Ongoing partnerships between transnational alcohol corporations and global social media platforms have transformed alcohol advertising in ways that undermine existing marketing regulations and threaten all forms of public oversight. In this paper I analyse this historic shift, arguing that new forms of programmatic alcohol advertising have emerged out of increasingly intensive processes of datafication on social media. Programmatic advertising is distinguished by increasing automation, turning advertising into a process of continually experimenting on the public to optimise advertising's "outputs", which now include conversions (sales). This experimental process relies on the delegation of agency to profit maximising, algorithmic machines that make alcohol advertising decisions with public health consequences. I contend that public health must now grapple with "algorithmic sovereignty": how private, corporate machines make decisions that challenge regulation and public oversight. Drawing on a case study of Meta's programmatic systems, I argue programmatic alcohol advertising exacerbates existing problems for the regulatory control of alcohol advertising on social media, while introducing entirely novel concerns. Machines make decisions in ways that are efficacious yet obscure, even to those who design and own them and to those who use them for marketing purposes. They allow for the maximisation of profit while obfuscating public oversight of the health impacts of alcohol advertising, and they make decisions in ways that are both predictive and pre-emptive, continuously nudging social media users towards consumption through altering, in real-time, the personalised content they encounter. This leaves established means for public oversight of alcohol marketing operating retrospectively while commodification of social life through alcohol advertising acts in the present to reshape the future. The machinic vision of programmatic alcohol advertising assesses social media users for their commercial utility, not as citizens with health needs, and may be producing evolving negative health outcomes that will only ever be understood in retrospect once their deleterious impact has become evident. Steps towards more effective public health interventions must begin with clearer recognition of these fundamental changes in advertising.