What I've noticed with random is that the more cards I've collected, the less I get 1-stars when random rule is in play.

Of course every here and then I get a full 1-star deck and it just makes me laugh because it's funny. Since what are the chances for that to happen with 100+ cards when 22 of available cards are 1-stars, 26 2-stars and 33 3-stars? Not to mention 4- and 5-stars that can take one slot out of 5?