Solution
= Solution
By part (a) and repeated use of the <Strong Markov property>, the probability of descending from $(2,k)$ to $(2,0)$ is
$$
\left(\frac23\right)^k.
$$
Starting from square 1 with £$m$, heads moves to $(2,m)$, whereas tails lands on square 3, loses £1, and moves to $(2,m-1)$. Therefore the loss probability is
$$
\frac12\left(\frac23\right)^m
+\frac12\left(\frac23\right)^{m-1}
=\boxed{\frac56\left(\frac23\right)^{m-1}}.
$$