Assume we have a bettor that bets bet $b$ which is $1/5$ of his bankroll $f$, $(b=1/5?f)$ and always gets a return of $11/10$ on the bet. The return, $b?11/10$ is added to the bank roll $f$. A new bet $b$, once again derived from $f$ is bet again with another return of $b?11/10$ then added to $f$. How to model this function?