The growth in the use of online advertising to foster brand awareness over recent years is largely attributable to the ubiquity of social media. One pivotal technology contributing to the success of online brand advertising is frequency capping, a mechanism that enables marketers to control the number of times an ad is shown to a specific user. However, the very foundation of this technology is being scrutinized as the industry gravitates towards advertising solutions that prioritize user privacy. This paper delves into the issue of reach measurement and optimization within the context of $k$-anonymity, a privacy-preserving model gaining traction across major online advertising platforms. We outline how to report reach within this new privacy landscape and demonstrate how probabilistic discounting, a probabilistic adaptation of traditional frequency capping, can be employed to optimize campaign performance. Experiments are performed to assess the trade-off between user privacy and the efficacy of online brand advertising. Notably, we discern a significant dip in performance as long as privacy is introduced, yet this comes with a limited additional cost for advertising platforms to offer their users more privacy.