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From AGEWiki

Terrain alters combat outcome in several ways. Most of the effects are quite intuitive: Difficult terrain and structures favor the defenders, cavalry is much more deadly in open terrain than it is in mountains, irregulars fight much better in difficult terrain ... .

How to read the terrain files

The source for information on terrain effects on combat are the terrain files. Normally, you'll find them in the GameData/Terrains folder of your game. It's more comfortable though, to have a look into the excel sheets AGEOD kindly offers to modders. The data we find there, looks like this:

(As there already exists an article about frontage and terrain, we'll focus on the direct battle effects.)

1. In snowy wheather, the maximum range a battle can reach in wooded hills, is two. So don't mind to bring your siege guns into a battle under those conditions - they cannot outplay there strength here.
2. Regulars are heavily penalized in our example. An element belonging to a stack with defensive command posture will have it's hitchance multiyplyed bei 0,75.
3. Irregulars really shine under the conditions of this battlefield. They are able to conduct sneaky attacks and make it very, very difficult for the enemy to hit them. A regular infantry element shooting at an attacking irregular element would have its hitchance multiplyed by another 0,81 (see Combat Explained for more information about hitchances).
4. Cavalry, on the contrary, obviously does not like the battlefield. The great strength of heavy cavalry, the usually high troop quality, (discipline) is reduced by 3 points when there's gale. This makes hits in assault combat much less likely.
5. It's also quite ovious that artillery impact will suffer under those conditions. It's heavily penalized in wooded hills. When there's a storm at top of it, you can be thankful that there's always a minimum hitchance of 5% for every element on the battlefield, because the regular hitchance would be multiplied by 0,25.

To this effects, you might add the impact of river crossings or amphibious landings.

A wise commanders will always pay great attention to the battlefield that he fights on. If not, he might be overwhelmed by an enemy with the right troop composition and combat stance.