I learned that some kids are just that way! I was always a big "play by myself" kid. My mother always told me that once my children became toddlers, I would have PLENTY of time to clean, cook, do laundry -even work on contracts that I took on. HA! What a joke! I learned that MOST toddlers do NOT play by themselves very easily or very long. I also have a great friend who was blessed with a child who is a lot like I was. He has ALWAYS played by himself for long periods of time. She could put the baby gate on his bedroom door, and he would play in there for 2 hours! She could turn on Saturday morning cartoons, put him in bed with her and go back to sleep -and he would sit there and watch! She's now finding out how the rest of us live with the 2 year old boy she has -there is no down time! I think it's really a personality thing. However most small children are not going to go play on their own for any length of time. Some do, but they're rare. My oldest just doesn't. He's 4.5 now, and he's gotten a lot better, but I've never had that down time. Even when we go to a bouncy play place, I watch other moms sit down and look at magazines, but not me -I have to be watching, jumping, sliding along with him.
My 2 year old, however, DOES play by himself! He won't do it for an hour or anything, but he'll actually go to his room or the living room and play with trucks and trains or look at books and sometimes I find myself in a panic because I realize I haven't seen or heard anything out of him in awhile! I'm so used to his older brother -it's shocking! So, sorry -but your 3 year old just isn't wired for it. He will get better about it though. As your 18 month old gets older, they'll also play together, and it's a wonderful thing!