Friendly games are matches where you can directly invite your friends to a game.

To initiate a friendly match, go to the Friends tab and tap on the friend you'd like to play with. You can invite your friend to a live match, or a casual match.

You can play a live match for free but this requires your friend to be idle and online. On the other hand, casual matches use 5 energy while giving you and your friend 72 hours to complete a turn.