play out has 4 distinct synonyms spread across 1 of its 4 senses. Each sense below keeps its own list, because a synonym belongs to a meaning and not to a word: swapping one sense's substitute into another sense's sentence is how a thesaurus makes writing worse. WordNet records no antonym for it — antonymy is a relation between word forms rather than concepts, so it is deliberately sparse.
Counts are distinct word forms across every sense. A synonym that appears under three senses is counted once here and shown three times below, under each sense it belongs to.
perform or be performed to the end
“How will the election drama be played out?”
play to a finish
“We have got to play this game out, even thought it is clear that we have last”
become spent or exhausted
“The champion's strength played out fast”
Synonyms, antonyms and the broader and narrower relations for play out come from Princeton University’s WordNet. Full sources and licences.