As idioms, "work out", "play out" and "turn out" may sometimes be interchangeable but they do have their own inferences.
"Work out" and "play out" are largely interchangeable. They both can be used to refer to the result of events, or outworkings. The only difference is that "work out" is more literal, referring to outworkings, whereas "play out" is a sporting analogy that would literally refer to the end result of a sports game but is used to refer to any situation in which an end result is anticipated.
"Turn out", of the three idioms in question, can uniquely be used to refer to a discovery. For example, "my teacher turned out to be nicer than I imagined".
can we substitute "work" or "play" for "turn"?
These words have very different meanings in isolation and are not usually interchangeable, except perhaps for in other idioms, for example, "close of play" is another idiom referring to the end of a working day. The literal meaning of 'work' and 'play' could not be more different.