This is a 19th century Americanism now means "an abundance". The original meaning is unclear. It has been suggested that it means "more than you can threaten" or "more than you can count" or even "more than you can believe".

The earliest reference of this was in 1818, "We have in Lancaster as many taverns as you can shake a stick at."
The term most probably comes from the Native American use of a device called a "Coup Stick". As a symbol of bravery, a warrior would often take a stick into battle, instead of a weapon. By touching a foe in the heat of battle, the brave proved that he was skilled enough to close with the enemy and touch him without getting hurt. It was also used when taunting the enemy, literally shaking a stick at them in contempt. This was called counting coup.

In modern usage, the term has come to mean an impressive array of goods or a situation not easily dismissed by waving one's coup stick at.

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