Meanings
Usage patterns
〈事〉という遊びをするto play a game called ~
The children played a game called hide-and-seek.
〈物〉に遊びがあるthere is some play/slack in ~ (mechanically)
This steering wheel has a bit of play in it.
〈事〉に遊びを持たせるto allow some leeway or flexibility in ~
I left some slack in the plan just in case.
遊び半分で〈動詞〉to do something half-jokingly, not seriously
He started the job half as a joke, not taking it seriously.
Expressions
遊びに行くgo out to have fun; go on an outing; go visit (a friend) 遊びに来るcome to visit; drop in; come and stay 子の日の遊びne-no-hi-no-asobi; New Year's herb gathering and pine pulling on the first Day of the Rat