $01$ subsequence in $S$ and removes it from $S$. 3. After both players have moved, the turn is called c