Bug or "feature"? The oracle is linked to your account, not your login session, so you get cards and electrum that it gives you. Plus, the game remembers when you used it last. Why isn't the prediction/pet part linked too?
I know most people won't log in, do oracle, and then log out, but I'm busy in the mornings, and sometimes don't get a game in. Today, it's a feature, because somehow I doubt my gnome rider pet is going to be enough to overthrow rainbow. So... I could just log out, and log back in for a random FG.