One of the reasons that I have a number of players on a friends list is that I can have a better chance of playing a multi-player game with people I know will be well suited to the group. Random players are not easy to find and may not fit the overall group.
You have played 4142 alternate shot games but have only 2 "friends". Why did you not send friend requests to some of these people you played with? If you had 200 friends you would find some who are ready for a game and might join you when you are trying to form a group. And some of the people who have joined your group might suggest some of their friends who are available. It really is not that hard to fill a foursome if you have a list to work with.
And surprise, surprise; some of these 'friends" might send you invitations to play.