Random walker on a 100-metre bridge

A man stands on a bridge $100$ metres long, $17$ metres from one end. Each step he moves one metre towards one end or the other with probability $\tfrac12$ each, and he stops once he reaches either end. What is the probability that he reaches the far end (the one $83$ metres away) first, and what is the expected number of steps until he stops?

Probability $0.17$; expected steps $17\times83=1411$. Position is a martingale, so $P(\text{far end})=\tfrac{17}{100}$. Also $X_t^2-t$ is a martingale, which gives $E[T]=a\,b$ for distances $a=17$ and $b=83$ to the two ends.