Challenge · Medium problem

In a round-robin tournament among $7$ players, every pair plays once and each game is won by either player with probability $\dfrac12$, independently. A cyclic triple is a set of three players $\{X,Y,Z\}$ with $X$ beating $Y$, $Y$ beating $Z$, and $Z$ beating $X$. If the expected number of cyclic triples is $\dfrac{m}{n}$ in lowest terms, find $m+n$.