How deep can discounts on Amazon get?
As a general practise discount can be quite big (I've seen -50% off) for a small set and tend to be much lower (around -25% off) for a large set.

Discounts tend to vary even during the same day. So it is worth keeping an eye. Some sites, like Brickset tend to announce LEGO sales too. They even have a tracker for Amazon and other services. I suggest to look here to have a sense of understanding how much discounted the set can get.