How to fix the random rule :
-Merge the deck from the 2 players together.
-Pick randomly from it, without restriction, for each player.
-????
-Profit.

This would make the random rule what it should really be : random.
You may get awesome card from your opponent and he might get your crappy 1 star card, true randomness, and might create funny scenario if both players end up with full 1 star card.