Marcia and John are playing the following game: Marcia think of a fraction, and John flip a coin. If the coin turn up head, Marcia multiplie the number he' thinking of by $\frac{7}{8}$. If the coin turn up tail, he multiplie the number he' thinking of by $\frac{8}{7}$. John flip the coin ten time, and after each flip Marcia multiplie the number in her head by either $\frac{7}{8}$ or $\frac{8}{7}$, depending on the coin flip. The ten coin flip turn out to be:\[
\text{HHHTHTTTHH},
\]where H mean 'head' and T mean 'tail.' What number i Marcia thinking of at the end of the game if he tart out with the fraction $\frac{1}{3}$?