How can an Ansible playbook roll out a new application version to many servers without downtime?

Update the servers in batches (for example 10 at a time). For each batch: take it out of monitoring and load balancing, stop services, deploy, then reverse those steps before moving on.

* Only one batch of 10 is out of service at a time, so the rest keep serving users. *

For each batch of 10 application servers:

1. Stop monitoring, so the planned outage doesn't trigger alarms.
2. Remove from load balancing, so no user traffic reaches these servers.
3. Stop services.
4. Deploy the application.
5. Reverse steps 3, 2, 1: start services, put the servers back into the load balancer, re-enable monitoring.
6. Move on to the next 10 servers.

Because only one batch is out of service at a time, the remaining servers carry the traffic and users see no outage. This is called a rolling update. In a playbook, the batch size is set with serial: 10, and the six steps are ordinary tasks. Orchestrating several systems in order (monitoring, load balancer, app servers) is exactly where a push-based tool shines.

Go deeper:

• Controlling playbook execution: strategies and more (official docs) — serial as a number, percentage or ramp-up list of batch sizes.
• Controlling where tasks run: delegation and local actions (official docs) — the official example of pulling web servers out of a load balancer with delegate_to during a serial rollout.
• Blue Green Deployment (Martin Fowler) — the main alternative zero-downtime pattern, for comparison with rolling updates.