# Self Indulgent and Gratuitous Maths

I’d consider myself a bit of a maths geek (yes that’s maths not math America) and it’s one of the aspects of wargaming that I love the most. The statistical analysis of your different tactical options, or Math-hammer (should be Maths-hammer… or Math-hammers?) as it’s commonly known because of you guessed it Warhammer just really floats my boat for some reason. In a very real way if you’re creating your own wargame you can’t avoid using maths, calculation of points values, or to simply make sure that weapons are most effective against the targets they’re supposed to be effective against.

In my own 15mm Fantasy battle game now called Armythica so I guess that makes this Armathsica I have a simple mechanic designed to give a player a little more decision making to do. You can have a unit ‘focus’ before it attacks an enemy. Focusing allows a unit to either increase their attacks stat by 1 (the number of dice they roll when they attack) or increase their cleave (armour penetration) by 1. As you can imagine each unit will have it’s preferred option, units with good armour penetration already will go for the buff in attacks, units with a good amount of attacks will probably prefer the buff to their armour penetration but this will also vary depending on the target each unit is facing.

I’ve recently added a third element, which hasn’t even been written in my notes for things to add to the rules yet. This third element was to solve a problem my original rules had created, although they were solid and worked rules sometime lead players to make decisions that their real world (or fantasy world) counterparts never would. Focusing a unit became more powerful than charging and attacking first, so units tended to not want to charge each other as it would be more effective to goad the other guy into charging you first. So to counteract that I knew I needed to buff charging.

Now when a unit charges you can re-roll any dice that fail to hit once each. so my big maths problem was set… what’s better in any given situation when your unit is facing off against your enemies unit?

A) Charge and get the re-rolls to hit.

For those playing along here’s how my current rules work for attacking:

Before attacking if a unit is in base to base contact with an enemy unit they can make a shuffle move. Each figure in the unit can be moved up to 1”. If a figure in the unit was in base to base contact with the enemy unit that figure must finish its move in base to base contact with the same enemy unit. Then the unit attacks:

• When a unit attacks first total the number of dice they will roll when they attack. This total is the number of figures in range of the enemy unit multiplied by the ATT (attacks) value of the attacking unit. You can split a unit’s attacks against different enemy units. If a unit is in base to base contact with an enemy unit or multiple enemy units only those units can be the targets of attacks. Any additional attacks gained by special rules can be allocated to any target unit.

Example – A unit of 10 Dwarfs is attacking a unit of Elves. 8 of the 10 Dwarfs are in base to base contact with the Elf unit. The Dwarfs have an ATT of 2 and so roll 16 dice.

• Each 4, 5 or 6 rolled in the attack counts as a successful hit. If the target unit is completely in cover and you are making a ranged attack against them each 5 or 6 hits. If the target unit is completely within a fortification and you are making a ranged attack against them each 6 counts as a hit. In any case each 6 rolled allows you to roll an additional attack die.

Example – Of the 16 previous dice 8 are hits (rolls of 4, 5 or 6). 2 of those hits are 6s and so 2 additional dice are rolled. One of those additional dice hits and is also a 6 so a further additional die is rolled; it is a 4 so another hit is scored. 10 hits in total are scored.

• Reduce the PRT (protection) of the enemy unit by the CLV (cleave) value of your attacking unit, and then divide the total the number of successful hits by that value. The enemy unit’s PRT can be reduced to a minimum of 1 regardless of the CLV of your unit. The final result is the number of damaging hits. A partial hit also counts as a hit, for example if you do 3.5 hits you actually score 4 hits.

Example – The Elf unit has a PRT of 3, the Dwarfs have a CLV of 1. The Elf unit’s PRT is reduced to 2 and the 10 hits are divided by that, leaving a total of 5 damaging hits.

• You opponent then rolls a die for each damaging hit against the VIT (vitality) of their unit. Each die that scores equal to or above their vitality is stopped. Each die that scores below their vitality causes a wound on the unit. Most units have a WN (wounds) characteristic of 1 and so for each wound a model is removed. Some units have multiple wounds and in this case a single figure receives all the wounds until they are removed before moving on to other figures.

Example – 5 dice are rolled for the damaging hits on the Elf unit. Their VIT is 4+and they have 1 wound each. Three of the dice score lower than 4 so three Elves are slain.

So let’s take a few basic units against a few basic targets and test out the various options available. I’m making a few assumptions here, mainly being that you’ll most likely be able to get five models from your unit to attack, since even if you choose to receive the charge you won’t be taking models away from the unit that are in prime positions to attack. Most units are 10 models, and so even if you lose 3, you’ll still get those 5 attackers.

So first up Elves with two handed weapons against some Dark Dwarf Halberdiers:

The Elves have 2 Attacks each with a Cleave of 2, an important thing to note here is that any Elf units get D3 additional attacks. The Dark Dwarves have a Protection of 3, Vitality 4+ and 2 Wounds each.

Charging the Elves score 10.5 hits, which equate to 10.5 damaging hits after dividing by their Dwarves Protection since it’s already reduced to 1. 5.25 Wounds after Vitality saves and therefore 2.625 kills. I think my maths is correct on this one, incorporating the exploding 6s is very difficult.

Receiving the Charge and then focusing their Attacks for the Elves works out to 2.479167 kills, slightly less and as expected focusing their Cleave is the worst option since their natural Cleave already reduced the Dark Dwarves Protection to 1 the lowest the rules allow. They only score 1.75 kills in that instance.

Elf Swords and Shields up next (1 Attack, 0 Cleave) against those same Dark Dwarves. Focusing Attacks came out slightly better here, 0.58 kills vs 0.51 for the other two options, not great in any case.

Finally I’ll try some Great Hawks (2 Attacks, 1 Cleave). The story here again is different: 1.31 kills for charging, 1.09 for focusing attacks and 1.75 for focusing cleave.

So what happens now if I take those same three units against some Undead instead?

Against Reapers (Protection 2, 3+ Vitality and 1 wound each):

The Two Handed Weapons stick with charging, the Swords and Shields switch to focusing their Cleave and the Great Hawks switch from focusing their Cleave against the Dwarves to Charging the Undead.

Here’s a nice table for you to peruse with two additional targets:

I like the idea that these are decisions you have to make for a unit on its own before adding additional buffing units like nearby heroes and wizards.

I hope all that was of some interest.