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One of my players would like to train a unit of infantry with the ability to use military oil as a throwing weapon. How would I use military oil from a unit perspective? Does it require training to use, in the same way a crossbow or a longbow does? How do I handle missed attack throws?
I haen't written rules for troops armed with military oil because it didn't show up in history as a weapon on the battlefield until the 20th century (the molotov cocktail), when gasoline was cheaply available. If molotov cocktails were widely available as a battlefield weapon, a lot of ancient battles might have been diferent!
For a unit to be trained to use military oil on the battlefield, they'd have to be drilled the same way firearms troops were drilled to be able to methodically handle flame and combustibles while under the enormous pressure of life-or-death combat. Doing so would be expensive. In ACKS we rate military oil as an extremely expensive item - each flask of military oil costs 2gp. 20 arrows costs 1gp so that's 40 times as expensive. If you assume they can train on ordinary oil, that's 3sp, or 6 times as expensive. At a minimum then I'd put their wage rate at six times that of bowmen - 9gp x 6 = 54gp per month - with an equivalent multiplier in cost to train and equip. You might even go higher.
To put them into Domains at War terms. I'm just riffing here:
Let's assume that the flasks of oil hit. Then we're talking about 1d8 points of damage. According to Domains at War, that should work out to Unit Number of Attacks of (120) x (1 + .35) x (4.5) / (60 x 4.5) = 2.7 attacks. The flasks will hit if the attack throw of the unit is exceeded on 1d20, regardless of target AC.
Now let's assume that under combat conditions, the flasks of oil are being hurled in volleys in the general direction of enemy units and deal splash damage in 5' radius even if they miss. If we assume that the front two ranks throw, and use a 120-man unit with a frontage 20 wide and 6 deep, aiming for center of mass of the enemy unit, then 20 wide x 2 ranks x (5^2 x 3.14) = 3,140 square feet. Meanwhile the unit is only (60' x 40') 2,400 square feet. So each target is likely to face 1.30 "splashes". Each splash deals 1d3 points of damage, averaging 2 points; 2 x 1.3 = 3 points of damage. Applying the Domains at War rules again, that would yield 1.8 attacks, which rounds to 2 attacks per round. But they would get a saving throw against each to avoid taking any damage.
A unit of normal men will have an attack throw of 11+ so 50% of the attacks will hit. That suggests average damage (because each D@W attack does 1 damage) of 2.7 x 0.5 + 1.8 x 0.5 = 1.35 + .9 = 2.25, or 1.35 + 4.5 = 1.8 on a successful saving throw.
You could handle this by ruling that the oil-equipped unit automatically hits an enemy unit within 2 hexes. The enemy unit must make a save vs. Blast. If it fails the save, it takes 3 uhp. If it succeeds, it takes 1d2 uhp. On the subsequent round, it takes 1d2 uhp, or no damage on a successful save.
But if we do that, we ignore the chance of mishap from oil. Each time the oil-equipped unit attacks, it's likely to lose two men (5% chance mishap, twenty men per rank, two ranks throwing oil). Since a unit is destroyed when 50% of its men are dead, that suggests (120/2 / 2) = 30 rounds; if the unit has 6 uhp, then that's 6/30 = 0.2 uhp per round, or a 1/5th chance of a uhp being lost with each attack. So let's say that the gameplay would be as follows:
1) Oil-equipped unit rolls 1d20 to attack. On a roll of 1-4, it suffers a mishap and takes 1 uhp. On a roll of 5-10, it splashes the target unit with oil. The target unit takes 2 uhp, or 1 uhp on a successful save vs. Blast, and is on fire. On a roll of 11-20, the target unit takes 3 uhp and is on fire. Loose units can withdraw to avoid damage as usual and if they reduce damage to 0 are not on fire. Units on fire suffer 2 uhp at the end of their next activation, or 1 on a successul save vs. Blast.
Anyway, that's something to go from.
Urban settlements of Mark 4 or higher are considered separate domains in the eyes of a conquerer and must be sieged like a stronghold. What is the stronghold value of a city? Is the gold being used to found/grow a market actually a measurement of the defenses of the city? Or is it some kind of hybrid between agricultural investments and defenses, and how should I measure that?
Right. The idea is that you can't just ignore a big city and claim you've conquered a domain. Sometimes the ruler's stronghold will be in the city, though, and that's a complicating factor. I would say that if the domain stronghold is outside the city then use the urban investment value of the city as the stronghold value when besieging it. If the domain's stronghold is IN the city, then add them together to find the stronghold value.
What is the purpose of siege engineers? An army can create constructions without them. From what I've seen there isn't a clear ruling on "who" can handle a siege weapon, other than through the proficiency itself, which would lead me to believe that the rank and file can't operate. However, in the elite troop section the stated proficiency only increases construction speed. They are the only specialists specifically listed as being able to operate them, but I'm aware there are a lot of nuances within the books that I might miss. S.O.S?
As far as why you need siege engineers, per Domains at War: Campaigns, "Each construction project must be overseen by a construction supervisor. Supervisors must either be siege engineers or engineers. A siege engineer may supervise one construction project of up to 25,000gp construction cost. An engineer may supervise one construction project of up to 100,000gp construction cost. Multiple engineers or siege engineers may work together to supervise large projects." (Strictly speaking then if you have engineers you don't need siege engineers, but siege engineers cost much less than engineers and are more common so they are preferable for small projects.)
As far as operating artillery, any troops can crew artillery, but "artillery crews without an artillerist specialist reduce their rate of fire by half." (Domains at War: Campaigns). Therefore you need one artillerist per artillery piece if you want to maximize rate of fire.
In the setting I am currently running, there is a monastic kingdom that has a higher than normal urban population. This in turn has made a lot of the cities large enough to affect each other, always more than 2 at a time, sometimes 4 or 5 as there are rivers webbing out throughout the area. The example in core lists what happens between two cities, but what about 4 cities connecting to each other? How should I handle their trade influence modifiers? Simply placing them side by side in an excel sheet and changing the modifiers by two as i go? Finding the average? I'm at a loss with this one.
There's no "right" answer. When you have multi-factor trade relationships things could (in reality) occur in all sorts of ways. The main point of the trade modifiers is to avoid circumstances where two cities that are right next to each other have trade routes that are incredibly profitable, and to allow for the influence of major trading hubs.
As a rule of thumb, the more urbanized and commercial your realms are, the more the market will be efficient, and the flatter the domain modifiers will be. So for instance, if you have four cities in a linear relationship of A -> B - > C -> D, prices can vary sharply between A and D. On the other hand, if all four cities are so large that they all trade directly with each other, then the prices between A and D will be much closer.
Lastly, is being a beastmen and also chaotic a requirement? I tend to run a bit more loosely with those rules, as I tend to treat beastmen as a bit more natural to the setting(or at least being in existance so long it's a mystery how they truly came to be) and there are kingdoms in my setting that use orcs raised from childbirth as janissaries(making them lawful), but I'd like to see how people tend to handle the concept. Are chaotic tribes doomed to always fight against civilization? Or is it possible to eventuallly convert them?
That's entirely up to you. I make beastmen inherently chaotic because otherwise my (kind-hearted and progressive) players spend a lot of time agonizing over whether it's permissible to kill them. They are literally still arguing about baby kobolds from a campaign I ran in 2004! By making the beastmen into evil chaos monsters, the moral choice is simplified. I wanted the players to be able to have the firm moral assurance of Ripley in Aliens - "nuke them from orbit, it's the only way to be sure". There is ample opportunity for more nuanced investigation of free will, moral choice, salvation, and so on if that's your preference, and you won't break anything mechanically.