A lot of people have been trying to break rat cage and relics in general, and here is the build that I've found the most success with and climbed from gold to top 200 masters with 65~70% winrate. This is a pretty aggro deck that is able to out-gas a lot of opposing decks thanks to being able to play 1 mana 3/3s and 3 mana 5/5s. Also, Courtier's ability often means that you are guaranteed to topdeck 100x better than your opponent. This deck is pretty hard to master and play well since it has a lot of sequencing decisions, need to know when to sacrifice units to push damage, as well as knowing which mode of DoK to use (I have used all 3 modes about equally) and which relic to fetch.
This deck wins by doing any combination of the following 3:
1) Rats+relics+obelisk and flood the board
2) Courtier+relics and bury them in card advantage
3) beating them down with 1 mana 3/3s and 3 mana 5/5s
I mull super aggressively with this deck and don’t keep hands unless they have either courtier or cage or something like t2 teacher with a t3 follow-up. Note that teacher is EXTREMELY good with this deck since weights count as a relic, so going something like t2 teacher, t3 rat cage+courtier often ends the game on the spot.
Bore can be an issue if they get it early enough, but the cool thing about this deck is that if you get far enough ahead, you often dont care that much about having all your relics removed since you just have lethal with a+space in one or two turns. I've had games where my opp goes borex6 to remove all my relics into concede =P