#probability

Counting unique visitors sounds like a set: add every user id, read its size. At a few billion ids that set is tens of gigabytes, kept only to produce one number. Do you need to remember who visited to count them?

A green tick appears before you've stopped typing, and behind it is a list of a billion taken names. It isn't one clever database query.

A 32-bit hash has 4.3 billion possible values. How many items can you hash before a collision is a coin flip? Not billions: about 77,000.