Dblade:
So am I correct in thinking ambidexterity doesn't matter in this tournament or not?
To be slightly more clear, there is no 'off-hand' when fighting unarmed. Boxing, Brawling, Karate, and Judo give single hand parries, so you may Parry without penalty with both hands (individual skills have individual penalties for parrying some types of attacks). Wrestling and Sumo require both hands in a Parry, so you don't have 'two separate hands' to Parry with.
Each hand's iterative parries are tracked separately. So, if you Parry twice with your right and once with the left, your first parries with each are at no penalty, the second with your right is at -4*. Further parries with either hand are at cumulative -4* (-8 for the third right hand, etc)
* -2 with
Trained by a Master or
Weapon Master (Unarmed Skill).