Symmetric walk from 80 absorbed at 0 or 1000

A simple symmetric random walk on the integers starts at $80$ and moves up or down by $1$ with equal probability at each step. It stops when it first hits either $0$ or $1000$. What is the probability that it stops at $0$?

$0.92$. The position is a martingale, so by optional stopping $80=1000\cdot\mathbb{P}(\text{hit }1000)$, giving $\mathbb{P}(\text{hit }1000)=0.08$ and $\mathbb{P}(\text{hit }0)=\tfrac{920}{1000}$.