Turn up for the book

Couldn't find any reference to this on the site - anyone know the origin ?

I would guess it comes from betting, especially on horse races. The 'book' is the record that a bookmaker, ie a taker of bets, keeps. Odds are placed against each horse in a race. If one does much better, or worse for that matter, than expected it's often called a 'turn up for the book'. However, why 'turn up' eludes me.