Quite smartly, you get xp scaling on length of games (there may be other factors, I'm sure there are i.e. vs basic ai, expert ai, real people, friends, real people ranked, etc.) You certainly don't have to play against the expert AI to get to lvl 10.
This is a simple way to stop people quitting games vs friends to lvl up quickly!
@Shraeye
I agree, that Rogue is essentially unplayable without any extra cards as there are no combo cards in basic. If you want to see extra cards, another way is to do arenas, though you do risk kinda wasting the gold if you arena without any experience, but you always get a pack.
@Kirian
4 wins is quite respectable in your first bunch of arenas, seems harsh not to even have seen an epic yet! Legendaries can be quite rare. Paladins are probably my strongest char in arena, because the character commons are all great (Truesilver, Consecration are both amazing) Aldor Peacekeeper and the Divine shield giving guy are also very strong.