Should ties destroy both auragons?

I originally decided that when dream combat produces a tie (both players deploy the same auragon), both auragons are destroyed. However, I have recently wondered about reversing this. The underlying reasoning is based on how long the game takes to play. Each player will, on average undergo two battles each night. If ties destroy auragons, then each player will, on average, lose 4/3 auragons each night. Players begin the game with 6 auragons; hence, the game will take 4.5 turns. If, on the other hand, ties do not destroy auragons, then players will lose only 2/3 auragons each night, and the game will take 9 turns to play. 
Gee, it's pretty obvious that 9 turns is better than 4.5 turns. That decides the matter: ties do not destroy auragons.