↑ Official Risk Rules.. Page 6 shows relevant information
"Territories. At the beginning of every turn (including your first), count the number of territories you currently occupy, then dicide the total by three (ignore any fraction). The answer is the number of armies you receive. Place the new armies on any territory you already occupy.
Example: 11 territories = 3 armies
14 territories = 4 armies
17 territories = 5 armies
You will always receive at least 3 armies on a turn, even if you occupy fewer than 9 territories."