DD is almost 10 years old - last year for Christmas I got her an easel, acrylic paints, some dry pastels, paint brushes. My MIL also got her a scrap booking kit that has kept her busy as well as a fun way to conserve photos and souvenirs.
My kids are 2,4, and 13. The older two took some "training" we would start a game (blocks, dolls, art) play for 10-30 minutes depending on age/mood and then have to leave (cooking dinner, check the mail, go to the bathroom) when we checked back in they usually are having fun on their own. We slowly cut back on getting the play started for them and would just suggest the games they could play. The youngest kid just started that way- a few minutes of parent playtime then let her have fun.
We do make sure there are total parent involvment games (art, board games, etc) each day. As long as they get time everyday with you then they don't mind being on their own.
Play is about reinacting experiences and relating it to what they see/real life. They are experimenting with life. Anyway, How do you encourage them to play independently? Give them the neccessary tools and they will soar. I do this for a living, feel free to message me :)
I only have one at home now. Sometimes I feel like I cheated my youngest out of something. I have to older kids that were only 18 months apart and they grew up together thick as thieves until their teens. Then some kind of rift formed between them. They always had each other to play with when they were little and on rainy days when they were older and had their own friends. I had my youngest when they were 11 1/2 & 13. By the time my baby was playing they weren't intersted in her and then they were gone. So my youngest is 10 and basically living the life of an only child. She plays independantly but not like the older 2 did, and certainly none of them played the way I did. Technology has ruined something for kids.