LabRats is the Large-scale Alternative Battle Resolution Algorithm with no convenienT acronymS. Here are the rules:

LabRats is designed to resolve battles between opposing armies. The part of an army involved in any particular battle will be collectively described as that army's 'force'.

Units

Each army's force is divided into 'units'. A unit may be of any size from a few dozen to a thousand or more, and consists of troops of similar ability outfitted with similar equipment. The area in which the battle takes place is mapped onto a grid, and each unit occupies one of the spaces on this grid.

Each unit belongs to one of the following types:

Infantry Units: Footsoldiers, average in all areas. These form the largest part of most forces.

Defensive Units: Units designed to form a strong defensive front, especially against mounted troops. Generally equipped with polearms.

Mounted Units: Stronger and faster than infantry on open ground, but not as hardy and less capable of negotiating difficult terrain.

Ranged Units: Troops outfitted with missile weapons, usually weak in melee but capable of inflicting great harm from a distance.

Artillery Units: Small in number and slow-moving (and completely incapable of being moved over some types of terrain), but devastating when used effectively. Artillery units have extremely long range and high offensive power. They are also capable of breaking through city walls and other fortifications which most other units cannot pass, and of destroying ships. However, artillery are also unique in that they have a very slow rate-of-fire, and can therefore only attack on alternate rounds.

Seafaring Units: Vessels capable of transporting land-based units across bodies of water. The strength of their crew is combined with the strength of any friendly unit that boards them, up to their maximum carrying capacity.

Irregular Units: Mages, priests, demons... a catchall for any unit not fitting into any other category.

Statistics

Units have various statistics which affect the way in which they perform in battle:

Population: The number of troops in a unit.

Offence: The ability of the troops in a unit to inflict harm upon opponents.

Defence: The amount of damage a unit's members can withstand.

Speed: The rate at which a unit moves. On open, flat terrain, each point of speed translates to a move of one space vertically or horizontally on the map grid. Movement rate through different terrain may be affected by factors other than speed.

Range: The maximum distance at which a unit can effectively attack. Of course, for units only capable of fighting in melee, range is 1.

Weight: This value affects how many troops in that unit can be carried by a boat without exceeding its weight allowance. As a general rule, unarmoured troops have a weight of 1; armoured troops, 2; mounted troops, 5; artillery, anything from 10 to 50 or more.

Morale: The overall effect of all the variable factors altering a unit's strength: courage, fatigue, injuries and so on. It normally starts at 100, and tends to decrease over time. Morale affects every action a unit takes. Leaders with high charisma have troops who start with slightly higher morale; conversely, leaders with low charisma have troops with low morale. Once a unit's morale hits zero, it is said to be 'exhausted' - its offence, defence, mobility and range are halved (fractional points rounded up). Keeping an exhausted unit in combat is generally a bad idea.

Capacity: For seafaring units only: the maximum weight a ship can carry. (The weight of the crew is already assumed to be factored into capacity.)

Rules

Several possible actions may be taken by a unit in any given round:

Movement: A unit may move up to the maximum allowed by its Speed and the terrain over which it travels. Moving one step over most terrain takes one unit of morale; some terrains deplete morale faster than this.

Attacking: A unit may attack at any point during its move, and any number of times during its move. However, a unit's offensive power is divided among all attacks it makes in that round.

The formula for calculating damage is as follows:

((P * O * (M+100)) / (D * (E+100))) / n

where P = Population, O = Offence, M = Attacker's Morale, D = Defender's Defence, E = Enemy Morale, n = number of attacks (including retaliations) made by attacker in that round

Damage inflicted is subtracted from enemy Population. Fractional damage is rounded down - if an attack kills 52.5 troops, it only kills 52.

The defender may choose to retaliate against an attack, if their attacker is within their range. A retaliation is identical to a normal attack in most ways, except its effects on morale. In an attack without retaliation, the attacker and defender both lose 5 morale; in an attack with retaliation, the attacker loses 5 morale and the defender loses 10 morale. It's possible for a fast unit to force a slow unit to attack only by retaliating, thus gaining a morale advantage.

Note that damage and the effects of changing morale are not calculated until the end of a round. Therefore, it's entirely possible for two units with relatively strong attack compared to their defence to attack and destroy each other in a single round.

Uniting/Dividing: If two or more units of the same type from the same force move into the same space on the map, they will unite into a single unit. The morale of this unit is equal to the average morale of the units which formed it, and its population is equal to the sum of the populations of the units forming it. Two units of different types from the same force may occupy the same space on the map, but will not form a single unit.

Any unit may divide into two or more smaller units of the same type. A unit with 200 troops, for example, could send 50 troops east and 150 troops west.

Entrenchment: A unit may spend a round fortifying its position to the exclusion of all other actions. Doing this increases its morale by 10.

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Units, terrains and weather next time. I just felt it was important to post the rules ASAP - once you've got those, you can really make up units and terrains yourself.