This game is ridiculously fun. I think there's a lot of potential here. I echo pretty much everything that was said here especially point 5 and the other post about multiples of the same card effects not stacking. Also one of the cards didn't seem to work like I expected, "something happens when the opponent gains AP". I thought the effect would trigger at the start of my opponent's turn and any other time he gained AP but it didn't seem to work.
I think the randomness needs to be blunted a little. Losing to the first opponent of a run due to a series of unlucky draws is a little annoying. Likewise starting over after getting to the final boss because a freak lightning bolt destroyed four cards doesn't feel good. Perhaps some kind of check point that you respawn at if you reach a certain point.
I also think the matches are typically over too quickly or maybe they're just really swingy. It's like there's no volleying just a series of aces and it starts to feel like multiplayer solitaire (well single player multiplayer solitaire). I think that's partially due to randomness and partially due to the low health totals. There's no feeling of whittling down a tough opponent when a lot of single cards could win you the game on any given turn. There's no feeling of building a cool card engine because the match is over long before that.
Lastly, I agree that there needs to be a mechanic to cull cards from your deck between matches. Maybe the option to cull a card in lieu of gaining one or something similar.