If you have a friend who you see is currently playing, it would be good to send them an invite which would only come visible to them AFTER their current round is over (provided you are still connected and free at that time, otherwise the invite should drop away).
Alternatively, or perhaps in addition, it would be good to get a specific notification of when your friend comes free - other than the noise. Maybe a "Notify me" button specific to player A for when they are finished a round or when they come on line.