  The three armies you get by default are not actually by default  it is actually calculated by the total number of territories you have, divided by three. If that number is less than three, it is rounded up to three  hence the default you start with. Any continent bonuses are added onto that.
Let's take your example: He has sixteen countries, including the continent of Australia. Armies per turn:
Total number of countries (16)
divided by 3:
_________________________
= 5 (rounded down from 5.33) armies per turn
+ 2 armies for Australia continent bonus
_________________________
= 7 armies per turn
Does that help?
