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Phrase(s): play both ends (against the middle)
Fig. [for one] to scheme in a way that pits two sides against each other (for one’s own gain). • I told my brother that Mary doesn’t like him. Then I told Mary that my brother doesn’t like her. They broke up, so now I can have the car this weekend. I succeeded in playing both ends against the middle. • If you try to play both ends, you’re likely to get in trouble with both sides.
McGrawhill's American Idioms And Phrasal Verbs