"Playing with her doll" OR "Playing her doll"??

When we play with something, it's either
-we spend time amusing ourselves with it
OR
- we fiddle/move it about using hands, etc.
"The boy is playing with his pencil." (he's fiddling the pencil in his fingers.)
"She always plays with her doll." (she usually moves her doll with her hands and makes herself amused playing with it)

When we play with someone, that means we play together with him/her.
"I play with my sister."

However, we use play something (without 'with') to show that we 'really take part in that playing activity/game'.
E.g.:
I play the guitar. (NOT 'I play with the guitar.')
I play chess everyday. (NOT 'I play with chess everyday.') 

Think!
Is it 'I play the ball everyday' OR 'I play with the ball everyday' ?

If you play with the ball, that means you take the ball and move it or bounce it without any rules.
However, when you play the ball, it could mean that you play the ball in a game such as football, etc.