7. Two people play a game: they continuously flip a coin several times, and the game ends when the cumulative number of times the head (or tail) side is up reaches 5. When the game ends, if the cumulative number of times the head side is up reaches 5, then $A$ wins; otherwise, $B$ wins. What is the probability that the game is decided in fewer than 9 flips? $\qquad$
$7: \frac{93}{128}$.
Consider the scenario where the game ends after 9 rotations. In this case, in the first 8 rotations, heads and tails each appear 4 times, with a probability of $\frac{C_{8}^{4}}{2^{8}}=\frac{35}{128}$. Therefore, the probability that the game ends before 9 rotations is $1-\frac{35}{128}=\frac{93}{128}$.