There were many times during testing that we accidentally rolled over ourselves in the second stage by playing too aggressively in the tutorial stage, so we're happy that playing against a copy of yourself provides a unique difficulty curve.
In the current build the moves are all one to one, so if the round continues longer then it won't have any moves to pull from. Because of this we've found that focusing on surviving early by playing a lot of cards in their defensive form allows you to roll over the opponent once they stop playing units. After the voting period, we'll probably cycle back to this and give the whole game a balance pass.