Number of occupied territories divided by 3 and rounded down.
Example, player occupies 8 territories: 14 / 3 = 4.7 Player can take 4 armies.
Example, player occupies 2 territories: 2 / 3 = 0.7 Player cannot take any armies.
Reminder: if you've decided to use the Reinforcements Special Rule, the player has the right to 1 additional army.