Conquer Club

Probably will make me sound like a total noob, which I am anyway.

Are the dice weighted to favor the defending army, or can my infuriatingly annoying losing streak be attributed only to dumb luck?

Both. The defender wins ties (though the attacker gets to roll 3 dice), but everybody gets bad dice every so often. Try sacrificing a virgin to the dice gods every month. They like that.

Dice are random and generated external to the site. (random.org)

However, since defender dice win ties, if you attack 2 on 2 the defender has distinct advantage. If you are attacking 3 on 2 the attacker has a probabilistic advantage:

Attacker wins - 2890/7776 = 37.17%
Defender wins - 2275/7776 = 29.26%
Both win one - 2611/7776 = 33.58%