To have a secret plan, idea, or advantage that you haven't revealed yet; to keep something in reserve.
This phrase originated in the 16th century when clothing had very wide sleeves that could conceal objects. Magicians and card cheats would literally hide cards or tricks up their sleeves, and the expression evolved to mean any concealed advantage or secret plan.
The phrase captures the theatrical nature of strategic thinking - like a magician, someone with something 'up their sleeve' controls the timing of revelation for maximum impact. Interestingly, modern clothing rarely has sleeves large enough to hide anything, yet the metaphor persists because it perfectly describes the feeling of having a hidden advantage.
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