My 3 year old DD literally never wants to play by herself, I love playing with her but can't do it all of the time.
It causes major problems if I'm not constantly available to play. She is very stubborn and refuses to play on her own, if I do manage to get her set up doing something it lasts maybe 2 minutes absolute maximum. She will pretend to fall over or hurt herself to get my attention.
Friends of hers will play upstairs for up to an hour or so alone but I'm starting to wonder if I'm being unreasonable to expect this? It's a constant battle and it's not making either of us happy.
If your child of a similar age does play independently, what do they play with for a decent length of time?