When you fill the cp bar you can raise an attacks damage by 1. It doesn't seem like much, but it means attacks with a common damage quantity will now win ties.
I actually wish multiplayer was AI rather than live opponents, at least matches would be more frequent and run smoother.
I like the human aspect when I find a match and playing room matches with friends is fun. It's clunky though, Make a room, make a key, share the room number and key number then wait for friend to find the room and type in key number and then battle. No friend list, no clans, no FB or Twitter or login options or even gamecenter. It's bizarre that in this age of IOS gaming I have to jump through so many hoops to battle my friends in this game. When it works it is great and when you get a multi-player room game going with a buddy its a lot of fun.