jmc

We can use casework to solve this. Case $1$: Same letter After choosing any letter, there are seven cards left, and only one of them will produce a winning pair. Therefore, the probability is $\frac{1}{7}$. Case $2$: Same color After choosing any letter, there are seven cards left. Three of them will make a winning pair, so the probability is $\frac{3}{7}$. Now that we have the probability for both cases, we can add them: $\frac{1}{7}+\frac{3}{7}=\boxed{\frac{4}{7}}$.