Consider a random walk in which the probability to move forward in time $t$ is $p_t$ and the probability to move backward is $q_t=1-p_t$ with $p_t<q_t$ with $p_t<p_{t+1}$ and $q_t>q_{t+1}$.
Moving forward will be by $f_t$ steps and moving backward by $b_t$ steps with $f_t>b_t$ but $f_{t+1}<f_t$ and $b_{t+1}>b_t$.
For example,
$p_1=0.4$, $q_1=0.6$, $f_1=10$,$b_1=5$.
$p_2=0.45$, $q_2=0.55$, $f_2=8$,$b_2=6$.
and so on,
At time $t=n$, $p_n=0.5$ and $q_n=0.5$ with $f_n=1$ and $b_n=1$.
The question is, is this random walk moving forward or backward, and if forward, what is the expected numbers of steps to move forward at time $t=n$?