We investigated the self-starting condition for additive-pulse mode locking in an arc-lamp-pumped cw Nd: YLF laser. We measured the first beat note of the free-running laser to estimate the cavity correlation time. We supplement the theoretical model for the self-starting condition, which was previously given in terms of the cavity correlation time and the critical buildup time, by including the effect of dynamic pin saturation. This modified model is compared with the experimental results.