# 9. Combat¶

## 9.1. Land combat¶

Battlefield

Province battle board in staggered layout of tiles (as in the main map) with 24 tiles side length, 3 tile (capital is 6 tiles) wide city

Time

• 5 battle turns per game turn at most
• If the city is occupied at any time during the battle, the attacker has won. Battle is over
• If all attacking units are destroyed or fleeing or the player aborts the attack, the defender has won. Battle is over.
• Otherwise (city not taken but attacking units are still present), the battle continues the next turn keeping the actual strategic position but with reinforcement possible

Damage model

• Two units are in combat with attack values $$a_i$$ and strengths $$s_i$$
• Damage dealt is then $$d_i=\mbox{max}(s_i, c(s_j a_j / a_i + \Delta )),j\neq i$$ or in words: a constant modifier ($$c$$ about 0.1) times the weighted strength of the other unit (weight is ratio of attack values) plus a noise term math:Delta with variance approx. 0.2 but which cannot be higher than our own strength in total
• Damage is calculated for both units and then subtracted from their strength
• Units with less than 30% strength will not attack anymore but flee automatically

No auto resolution of battle

• Actually there is auto battle, you can let an officer take over which will use AI routines. But apart from that the real model is used – no other calculations.

Special bonuses

• Encirclement factor of provinces = Number of own surrounding provinces minus Number of provinces of the enemy divided by the sum of both gives up to 50% bonus for attacker or defender. Reason: avoid isolated provinces in foreign territory, favor straight front lines
• Sea invasion ignores Encirclement factor but gives fixed 20% penalty to invader because it is more difficult.