Coming back before the end

Idea. After the first step, the walk is one step away from 17 and must reach 17 before the nearer end of the board. Each side is a gambler's ruin problem.

Step 1: down first. From 16, the walk must reach 17 before 0. A fair walk started at 16 on $[0,17]$ hits 17 first with probability $\frac{16}{17}$.

Step 2: up first. From 18, the walk must reach 17 before 100. On $[17,100]$, starting 1 step from 17 and 82 steps from 100, it hits 17 first with probability $\frac{82}{83}$.

Step 3. $$\begin{array}{rl}\frac{1}{2}\cdot \frac{16}{17}+\frac{1}{2}\cdot \frac{82}{83}& =\frac{16\cdot 83+82\cdot 17}{2\cdot 1411}\\ & =\frac{1361}{1411}\approx \mathrm{0.965.}\end{array}$$

Interpretation. The walk comes back to 17 about 96.5% of the time before stopping. The number of visits to 17 is geometric: on average the walk visits 17 about $\frac{1}{1-0.965}\approx 28$ times, counting the start.