My boy is 20 months. He will sometimes play alone in his room. He likes to open and close the drawers, push cars along the windowsills, play with the kid sized punching bag, and just look at books or musical toys. He manages to entertain himself for as long as 15-20 minutes at a time, and his ability to concentrate on any given task is improving with age and with daycare. He's had an independent/ self sufficient streak from the outset.
Our circumstances don't compell us to require him to play alone in his room. He's an only child, both of us work so its not as though we were hoping for and actively cultivating this independent play so that we could get a moments peace. He just does it naturally.
When he was truely little, I thought it was a bit odd. Older/ wiser/ more experienced parents told me not to undermine this excellent trait because I selfishly want to play with him. They said there would be opportunity enough for interaction. They were right.
So by way of synopsis. He has a natural inclination. We proved lucky. We were smart enough not to undermine this proclivity.
Also, we are in a small 2 bed apartment. So I am steps away and always within earshot, even behind closed doors.
good luck to you and yours,
F. B.