Etymology

tell you what

Today it means: Introduces a compromise or arrangement where the interlocutor has some benefit or advantage. Full definition →

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The story

Ellipsis of I'll tell you what or I tell you what. The sense introducing an arrangement also corresponds to another, longer established collocation of I'll tell you what I'm gonna do or let me tell you what I'm gonna do.

Etymology from Wiktionary, CC BY-SA 4.0.