Win rates at first-passage times for biased simple random walks

F. Thomas Bruss, Davy Paindaveine

We study the win rate $R_{N_d}/N_d$ of a biased simple random walk $S_n$ on $\mathbb{Z}$ at the first-passage time $N_d=\inf \{n\ge 0:S_n=d\}$, with $p=P[X_1=+1]\in [1/2,1)$. Using g…