Explain how 'run_once' interacts with 'serial'

docsite/rst/playbooks_delegation.rst

@@ -182,13 +182,18 @@ This can be optionally paired with "delegate_to" to specify an individual host t
           delegate_to: web01.example.org
 
 When "run_once" is not used with "delegate_to" it will execute on the first host, as defined by inventory,
-in the group(s) of hosts targeted by the play. e.g. webservers[0] if the play targeted "hosts: webservers".
+in the group(s) of hosts targeted by the play - e.g. webservers[0] if the play targeted "hosts: webservers".
 
-This approach is similar, although more concise and cleaner than applying a conditional to a task such as::
+This approach is similar to applying a conditional to a task such as::
 
         - command: /opt/application/upgrade_db.py
           when: inventory_hostname == webservers[0]
 
+.. note::
+     When used together with "serial", tasks marked as "run_once" will be ran on one host in *each* serial batch.
+     If it's crucial that the task is run only once regardless of "serial" mode, use
+     :code:`inventory_hostname == my_group_name[0]` construct.
+
 .. _local_playbooks:
 
 Local Playbooks