II. Assaulting Your Enemies
You may now assault any opponent's region from one of yours, as long as both regions are adjacent and your assaulting region has a minimum of two troops. This part is optional in that you may choose not to assault anyone.
Each time combat is initiated, the game engine will generate a random intensity cube for each troop involved. The outcome is determined by the intensity of the assaulting troops versus the intensity of the repelling troops. There are 6 possible intensity cubes that may be assigned, listed here from weakest to strongest:
The more troops involved on either side, the better the chances that side has of winning. But not all troops in the regions are necessarily involved. To be more specific, the game engine will assigned a random intensity cube for each assaulting troop, less 1 troop that stays behind, up to a maximum of 3 troops. Likewise, the game engine will assign a random intensity cube for each repelling troop, up to a maximum of 2 troops.
The outcome of combat is determined by comparing the strongest intensity cubes of either side. If the assault was stronger, then the repelling region loses a troop. If the repel was stronger or equal, than the assaulting region loses a troop. This process is repeated once more if other troops remain involved on both sides.
If you destroy all of the troops in your opponent's region, you will then have to occupy it right away by advancing some of your troops (but not all and at least 1) from your assaulting region to the conquered region. If you conquer a player's last region, (thus eliminating him/her from the game) the former opponent's spoils become yours!
During this part of your turn, you may assault any adjacent regions, as many times as possible, until you decide to stop. For example, you may assault one or more times from one region, switch to another region and then back to the original.
When reading this from the notes page, it implies that the attacker/defender are given an intensity level.