I didn't even know we could display battery cycle count. But, it's at About Phone > Battery Information. Cycle count = 377.
I regularly charge my phone to 100% in the morning and when I wake up the next morning, it's usually in the 60-70% range.
EDIT: And, looking at my original post, I now see a whopping great grammar error. When I said "my phone has now entirely discharged twice in less than one day," I meant "twice, now, my phone has entirely discharged in less than one day." So, two episodes on two separate days. Not two episodes in one day. Sorry, again.