Iceland survived with anarchy for over 290 years without any large scale civil war. Ireland lasted for 1000 years. They collapsed when they had become less anarchic and/or when they were invaded by armies of foreign non-anarchic states.
In an anarchy it doesn't matter who has the most arms, because you cannot simply order one group of people beyond their free will to go fight another group. Anyone who had leadership of any group was at the mercy of whether or not the followers agreed with who they agreed upon as the leader. A leader comes about as other people willingly follow, because they feel that the leader is going to lead with their best interest. If a leader wants to fight another group of people and the followers do not feel the need to attack, they can simply ignore the leader and the leader would be left to fight another group on their own or possibly with small support against what they individually consider an "enemy" of unknown size and strength.
People will go with ruling that is profitable, and war is not profitable.