Per Paper density - Wikipedia, I WAG 10# paper as having a thickness of .0017 inches = 1.7E-3 inches per sheet.
American style bingo cards come in 5.5E23 or 5.5E26 varieties depending on who you believe upthread. (sextillion vs septillion).
So assuming the smaller number, that’s a stack just ~1.5E16 miles tall. If it’s really septillions then your stack is 1.5E19 miles tall.
For English style bingo cards available in a mere 1.1E17 varieties, your stack will be a mere 2.9E9 miles tall.
IOW the short English stack will reach to more or less Pluto.
The taller of the two American stacks will reach 10 billion *times *farther than Pluto. In fact it’ll be about 2.5 million light years tall. Which is far enough to reach the Andromeda Galaxy Andromeda Galaxy - Wikipedia
And yes, I ignored the effect the stack’s gravity will have on itself. Certainly a recangular stack of paper roughly 5 inches by 8 inches by 2.5 million light years will generate enough gravity to tend to collapse into a sphere.