$6 、 A 、 B$ two teams are holding a table tennis team competition, each team has three players, and each player appears once. $A$ team's three players are $A_{1}, A_{2}, A_{3}, B$ team's three players are $B_{1}, B_{2}, B_{3}$, and the winning rate of $A_{i}$ against $B_{j}$ is $\frac{i}{i+j}(1 \leq i, j \leq 3)$, the winner gets 1 point, then the maximum possible value of the expected score of $A$ team is