Before Invoke Despair was banned, the presence of the card meant that The Cruelty of Gix was cast for its third chapter most of the time.
However, it’s now common for us to cast the saga at chapter one or two to get more value out of it.
If you have a Big Score or Atraxa, Grand Unifier in hand, or a blood token in play, with chapter two you can find the missing piece (either an Atraxa or a Big Score), and then discard the Atraxa at instant-speed before you hit chapter three on the following turn.
If you are not being pressured on the board, and you’re not worried about The Cruelty of Gix being removed, it’s often better to start the Cruelty at chapter two to fetch a card you want, and then return Atraxa the following turn. This way you get the card you were looking for instead of relying on finding it with the Atraxa, plus you get to reanimate Atraxa with open mana, so you can cast the spells you find off her straight away.
Be aware of the three life you lose on chapter two, and against decks like Mono Red, you actively never want to cast it on chapter one or two (casting it on chapter one will still lead to three life being lost the following turn).