I've seen the posts about the order of the chest cycles; but, I have not seen a way to figure out how many I have opened. It would be nice if it was a 1:1 win:open ratio... but... I have played a LOT of games with full chests slots. As I know this doesn't progress me through the chest order... How does one figure out where they are?
Start a list and see where it overlaps with this list. It may take a bit, but you should be able to find it out as soon as you hit one of the more rare chests, provided Supercell hasn't changed the order.
Since the cycle repeats itself, if you've played for long enough it can be difficult to determine where you are quickly, but as others have mentioned it all comes down to pattern matching. agent86ix put together a Chest Calculator which you can use to enter your recent Chests and get a hint at one or multiple places you may be in the cycle. Going as fast as you can possibly open chests (and assuming you don't gem), the Chest Cycle takes a little more than 40 days, so since the game has not been out long yet it is likely that you are in a position below 240. That, plus the number of Magical and Giant chests you've received, plus the pattern of the most recent 5-6 Silver/Golds you've received should help you nail it down.
Entering your player tag on http://statsroyale.com/ will let you see your position in your the chest cycle showing your upcoming chests and even offers
Although starting a list may be helpful. The cycle is fairly monotonous and if you don't have a remote idea where you might be, It's going to be very difficult to find yourself.
As suggested on the reddit talking about the cycle, the best bet is to wait for a magical or giant chest, and then count from there.
Super magical is random and not part of the lest, hence it won't help you get your bearings around.
Something worth pointing out though, is the list is not applicable to everyone, and so far I haven't seen any reason why some players report it's 100% accurate, while my friend for instance, and many others, claim the list is not accurate for them.