$X$ be the number of wins and $Y$ the sum won (or lost if negative!) after $n=200$ rounds. Since each bet $X_i\in\{0,1\}$ is an independent Bernoulli trial with success (and failure) probability $p=\frac12$ and outcome $Y_i=100(3X_i-1)=200$ or $-100$, the sums are Binomially distributed $$ \eqalign{ X &= \sum_{i=1}^n X_i = \operatorname{Binom}\left(n=200,p=\frac12\right) \\