Let me suggest a rule change right off the bat: Allow only the loser of the previous game to change their decks between games. That will ensure some strategical considerations instead of just randomly choosing one deck you have. Since you know nothing about the opponent's 3 decks, you cannot really give any thought as to what deck to play. So you might as well roll a dice.
If only the loser is allowed to change, s/he might at least give some thought to it.
so fer example.
I lose game 1. I'm allowed to change my deck my opponent is not.
I win game 2. Only my opponent is allowed to change. He thinks about it but doesnt change.
I win game 3 too. My opponent thinks about it and changes.
I lose game 4. I can change my deck.
etc etc.