Substring Removal Game

Alice and Bob play a game. They have a binary string $$$s$$$ (a string such that each character in it is either $$$0$$$ or $$$1$$$). Alice moves first, then Bob, then Alice again, and so on.

During their move, the player can choose any number (not less than one) of consecutive equal characters in $$$s$$$ and delete them.

For example, if the string is $$$10110$$$, there are $$$6$$$ possible moves (deleted characters are bold):

1. $$$\textbf{1}0110 \to 0110$$$;
2. $$$1\textbf{0}110 \to 1110$$$;
3. $$$10\textbf{1}10 \to 1010$$$;
4. $$$101\textbf{1}0 \to 1010$$$;
5. $$$10\textbf{11}0 \to 100$$$;
6. $$$1011\textbf{0} \to 1011$$$.

After the characters are removed, the characters to the left and to the right of the removed block become adjacent. I. e. the following sequence of moves is valid: $$$10\textbf{11}0 \to 1\textbf{00} \to 1$$$.

The game ends when the string becomes empty, and the score of each player is the number of $$$1$$$-characters deleted by them.

Each player wants to maximize their score. Calculate the resulting score of Alice.