Battle Resolution for Engle Matrix Games

In the absence of other ways of resolving battles within an Campaign using the approach of Engle Matrix Games try these simple rules. They were devised by Arthur Harman but revised by me (Steven Thomas).


Opposing forces are deployed in line, facing each other. The larger side can oppose two units to any one enemy unit, and/or keep troops in reserve.

Combat Resolution Dice

The attacker chooses the order in which combats are resolved. A die is rolled for each unit in the battle line. Combat is resolved by comparing the dice thrown for opposing units. If two units are opposing the same enemy unit, combine their scores together.

The combat dice can be modified for a variety of reasons. Many arguments in a Matrix game will result in modifiers during battle. This will be either a +1 if a force is advantaged by the argument, or -1 if disadvantaged. An argument will never both advantage one side and disadvantage the other.

The quality of the troops may have an effect on the dice, for instance British Red Coats might gain a +1 for their superior training and discipline. This will be decided at the start of a campaign.


The larger side may have retained units in reserve. If so, the player may feed these units into the front line as they see the results of each combat. Essentially the player adds reserve units to existing combats. A reserve unit rolls its combat die and takes a -1 modifier. This is added to the players existing combat roll. A player can send as many units as they want into the same combat. Once the player has accepted the result of a particular combat they can not send reserves into it.

Combat Resolution Table

When the scores of opposing units have been modified by the factors above, compare the resulting totals. The lower score loses the combat. The ratio of higher score to lower score determines the outcome:

Ratio Outcome
Even No advantage to either side; leave troops facing each other
< 2:1 Loser repulsed; move troops back, facing enemy
< 3:1 Loser beaten; move troops to rear with backs to enemy
3:1 or more Loser routed; remove troops

Results of the Battle

Compare the opposing lines of battle after all combats have been resolved. Total the casualty points for each army. Count each unit as:

State of unit Causality points
Routed 3
Beaten 2
Repulsed 1

The force with the higher total is the loser of the battle. Consult the table below to discover the effect of the battle on each side:

Army State Effect

The effect on each side depends on the number of units in each state and whether the army was the winner or loser.

State of units If Loser If Winner
No units routed or beaten Can hold ground or retire. Can pursue.
No units routed, but some beaten Retires to any adjacent enemy-free zone. Cannot pursue.
Some units routed or > 1/2 units beaten Retreats into enemy-free zone of winner’s choice.
at -1 for exhaustion if fight next turn.
Cannot pursue.
At -1 for exhaustion if fight next turn.
> 1/2 units routed Must withdraw towards nearest friendly force, fort or secure area.
At -1 for exhaustion if fight next turn.
disperses into surrounding enemy-free zones of winner’s choice
At -1 for exhaustion if fight next turn.

Skirmishes and Ambushes

Skirmishes and ambushes are fought using the same rules as open battles. Ambushing units get a +1 in battle.

Skirmishes differ from open battles in that initially only one unit of each side fights. Up to two other units on each side count as a reserve. If both sides use all of their reserve, then an open battle is fought immediately with the full armies.

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