How many senate votes totals are greater than the number of senators (like today’s 51-50 vote)

It seems to me that the number of Senate votes decided by the President of the Senate (aka “the VP of the US”) is quite low.

I can only remember this happening a handful of times in my life (and I’m old enough to have voted for Walter Mondale for president).

But maybe it happens a lot, and I just haven’t been paying attention.

Also, has there ever been a tie breaking vote case with a less-than-full chamber? (For example, a 49-50 vote when two senators were absent.)