"more than you can shake a stick at"

     [This is a fast-access FAQ excerpt.]
This 19th-century Americanism now means "an abundance"; but its
original meaning is unclear.  Suggestions have included "more than
one can count" (OED, AHD3), "more than one can threaten" (Charles
Earle Funk), and "more than one can believe" (Dictionary of American
English).  No one of these seems easy to reconcile with all the
following citations:  "We have in Lancaster as many taverns as you
can shake a stick at." (1818)  "This was a temperance house, and
there was nothing to treat a friend to that was worth shaking a
stick at."  (David Crockett, Tour to the North and Down East,
1835)  "Our queen snake was [...] retiring, attended by more of her
subjects than we even dared to shake a stick at." (1843)  "I have
never sot eyes on anything that could shake a stick at that."
(= "set eyes on anything that could compare with that", 1843)
"[...] Uncle Sam [...] has more acres than you can throw a stick
at." (1851)  "She got onto the whappiest, biggest, rustiest yaller
moccasin that ever you shuck er stick at." (1851)
   A connection with the British expression "hold (the) sticks
with", meaning "compete on equal terms with" and attested since
1817, is not impossible.
   OED staff told me:  "The US usages in DAE do appear to have a
different sense to that given in OED. [...]  All the modern examples
I've found on our databases conform to OED's definition so I think
this is still the most common usage."
   Merriam-Webster staff opined that the "count" interpretation
"works as well for 'as many as you can shake a stick at' [...] if
you take it to mean that there is no limit to how many of the
objects in question one could shake one's stick at. [...]  We would
consider 'A can't shake a stick at B' a different expression
entirely, with a meaning similar to 'A can't hold a candle to
B' [...]."
   In their 1897 work A Dictionary of Slang, Jargon & Cant,
Albert Barrere and Charles Leland suggested that Dutch immigrants
originated the expression using the Dutch word schok = "to shake
or hit."