C.15 Number of successive victories

Taro and Jiro played game that the victory or defeat was decided on every once by all means.

Taro started winning successive victories in Jiro, but he lost five consecutive games afterwards and thereafter finished a game by five successive victories.

Winning rate (ratio of the number of the victories for the number of games) of Taro was 0.8.

Find the number of times that Taro won successive victories first.