Suggest you re-read the last paragraph on page 93 and the first paragraph on page 94.This is just a thought experiment, because my previous understanding would have been that you loose any and all half dice. In other words, the LBs get 4 dice and the Bows get only 4 dice as well. Even if they had the same type of weapon, they would still only get 4 dice each.
Since bow are normally at the same or worse POA than LB you would have 4 LB dice and 5 Bow dice.


