How does Twisted Fate's rotation for cards work?

I can't tell how it works, I feel like it may be on its own timer that constantly counts. However I also feel like it might just go to the next card in the list, since in fights it always seems to do that.

So, how does it work?

Side note: you can use your w to reset your auto slightly, depending on your timing. It feels great chaining it into an E proc.