<<Disclaimer: Verify this information before applying it to your situation.>>

this pretty much sums it up about relying on deli meats cut in the deli
counter;

"Unfortunately you can't.  One reason is cross contamination of
gluten-containing deli meats cut on the same slicer.  You can ask them to
wipe down the first as some people do; others only eat the deli from the
middle onces it's sliced, never from the ends.  Also, only certain meats are
gluten free. Boars Head (most items) and Hebrew National (most items) are.
"

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