What cycles the player through the drop cycle?
EDIT: Following the recent update as of 03/05/2016 the current chest cycle can be found HERE
Original Answer: The comments are right, and apparently also is the reddit post.
It is pre-determined when you get a drop by this updated list (to include new chests). I just got a giant, so I know exactly where in the list I am, and can start logging from there. Few things to note:
1. Having no free space, but wining a battle, moves you to the next chest. So In theory you can always get golden and above.
- The list might get updated or the entire system scrapped by Supercell at any time, given they are the developers and can do whatever they please.
- Having gone trough the list, it starts over from 9.
A win would push you forward in the cycle, regardless if you have a free slot or not. That's a win where trophies exchange place (eg. not against clan-member in a friendly match)
EDIT: What I've just red on this FAQ is having full chest slots and wining does not progress you on the list