Summary: In this note we consider the on-line Ramsey numbers \(\overline {\mathcal {R}}(P_n,P_m)\) for paths. Using a high performance computing cluster, we calculated the values for off-diagonal numbers for paths of lengths at most 8. We were also able to check that \(\overline {\mathcal {R}}(P_9,P_9)=17\), thus solving the problem raised in the author’s paper [Australas. J. Comb. 40, 27–36 (2008; Zbl 1141.05061)].