My solution: The answer is $0$. Alya's and Bob's final scores are the same. In fact, we now prove that no matter how Alya and Bob play the game, they will always get a total score of $190$ respectively at the end of the game. We claim that given a number, $n\geq 2$, on an empty whiteboard, if a player proceeds to play the game, he will get a total score of $\frac{n(n-1)}{2}$. We now prove this by strong induction. The base case, $n=2$ is trivial. Assume that for all $n=2,3,\cdots ,k$ our statement holds where he will only get one score of $\frac{k(k-1)}{2}$ at the end. Now for $n=k+1$, he will erase $k+1$ and write it as $k+1-j$ and $j$ where $j\in \{1,2,\cdots ,k\}$. Then by our inductive hypothesis, the final score will be \[j(k+1-j)+\frac{(k+1-j)(k-j)}{2}+\frac{j(j-1)}{2}=\frac{(k+1)k}{2}\]which completes our inductive step. $\blacksquare$